1.
Integer
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An integer is a number that can be written without a fractional component. For example,21,4,0, and −2048 are integers, while 9.75, 5 1⁄2, the set of integers consists of zero, the positive natural numbers, also called whole numbers or counting numbers, and their additive inverses. This is often denoted by a boldface Z or blackboard bold Z standing for the German word Zahlen, ℤ is a subset of the sets of rational and real numbers and, like the natural numbers, is countably infinite. The integers form the smallest group and the smallest ring containing the natural numbers, in algebraic number theory, the integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, the integers are the integers that are also rational numbers. Like the natural numbers, Z is closed under the operations of addition and multiplication, that is, however, with the inclusion of the negative natural numbers, and, importantly,0, Z is also closed under subtraction. The integers form a ring which is the most basic one, in the following sense, for any unital ring. This universal property, namely to be an object in the category of rings. Z is not closed under division, since the quotient of two integers, need not be an integer, although the natural numbers are closed under exponentiation, the integers are not. The following lists some of the properties of addition and multiplication for any integers a, b and c. In the language of algebra, the first five properties listed above for addition say that Z under addition is an abelian group. As a group under addition, Z is a cyclic group, in fact, Z under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to Z. The first four properties listed above for multiplication say that Z under multiplication is a commutative monoid. However, not every integer has an inverse, e. g. there is no integer x such that 2x =1, because the left hand side is even. This means that Z under multiplication is not a group, all the rules from the above property table, except for the last, taken together say that Z together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of algebraic structure. Only those equalities of expressions are true in Z for all values of variables, note that certain non-zero integers map to zero in certain rings. The lack of zero-divisors in the means that the commutative ring Z is an integral domain
2.
Negative number
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In mathematics, a negative number is a real number that is less than zero. If positive represents movement to the right, negative represents movement to the left, if positive represents above sea level, then negative represents below level. If positive represents a deposit, negative represents a withdrawal and they are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, if a quantity may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. In the medical context of fighting a tumor, an expansion could be thought of as a negative shrinkage, negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common idea of an opposite is reflected in arithmetic. For example, − −3 =3 because the opposite of an opposite is the original thing, negative numbers are usually written with a minus sign in front. For example, −3 represents a quantity with a magnitude of three, and is pronounced minus three or negative three. To help tell the difference between a subtraction operation and a number, occasionally the negative sign is placed slightly higher than the minus sign. Conversely, a number that is greater than zero is called positive, the positivity of a number may be emphasized by placing a plus sign before it, e. g. +3. In general, the negativity or positivity of a number is referred to as its sign, every real number other than zero is either positive or negative. The positive whole numbers are referred to as natural numbers, while the positive and negative numbers are referred to as integers. In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, Liu Hui established rules for adding and subtracting negative numbers. By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers, islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients. Western mathematicians accepted the idea of numbers by the 17th century. Prior to the concept of numbers, mathematicians such as Diophantus considered negative solutions to problems false. Negative numbers can be thought of as resulting from the subtraction of a number from a smaller. For example, negative three is the result of subtracting three from zero,0 −3 = −3, in general, the subtraction of a larger number from a smaller yields a negative result, with the magnitude of the result being the difference between the two numbers
3.
100 (number)
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100 or one hundred is the natural number following 99 and preceding 101. In medieval contexts, it may be described as the hundred or five score in order to differentiate the English. The standard SI prefix for a hundred is hecto-,100 is the basis of percentages, with 100% being a full amount. 100 is the sum of the first nine prime numbers, as well as the sum of pairs of prime numbers e. g.3 +97,11 +89,17 +83,29 +71,41 +59. 100 is the sum of the cubes of the first four integers and this is related by Nicomachuss theorem to the fact that 100 also equals the square of the sum of the first four integers,100 =102 =2. 26 +62 =100, thus 100 is a Leyland number and it is divisible by the number of primes below it,25 in this case. It can not be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient and it can be expressed as a sum of some of its divisors, making it a semiperfect number. 100 is a Harshad number in base 10, and also in base 4, there are exactly 100 prime numbers whose digits are in strictly ascending order. 100 is the smallest number whose common logarithm is a prime number,100 senators are in the U. S One hundred is the atomic number of fermium, an actinide. On the Celsius scale,100 degrees is the temperature of pure water at sea level. The Kármán line lies at an altitude of 100 kilometres above the Earths sea level and is used to define the boundary between Earths atmosphere and outer space. There are 100 blasts of the Shofar heard in the service of Rosh Hashana, a religious Jew is expected to utter at least 100 blessings daily. In Hindu Religion - Mythology Book Mahabharata - Dhritarashtra had 100 sons known as kauravas, the United States Senate has 100 Senators. Most of the currencies are divided into 100 subunits, for example, one euro is one hundred cents. The 100 Euro banknotes feature a picture of a Rococo gateway on the obverse, the U. S. hundred-dollar bill has Benjamin Franklins portrait, the Benjamin is the largest U. S. bill in print. American savings bonds of $100 have Thomas Jeffersons portrait, while American $100 treasury bonds have Andrew Jacksons portrait, One hundred is also, The number of years in a century. The number of pounds in an American short hundredweight, in Greece, India, Israel and Nepal,100 is the police telephone number. In Belgium,100 is the ambulance and firefighter telephone number, in United Kingdom,100 is the operator telephone number
4.
Factorization
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In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 ×5, in all cases, a product of simpler objects is obtained. The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viètes formulas relate the coefficients of a polynomial to its roots, the opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms. Integer factorization for large integers appears to be a difficult problem, there is no known method to carry it out quickly. Its complexity is the basis of the security of some public key cryptography algorithms. A matrix can also be factorized into a product of matrices of special types, One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types, QR decomposition, LQ, QL, RQ and this situation is generalized by factorization systems. By the fundamental theorem of arithmetic, every integer greater than 1 has a unique prime factorization. Given an algorithm for integer factorization, one can factor any integer down to its constituent primes by repeated application of this algorithm, for very large numbers, no efficient classical algorithm is known. Modern techniques for factoring polynomials are fast and efficient, but use sophisticated mathematical ideas and these techniques are used in the construction of computer routines for carrying out polynomial factorization in Computer algebra systems. This article is concerned with classical techniques. While the general notion of factoring just means writing an expression as a product of simpler expressions, when factoring polynomials this means that the factors are to be polynomials of smaller degree. Thus, while x 2 − y = is a factorization of the expression, another issue concerns the coefficients of the factors. It is not always possible to do this, and a polynomial that can not be factored in this way is said to be irreducible over this type of coefficient, thus, x2 -2 is irreducible over the integers and x2 +4 is irreducible over the reals. In the first example, the integers 1 and -2 can also be thought of as real numbers, and if they are, then x 2 −2 = shows that this polynomial factors over the reals. Similarly, since the integers 1 and 4 can be thought of as real and hence complex numbers, x2 +4 splits over the complex numbers, i. e. x 2 +4 =. The fundamental theorem of algebra can be stated as, Every polynomial of n with complex number coefficients splits completely into n linear factors
5.
Divisor
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In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some other integer to produce n. In this case one says also that n is a multiple of m, an integer n is divisible by another integer m if m is a divisor of n, this implies dividing n by m leaves no remainder. Under this definition, the statement m ∣0 holds for every m, as before, but with the additional constraint k ≠0. Under this definition, the statement m ∣0 does not hold for m ≠0, in the remainder of this article, which definition is applied is indicated where this is significant. Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4, they are 1,2,4, −1, −2, and −4,1 and −1 divide every integer. Every integer is a divisor of itself, every integer is a divisor of 0. Integers divisible by 2 are called even, and numbers not divisible by 2 are called odd,1, −1, n and −n are known as the trivial divisors of n. A divisor of n that is not a divisor is known as a non-trivial divisor. A non-zero integer with at least one divisor is known as a composite number, while the units −1 and 1. There are divisibility rules which allow one to recognize certain divisors of a number from the numbers digits, the generalization can be said to be the concept of divisibility in any integral domain. 7 is a divisor of 42 because 7 ×6 =42 and it can also be said that 42 is divisible by 7,42 is a multiple of 7,7 divides 42, or 7 is a factor of 42. The non-trivial divisors of 6 are 2, −2,3, the positive divisors of 42 are 1,2,3,6,7,14,21,42. 5 ∣0, because 5 ×0 =0, if a ∣ b and b ∣ a, then a = b or a = − b. If a ∣ b and a ∣ c, then a ∣ holds, however, if a ∣ b and c ∣ b, then ∣ b does not always hold. If a ∣ b c, and gcd =1, then a ∣ c, if p is a prime number and p ∣ a b then p ∣ a or p ∣ b. A positive divisor of n which is different from n is called a proper divisor or a part of n. A number that does not evenly divide n but leaves a remainder is called an aliquant part of n, an integer n >1 whose only proper divisor is 1 is called a prime number
6.
Greek numerals
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Greek numerals are a system of writing numbers using the letters of the Greek alphabet. These alphabetic numerals are known as Ionic or Ionian numerals, Milesian numerals. In modern Greece, they are used for ordinal numbers. For ordinary cardinal numbers, however, Greece uses Arabic numerals, attic numerals, which were later adopted as the basis for Roman numerals, were the first alphabetic set. They were acrophonic, derived from the first letters of the names of the numbers represented and they ran =1, =5, =10, =100, =1000, and =10000. 50,500,5000, and 50000 were represented by the letter with minuscule powers of ten written in the top right corner, the same system was used outside of Attica, but the symbols varied with the local alphabets, in Boeotia, was 1000. The present system probably developed around Miletus in Ionia, 19th-century classicists placed its development in the 3rd century BC, the occasion of its first widespread use. The present system uses the 24 letters adopted by Euclid as well as three Phoenician and Ionic ones that were not carried over, digamma, koppa, and sampi. The position of characters within the numbering system imply that the first two were still in use while the third was not. Greek numerals are decimal, based on powers of 10, the units from 1 to 9 are assigned to the first nine letters of the old Ionic alphabet from alpha to theta. Each multiple of one hundred from 100 to 900 was then assigned its own separate letter as well and this alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total. For example,241 was represented as, in ancient and medieval manuscripts, these numerals were eventually distinguished from letters using overbars, α, β, γ, etc. In medieval manuscripts of the Book of Revelation, the number of the Beast 666 is written as χξϛ, although the Greek alphabet began with only majuscule forms, surviving papyrus manuscripts from Egypt show that uncial and cursive minuscule forms began early. These new letter forms sometimes replaced the ones, especially in the case of the obscure numerals. The old Q-shaped koppa began to be broken up and simplified, the numeral for 6 changed several times. During antiquity, the letter form of digamma came to be avoided in favor of a special numerical one. By the Byzantine era, the letter was known as episemon and this eventually merged with the sigma-tau ligature stigma. In modern Greek, a number of changes have been made
7.
Roman numerals
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The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet, Roman numerals, as used today, are based on seven symbols, The use of Roman numerals continued long after the decline of the Roman Empire. The numbers 1 to 10 are usually expressed in Roman numerals as follows, I, II, III, IV, V, VI, VII, VIII, IX, Numbers are formed by combining symbols and adding the values, so II is two and XIII is thirteen. Symbols are placed left to right in order of value. Named after the year of its release,2014 as MMXIV, the year of the games of the XXII Olympic Winter Games The standard forms described above reflect typical modern usage rather than a universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval, Roman inscriptions, especially in official contexts, seem to show a preference for additive forms such as IIII and VIIII instead of subtractive forms such as IV and IX. Both methods appear in documents from the Roman era, even within the same document, double subtractives also occur, such as XIIX or even IIXX instead of XVIII. Sometimes V and L are not used, with such as IIIIII. Such variation and inconsistency continued through the period and into modern times. Clock faces that use Roman numerals normally show IIII for four o’clock but IX for nine o’clock, however, this is far from universal, for example, the clock on the Palace of Westminster in London uses IV. Similarly, at the beginning of the 20th century, different representations of 900 appeared in several inscribed dates. For instance,1910 is shown on Admiralty Arch, London, as MDCCCCX rather than MCMX, although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used
8.
Binary number
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The base-2 system is a positional notation with a radix of 2. Because of its implementation in digital electronic circuitry using logic gates. Each digit is referred to as a bit, the modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de lArithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions, the method used for ancient Egyptian multiplication is also closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, the I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique and it is based on taoistic duality of yin and yang. Eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, the Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, Pingalas Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingalas system increases towards the right, the residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Africa, sets of binary combinations similar to the I Ching have also been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been applied in sub-Saharan Africa. Leibnizs system uses 0 and 1, like the modern binary numeral system, Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own beliefs as a Christian. Binary numerals were central to Leibnizs theology and he believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. Is not easy to impart to the pagans, is the ex nihilo through Gods almighty power. In 1854, British mathematician George Boole published a paper detailing an algebraic system of logic that would become known as Boolean algebra
9.
Ternary numeral system
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The ternary numeral system has three as its base. Analogous to a bit, a digit is a trit. One trit is equivalent to bits of information. Representations of integer numbers in ternary do not get uncomfortably lengthy as quickly as in binary, for example, decimal 365 corresponds to binary 101101101 and to ternary 111112. However, they are far less compact than the corresponding representations in bases such as decimal – see below for a compact way to codify ternary using nonary. The value of a number with n bits that are all 1 is 2n −1. Then N = M, N = /, and N = bd −1, for a three-digit ternary number, N =33 −1 =26 =2 ×32 +2 ×31 +2 ×30 =18 +6 +2. Nonary or septemvigesimal can be used for representation of ternary. A base-three system is used in Islam to keep track of counting Tasbih to 99 or to 100 on a hand for counting prayers. In certain analog logic, the state of the circuit is often expressed ternary and this is most commonly seen in Transistor–transistor logic using 7406 open collector logic. The output is said to either be low, high, or open, in this configuration the output of the circuit is actually not connected to any voltage reference at all. Where the signal is usually grounded to a reference, or at a certain voltage level. Thus, the voltage level is sometimes unpredictable. A rare ternary point is used to denote fractional parts of an inning in baseball, since each inning consists of three outs, each out is considered one third of an inning and is denoted as.1. For example, if a player pitched all of the 4th, 5th and 6th innings, plus 2 outs of the 7th inning, his Innings pitched column for that game would be listed as 3.2, meaning 3⅔. In this usage, only the part of the number is written in ternary form. Ternary numbers can be used to convey self-similar structures like the Sierpinski triangle or the Cantor set conveniently, additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed. The Cantor set consists of the points from 0 to 1 that have an expression that does not contain any instance of the digit 1
10.
Quaternary numeral system
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Quaternary is the base-4 numeral system. It uses the digits 0,1,2 and 3 to represent any real number. Four is the largest number within the range and one of two numbers that is both a square and a highly composite number, making quaternary a convenient choice for a base at this scale. Despite being twice as large, its economy is equal to that of binary. However, it no better in the localization of prime numbers. See decimal and binary for a discussion of these properties, as with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system. Each radix 4,8 and 16 is a power of 2, so the conversion to and from binary is implemented by matching each digit with 2,3 or 4 binary digits, for example, in base 4,302104 =11001001002. Although octal and hexadecimal are widely used in computing and computer programming in the discussion and analysis of binary arithmetic and logic, by analogy with byte and nybble, a quaternary digit is sometimes called a crumb. There is a surviving list of Ventureño language number words up to 32 written down by a Spanish priest ca, the Kharosthi numerals have a partial base 4 counting system from 1 to decimal 10. Quaternary numbers are used in the representation of 2D Hilbert curves, here a real number between 0 and 1 is converted into the quaternary system. Every single digit now indicates in which of the respective 4 sub-quadrants the number will be projected, parallels can be drawn between quaternary numerals and the way genetic code is represented by DNA. The four DNA nucleotides in order, abbreviated A, C, G and T, can be taken to represent the quaternary digits in numerical order 0,1,2. With this encoding, the complementary digit pairs 0↔3, and 1↔2 match the complementation of the pairs, A↔T and C↔G. For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010, quaternary line codes have been used for transmission, from the invention of the telegraph to the 2B1Q code used in modern ISDN circuits
11.
Quinary
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Quinary is a numeral system with five as the base. A possible origination of a system is that there are five fingers on either hand. The base five is stated from 0–4, in the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100, today, the main usage of base 5 is as a biquinary system, which is decimal using five as a sub-base. Another example of a system, is sexagesimal, base 60. Each quinary digit has log25 bits of information, many languages use quinary number systems, including Gumatj, Nunggubuyu, Kuurn Kopan Noot, Luiseño and Saraveca. Gumatj is a true 5–25 language, in which 25 is the group of 5. The Gumatj numerals are shown below, In the video game Riven and subsequent games of the Myst franchise, a decimal system with 2 and 5 as a sub-bases is called biquinary, and is found in Wolof and Khmer. Roman numerals are a biquinary system, the numbers 1,5,10, and 50 are written as I, V, X, and L respectively. Eight is VIII and seventy is LXX, most versions of the abacus use a biquinary system to simulate a decimal system for ease of calculation. Urnfield culture numerals and some tally mark systems are also biquinary, units of currencies are commonly partially or wholly biquinary. A vigesimal system with 4 and 5 as a sub-bases is found in Nahuatl, pentimal system Quibinary Yan Tan Tethera References, Quinary Base Conversion, includes fractional part, from Math Is Fun Media related to Quinary numeral system at Wikimedia Commons
12.
Senary
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
13.
Octal
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The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping binary digits into groups of three. For example, the representation for decimal 74 is 1001010. Two zeroes can be added at the left,1001010, corresponding the octal digits 112, in the decimal system each decimal place is a power of ten. For example,7410 =7 ×101 +4 ×100 In the octal system each place is a power of eight. The Yuki language in California and the Pamean languages in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves and it has been suggested that the reconstructed Proto-Indo-European word for nine might be related to the PIE word for new. Based on this, some have speculated that proto-Indo-Europeans used a number system. In 1716 King Charles XII of Sweden asked Emanuel Swedenborg to elaborate a number based on 64 instead of 10. Swedenborg however argued that for people with less intelligence than the king such a big base would be too difficult, in 1718 Swedenborg wrote a manuscript, En ny rekenkonst som om vexlas wid Thalet 8 i stelle then wanliga wid Thalet 10. The numbers 1-7 are there denoted by the l, s, n, m, t, f, u. Thus 8 = lo,16 = so,24 = no,64 = loo,512 = looo etc, numbers with consecutive consonants are pronounced with vowel sounds between in accordance with a special rule. Writing under the pseudonym Hirossa Ap-Iccim in The Gentlemans Magazine, July 1745, Hugh Jones proposed a system for British coins, weights. In 1801, James Anderson criticized the French for basing the Metric system on decimal arithmetic and he suggested base 8 for which he coined the term octal. In the mid 19th century, Alfred B. Taylor concluded that Our octonary radix is, therefore, so, for example, the number 65 would be spoken in octonary as under-un. Taylor also republished some of Swedenborgs work on octonary as an appendix to the above-cited publications, in the 2009 film Avatar, the language of the extraterrestrial Navi race employs an octal numeral system, probably due to the fact that they have four fingers on each hand. In the TV series Stargate SG-1, the Ancients, a race of beings responsible for the invention of the Stargates, in the tabletop game series Warhammer 40,000, the Tau race use an octal number system. Octal became widely used in computing systems such as the PDP-8, ICL1900. Octal was an abbreviation of binary for these machines because their word size is divisible by three
14.
Duodecimal
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The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written by a rotated 2 and this notation was introduced by Sir Isaac Pitman. These digit forms are available as Unicode characters on computerized systems since June 2015 as ↊ and ↋, other notations use A, T, or X for ten and B or E for eleven. The number twelve is written as 10 in duodecimal, whereas the digit string 12 means 1 dozen and 2 units. Similarly, in duodecimal 100 means 1 gross,1000 means 1 great gross, the number twelve, a superior highly composite number, is the smallest number with four non-trivial factors, and the smallest to include as factors all four numbers within the subitizing range. As a result, duodecimal has been described as the number system. Of its factors,2 and 3 are prime, which means the reciprocals of all 3-smooth numbers have a representation in duodecimal. In particular, the five most elementary fractions all have a terminating representation in duodecimal. This all makes it a convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary. Although the trigesimal and sexagesimal systems do even better in respect, this is at the cost of unwieldy multiplication tables. In this section, numerals are based on decimal places, for example,10 means ten,12 means twelve. Languages using duodecimal number systems are uncommon, germanic languages have special words for 11 and 12, such as eleven and twelve in English. However, they are considered to come from Proto-Germanic *ainlif and *twalif, historically, units of time in many civilizations are duodecimal. There are twelve signs of the zodiac, twelve months in a year, traditional Chinese calendars, clocks, and compasses are based on the twelve Earthly Branches. There are 12 inches in a foot,12 troy ounces in a troy pound,12 old British pence in a shilling,24 hours in a day. The Romans used a system based on 12, including the uncia which became both the English words ounce and inch. The importance of 12 has been attributed to the number of cycles in a year. It is possible to count to 12 with the acting as a pointer
15.
Hexadecimal
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In mathematics and computing, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, Hexadecimal numerals are widely used by computer system designers and programmers. As each hexadecimal digit represents four binary digits, it allows a more human-friendly representation of binary-coded values, one hexadecimal digit represents a nibble, which is half of an octet or byte. For example, a byte can have values ranging from 00000000 to 11111111 in binary form. In a non-programming context, a subscript is typically used to give the radix, several notations are used to support hexadecimal representation of constants in programming languages, usually involving a prefix or suffix. The prefix 0x is used in C and related languages, where this value might be denoted as 0x2AF3, in contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers expressed in other bases. There are several conventions for expressing values unambiguously, a numerical subscript can give the base explicitly,15910 is decimal 159,15916 is hexadecimal 159, which is equal to 34510. Some authors prefer a text subscript, such as 159decimal and 159hex, or 159d and 159h. example. com/name%20with%20spaces where %20 is the space character, thus ’, represents the right single quotation mark, Unicode code point number 2019 in hex,8217. In the Unicode standard, a value is represented with U+ followed by the hex value. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #, white, CSS allows 3-hexdigit abbreviations with one hexdigit per component, #FA3 abbreviates #FFAA33. *nix shells, AT&T assembly language and likewise the C programming language, to output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h, some assembly languages use the notation HABCD. Ada and VHDL enclose hexadecimal numerals in based numeric quotes, 16#5A3#, for bit vector constants VHDL uses the notation x5A3. Verilog represents hexadecimal constants in the form 8hFF, where 8 is the number of bits in the value, the Smalltalk language uses the prefix 16r, 16r5A3 PostScript and the Bourne shell and its derivatives denote hex with prefix 16#, 16#5A3. For PostScript, binary data can be expressed as unprefixed consecutive hexadecimal pairs, in early systems when a Macintosh crashed, one or two lines of hexadecimal code would be displayed under the Sad Mac to tell the user what went wrong. Common Lisp uses the prefixes #x and #16r, setting the variables *read-base* and *print-base* to 16 can also used to switch the reader and printer of a Common Lisp system to Hexadecimal number representation for reading and printing numbers. Thus Hexadecimal numbers can be represented without the #x or #16r prefix code, MSX BASIC, QuickBASIC, FreeBASIC and Visual Basic prefix hexadecimal numbers with &H, &H5A3 BBC BASIC and Locomotive BASIC use & for hex. TI-89 and 92 series uses a 0h prefix, 0h5A3 ALGOL68 uses the prefix 16r to denote hexadecimal numbers, binary, quaternary and octal numbers can be specified similarly
16.
Vigesimal
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The vigesimal or base 20 numeral system is based on twenty. In a vigesimal system, twenty individual numerals are used. One modern method of finding the extra needed symbols is to write ten as the letter A20, to write nineteen as J20, and this is similar to the common computer-science practice of writing hexadecimal numerals over 9 with the letters A–F. Another method skips over the letter I, in order to avoid confusion between I20 as eighteen and one, so that the number eighteen is written as J20, the number twenty is written as 1020. According to this notation,2020 means forty in decimal = + D020 means two hundred and sixty in decimal = +10020 means four hundred in decimal = + +, in the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example,10 means ten,20 means twenty, in decimal, dividing by three twice only gives one digit periods because 9 is the number below ten. 21, however, the adjacent to 20 that is divisible by 3, is not divisible by 9. Ninths in vigesimal have six-digit periods, the prime factorization of twenty is 22 ×5, so it is not a perfect power. However, its part,5, is congruent to 1. Thus, according to Artins conjecture on primitive roots, vigesimal has infinitely many cyclic primes, but the fraction of primes that are cyclic is not necessarily ~37. 395%. An UnrealScript program that computes the lengths of recurring periods of various fractions in a set of bases found that, of the first 15,456 primes. In many European languages,20 is used as a base, vigesimal systems are common in Africa, for example in Yoruba. Ogún,20, is the basic numeric block, ogójì,40, =20 multiplied by 2. Ogota,60, =20 multiplied by 3, ogorin,80, =20 multiplied by 4. Ogorun,100, =20 multiplied by 5, twenty was a base in the Maya and Aztec number systems. The Maya used the names for the powers of twenty, kal, bak, pic, calab, kinchil. See also Maya numerals and Maya calendar, Mayan languages, Yucatec, the Aztec called them, cempoalli, centzontli, cenxiquipilli, cempoalxiquipilli, centzonxiquipilli and cempoaltzonxiquipilli. Note that the ce prefix at the beginning means one and is replaced with the number to get the names of other multiples of the power
17.
Base 36
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
18.
Hebrew language
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Hebrew is a language native to Israel, spoken by over 9 million people worldwide, of whom over 5 million are in Israel. Historically, it is regarded as the language of the Israelites and their ancestors, the earliest examples of written Paleo-Hebrew date from the 10th century BCE. Hebrew belongs to the West Semitic branch of the Afroasiatic language family, Hebrew is the only living Canaanite language left, and the only truly successful example of a revived dead language. Hebrew had ceased to be a spoken language somewhere between 200 and 400 CE, declining since the aftermath of the Bar Kokhba revolt. Aramaic and to a lesser extent Greek were already in use as international languages, especially among elites and it survived into the medieval period as the language of Jewish liturgy, rabbinic literature, intra-Jewish commerce, and poetry. Then, in the 19th century, it was revived as a spoken and literary language, and, according to Ethnologue, had become, as of 1998, the language of 5 million people worldwide. After Israel, the United States has the second largest Hebrew-speaking population, with 220,000 fluent speakers, Modern Hebrew is one of the two official languages of the State of Israel, while premodern Hebrew is used for prayer or study in Jewish communities around the world today. Ancient Hebrew is also the tongue of the Samaritans, while modern Hebrew or Arabic is their vernacular. For this reason, Hebrew has been referred to by Jews as Leshon Hakodesh, the modern word Hebrew is derived from the word Ivri, one of several names for the Israelite people. It is traditionally understood to be a based on the name of Abrahams ancestor, Eber. This name is based upon the root ʕ-b-r meaning to cross over. Interpretations of the term ʕibrim link it to this verb, cross over, in the Bible, the Hebrew language is called Yәhudit because Judah was the surviving kingdom at the time of the quotation. In Isaiah 19,18 it is called the Language of Canaan, Hebrew belongs to the Canaanite group of languages. In turn, the Canaanite languages are a branch of the Northwest Semitic family of languages, according to Avraham ben-Yosef, Hebrew flourished as a spoken language in the Kingdoms of Israel and Judah during about 1200 to 586 BCE. Scholars debate the degree to which Hebrew was a vernacular in ancient times following the Babylonian exile. In July 2008 Israeli archaeologist Yossi Garfinkel discovered a ceramic shard at Khirbet Qeiyafa which he claimed may be the earliest Hebrew writing yet discovered, dating around 3000 years ago. The Gezer calendar also dates back to the 10th century BCE at the beginning of the Monarchic Period, classified as Archaic Biblical Hebrew, the calendar presents a list of seasons and related agricultural activities. The Gezer calendar is written in an old Semitic script, akin to the Phoenician one that through the Greeks, the Gezer calendar is written without any vowels, and it does not use consonants to imply vowels even in the places where later Hebrew spelling requires it
19.
Natural number
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In mathematics, the natural numbers are those used for counting and ordering. In common language, words used for counting are cardinal numbers, texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers. These chains of extensions make the natural numbers canonically embedded in the number systems. Properties of the numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics, the most primitive method of representing a natural number is to put down a mark for each object. Later, a set of objects could be tested for equality, excess or shortage, by striking out a mark, the first major advance in abstraction was the use of numerals to represent numbers. This allowed systems to be developed for recording large numbers, the ancient Egyptians developed a powerful system of numerals with distinct hieroglyphs for 1,10, and all the powers of 10 up to over 1 million. A stone carving from Karnak, dating from around 1500 BC and now at the Louvre in Paris, depicts 276 as 2 hundreds,7 tens, and 6 ones, and similarly for the number 4,622. A much later advance was the development of the idea that 0 can be considered as a number, with its own numeral. The use of a 0 digit in place-value notation dates back as early as 700 BC by the Babylonians, the Olmec and Maya civilizations used 0 as a separate number as early as the 1st century BC, but this usage did not spread beyond Mesoamerica. The use of a numeral 0 in modern times originated with the Indian mathematician Brahmagupta in 628, the first systematic study of numbers as abstractions is usually credited to the Greek philosophers Pythagoras and Archimedes. Some Greek mathematicians treated the number 1 differently than larger numbers, independent studies also occurred at around the same time in India, China, and Mesoamerica. In 19th century Europe, there was mathematical and philosophical discussion about the nature of the natural numbers. A school of Naturalism stated that the numbers were a direct consequence of the human psyche. Henri Poincaré was one of its advocates, as was Leopold Kronecker who summarized God made the integers, in opposition to the Naturalists, the constructivists saw a need to improve the logical rigor in the foundations of mathematics. In the 1860s, Hermann Grassmann suggested a recursive definition for natural numbers thus stating they were not really natural, later, two classes of such formal definitions were constructed, later, they were shown to be equivalent in most practical applications. The second class of definitions was introduced by Giuseppe Peano and is now called Peano arithmetic and it is based on an axiomatization of the properties of ordinal numbers, each natural number has a successor and every non-zero natural number has a unique predecessor. Peano arithmetic is equiconsistent with several systems of set theory
20.
Square number
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In mathematics, a square number or perfect square is an integer that is the square of an integer, in other words, it is the product of some integer with itself. For example,9 is a number, since it can be written as 3 × 3. The usual notation for the square of a n is not the product n × n. The name square number comes from the name of the shape, another way of saying that a integer is a square number, is that its square root is again an integer. For example, √9 =3, so 9 is a square number, a positive integer that has no perfect square divisors except 1 is called square-free. For a non-negative integer n, the nth square number is n2, the concept of square can be extended to some other number systems. If rational numbers are included, then a square is the ratio of two integers, and, conversely, the ratio of two square integers is a square, e. g.49 =2. Starting with 1, there are ⌊√m⌋ square numbers up to and including m, the squares smaller than 602 =3600 are, The difference between any perfect square and its predecessor is given by the identity n2 −2 = 2n −1. Equivalently, it is possible to count up square numbers by adding together the last square, the last squares root, and the current root, that is, n2 =2 + + n. The number m is a number if and only if one can compose a square of m equal squares. Hence, a square with side length n has area n2, the expression for the nth square number is n2. This is also equal to the sum of the first n odd numbers as can be seen in the above pictures, the formula follows, n 2 = ∑ k =1 n. So for example,52 =25 =1 +3 +5 +7 +9, there are several recursive methods for computing square numbers. For example, the nth square number can be computed from the square by n2 =2 + + n =2 +. Alternatively, the nth square number can be calculated from the two by doubling the th square, subtracting the th square number, and adding 2. For example, 2 × 52 −42 +2 = 2 × 25 −16 +2 =50 −16 +2 =36 =62, a square number is also the sum of two consecutive triangular numbers. The sum of two square numbers is a centered square number. Every odd square is also an octagonal number
21.
20 (number)
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20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score,20 is a tetrahedral number as 1,4,10,20. 20 is the basis for vigesimal number systems,20 is the third composite number comprising the product of a squared prime and a prime, and also the second member of the q family in this form. 20 has a sum of 22. Accordingly,20 is the abundant number and demonstrates an 8-member aliquot sequence. 20 is the smallest primitive abundant number,20 is the 4th composite number in the 7-aliquot tree. Two numbers have 20 as their sum, the discrete semiprime 34. Only 2 other square primes are abundant 12 and 18,20 can be written as the sum of three Fibonacci numbers uniquely, i. e.20 =13 +5 +2. The product of the number of divisors and the number of divisors of 20 is exactly 20. 20 is the number of required to optimally solve a Rubiks Cube in the worst case. 20 is the number with more than one digit that can be written from base 2 to base 20 using only the digits 0 to 9. The third magic number in physics, the IAU shower number for Coma Berenicids. The number of amino acids that are encoded by the standard genetic code. In some countries, the number 20 is used as an index in measuring visual acuity, 20/20 indicates normal vision at 20 feet, although it is commonly used to mean perfect vision. When someone is able to see only after an event how things turned out, the Baltimore Orioles and Cincinnati Reds, both for Hall of Famer Frank Robinson. The Kansas City Royals, for Frank White, the Los Angeles Dodgers, for Hall of Famer Don Sutton. The Philadelphia Phillies, for Hall of Famer Mike Schmidt, the Pittsburgh Pirates, for Hall of Famer Pie Traynor. The St. Louis Cardinals, for Hall of Famer Lou Brock, the San Francisco Giants, for Hall of Famer Monte Irvin, who played for the team when it was the New York Giants
22.
Circle
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A circle is a simple closed shape in Euclidean geometry. The distance between any of the points and the centre is called the radius, a circle is a simple closed curve which divides the plane into two regions, an interior and an exterior. Annulus, the object, the region bounded by two concentric circles. Arc, any connected part of the circle, centre, the point equidistant from the points on the circle. Chord, a segment whose endpoints lie on the circle. Circumference, the length of one circuit along the circle, or the distance around the circle and it is a special case of a chord, namely the longest chord, and it is twice the radius. Disc, the region of the bounded by a circle. Lens, the intersection of two discs, passant, a coplanar straight line that does not touch the circle. Radius, a line segment joining the centre of the circle to any point on the circle itself, or the length of such a segment, sector, a region bounded by two radii and an arc lying between the radii. Segment, a region, not containing the centre, bounded by a chord, secant, an extended chord, a coplanar straight line cutting the circle at two points. Semicircle, an arc that extends from one of a diameters endpoints to the other, in non-technical common usage it may mean the diameter, arc, and its interior, a two dimensional region, that is technically called a half-disc. A half-disc is a case of a segment, namely the largest one. Tangent, a straight line that touches the circle at a single point. The word circle derives from the Greek κίρκος/κύκλος, itself a metathesis of the Homeric Greek κρίκος, the origins of the words circus and circuit are closely related. The circle has been known since before the beginning of recorded history, natural circles would have been observed, such as the Moon, Sun, and a short plant stalk blowing in the wind on sand, which forms a circle shape in the sand. The circle is the basis for the wheel, which, with related inventions such as gears, in mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Some highlights in the history of the circle are,1700 BCE – The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256/81 as a value of π.300 BCE – Book 3 of Euclids Elements deals with the properties of circles
23.
Degree (angle)
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A degree, usually denoted by °, is a measurement of a plane angle, defined so that a full rotation is 360 degrees. It is not an SI unit, as the SI unit of measure is the radian. Because a full rotation equals 2π radians, one degree is equivalent to π/180 radians, the original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the path over the course of the year. Some ancient calendars, such as the Persian calendar, used 360 days for a year, the use of a calendar with 360 days may be related to the use of sexagesimal numbers. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle, a chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree, Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes, eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts. Furthermore, it is divisible by every number from 1 to 10 except 7 and this property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention. Finally, it may be the case more than one of these factors has come into play. For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates, degree measurements may be written using decimal degrees, with the symbol behind the decimals. Alternatively, the sexagesimal unit subdivisions can be used. One degree is divided into 60 minutes, and one minute into 60 seconds, use of degrees-minutes-seconds is also called DMS notation. These subdivisions, also called the arcminute and arcsecond, are represented by a single and double prime. For example,40. 1875° = 40° 11′ 15″, or, using quotation mark characters, additional precision can be provided using decimals for the arcseconds component. The older system of thirds, fourths, etc. which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today
24.
Radian
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The radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a circle is numerically equal to the measurement in radians of the angle that it subtends. The unit was formerly an SI supplementary unit, but this category was abolished in 1995, separately, the SI unit of solid angle measurement is the steradian. The radian is represented by the symbol rad, so for example, a value of 1.2 radians could be written as 1.2 rad,1.2 r,1. 2rad, or 1. 2c. Radian describes the angle subtended by a circular arc as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Conversely, the length of the arc is equal to the radius multiplied by the magnitude of the angle in radians. As the ratio of two lengths, the radian is a number that needs no unit symbol, and in mathematical writing the symbol rad is almost always omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and it follows that the magnitude in radians of one complete revolution is the length of the entire circumference divided by the radius, or 2πr / r, or 2π. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees, the concept of radian measure, as opposed to the degree of an angle, is normally credited to Roger Cotes in 1714. He described the radian in everything but name, and he recognized its naturalness as a unit of angular measure, the idea of measuring angles by the length of the arc was already in use by other mathematicians. For example, al-Kashi used so-called diameter parts as units where one part was 1/60 radian. The term radian first appeared in print on 5 June 1873, in examination questions set by James Thomson at Queens College, Belfast. He had used the term as early as 1871, while in 1869, Thomas Muir, then of the University of St Andrews, in 1874, after a consultation with James Thomson, Muir adopted radian. As stated, one radian is equal to 180/π degrees, thus, to convert from radians to degrees, multiply by 180/π. The length of circumference of a circle is given by 2 π r, so, to convert from radians to gradians multiply by 200 / π, and to convert from gradians to radians multiply by π /200. This is because radians have a mathematical naturalness that leads to a more elegant formulation of a number of important results, most notably, results in analysis involving trigonometric functions are simple and elegant when the functions arguments are expressed in radians. Because of these and other properties, the trigonometric functions appear in solutions to problems that are not obviously related to the functions geometrical meanings
25.
International System of Units
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The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version
26.
Athens
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Athens is the capital and largest city of Greece. In modern times, Athens is a cosmopolitan metropolis and central to economic, financial, industrial, maritime. In 2015, Athens was ranked the worlds 29th richest city by purchasing power, Athens is recognised as a global city because of its location and its importance in shipping, finance, commerce, media, entertainment, arts, international trade, culture, education and tourism. It is one of the biggest economic centres in southeastern Europe, with a financial sector. The municipality of Athens had a population of 664,046 within its limits. The urban area of Athens extends beyond its administrative city limits. According to Eurostat in 2011, the Functional urban areas of Athens was the 9th most populous FUA in the European Union, Athens is also the southernmost capital on the European mainland. The city also retains Roman and Byzantine monuments, as well as a number of Ottoman monuments. Athens is home to two UNESCO World Heritage Sites, the Acropolis of Athens and the medieval Daphni Monastery, Athens was the host city of the first modern-day Olympic Games in 1896, and 108 years later it welcomed home the 2004 Summer Olympics. In Ancient Greek, the name of the city was Ἀθῆναι a plural, in earlier Greek, such as Homeric Greek, the name had been current in the singular form though, as Ἀθήνη. It was possibly rendered in the later on, like those of Θῆβαι and Μυκῆναι. During the medieval period the name of the city was rendered once again in the singular as Ἀθήνα, an etiological myth explaining how Athens has acquired its name was well known among ancient Athenians and even became the theme of the sculpture on the West pediment of the Parthenon. The goddess of wisdom, Athena, and the god of the seas, Poseidon had many disagreements, in an attempt to compel the people, Poseidon created a salt water spring by striking the ground with his trident, symbolizing naval power. However, when Athena created the tree, symbolizing peace and prosperity. Different etymologies, now rejected, were proposed during the 19th century. Christian Lobeck proposed as the root of the name the word ἄθος or ἄνθος meaning flower, ludwig von Döderlein proposed the stem of the verb θάω, stem θη- to denote Athens as having fertile soil. In classical literature, the city was referred to as the City of the Violet Crown, first documented in Pindars ἰοστέφανοι Ἀθᾶναι. In medieval texts, variant names include Setines, Satine, and Astines, today the caption η πρωτεύουσα, the capital, has become somewhat common
27.
HTTP status code
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This is a list of Hypertext Transfer Protocol response status codes. It includes codes from IETF Request for Comments, other specifications, the first digit of the status code specifies one of five standard classes of responses. The message phrases shown are typical, but any human-readable alternative may be provided, unless otherwise stated, the status code is part of the HTTP/1.1 standard. The Internet Assigned Numbers Authority maintains the registry of HTTP status codes. An informational response indicates that the request was received and understood and it is issued on a provisional basis while request processing continues. It alerts the client to wait for a final response, the message consists only of the status line and optional header fields, and is terminated by an empty line. As the HTTP/1.0 standard did not define any 1xx status codes,100 Continue The server has received the request headers and the client should proceed to send the request body. Sending a large request body to a server after a request has been rejected for inappropriate headers would be inefficient. To have a check the requests headers, a client must send Expect, 100-continue as a header in its initial request. The response 417 Expectation Failed indicates the request should not be continued,101 Switching Protocols The requester has asked the server to switch protocols and the server has agreed to do so. 102 Processing A WebDAV request may contain many sub-requests involving file operations and this code indicates that the server has received and is processing the request, but no response is available yet. This prevents the client from timing out and assuming the request was lost and this class of status codes indicates the action requested by the client was received, understood, accepted, and processed successfully. 200 OK Standard response for successful HTTP requests, the actual response will depend on the request method used. In a GET request, the response will contain an entity corresponding to the requested resource, in a POST request, the response will contain an entity describing or containing the result of the action. 201 Created The request has been fulfilled, resulting in the creation of a new resource,202 Accepted The request has been accepted for processing, but the processing has not been completed. The request might or might not be acted upon. 203 Non-Authoritative Information The server is a proxy that received a 200 OK from its origin. 204 No Content The server successfully processed the request and is not returning any content,205 Reset Content The server successfully processed the request, but is not returning any content
28.
Ward McAllister
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Samuel Ward McAllister was the self-appointed arbiter of New York society from the 1860s to the early 1890s. Born Samuel Ward McAllister to a socially prominent Savannah, Georgia judicial family and he used the earnings from his legal prowess to journey throughout Europes great cities and spas—Bath, Pau, Bad Nauheim, and the like—where he observed the mannerisms of the titled nobility. Upon his return to the United States, McAllister settled in New York City with his wife, heiress Sarah Taintor Gibbons, above all in McAllisters life was his desire for social recognition and what he termed Tong, the cream of society. In his glory, McAllister referred to his patroness, Mrs. Caroline Astor and his gift for party and picnic planning soon made him a society darling. Among the undesirables McAllister endeavored to exclude from the circle of the Four Hundred were the many nouveau riche Midwesterners who poured into New York seeking social recognition. The Chicago Journal replied, The mayor will not frappé his wine too much and he will frappé it just enough so the guests can blow the foam off the tops of the glasses without a vulgar exhibition of lung and lip power. Pigs feet, will be triumphs of the gastronomic art, McAllisters downfall came when he published a book of memoirs entitled Society as I Have Found It in 1890. The book, and his hunger for attention, did little to endear him to the old guard. In disgrace, McAllister died while dining alone at New Yorks Union Club and his funeral, held on February 5,1895, was well attended by many society figures of the day, including Chauncey Depew and Cornelius Vanderbilt II. McAllister is interred at Green-Wood Cemetery in Brooklyn, New York, McAllister coined the phrase The Four Hundred. According to him, this was the number of people in New York who really mattered, the number was popularly supposed to be the capacity of Mrs William Backhouse Astor Jr. s ballroom. The Four Million, the title of a book by O. Henry, was a reaction to this phrase, social Crimes, by Jane Stanton Hitchcock. McCallister biography at Class and Leisure at Americas First Resort Biographical sketch at The History Box
29.
Atari 8-bit family
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The Atari 8-bit family is a series of 8-bit home computers introduced by Atari, Inc. in 1979 and manufactured until 1992. All of the machines in the family are similar and differ primarily in packaging. They are based on the MOS Technology 6502 CPU running at 1.79 MHz, star Raiders is widely considered the platforms killer app. The original Atari 400 and 800 models were released with a series of plug-n-play peripherals that used Ataris SIO serial bus system, to meet stringent FCC requirements, the early machines were completely enclosed in a solid cast aluminum block, which made them physically robust but expensive to produce. Over the following decade, the models were replaced by the XL and XE series which had the same basic logical design. The Atari 8-bit computer line sold two million units during its production run between late 1979 and mid-1985. They were not only sold through dedicated computer retailers, but department stores such as Sears, the primary competition in the worldwide market was, starting in 1982, the Commodore 64. This was the first computer to offer similar performance. Atari also found a market in Eastern Europe and had something of a renaissance in the early 1990s as these countries joined a uniting Europe. On January 1,1992, Atari corp, officially dropped all remaining support of the 8-bit line. Design of the 8-bit series of machines started at Atari as soon as the Atari 2600 games console was released in late 1977. While designing the 2600 in 1976, the team from Atari Grass Valley Research Center felt that the 2600 would have about a three-year lifespan before becoming obsolete. They started blue sky designs for a new console that would be ready to replace it around 1979, what they ended up with was essentially a greatly updated version of the 2600, fixing its more obvious limitations but sharing a similar overall design philosophy. The newer design would be faster than the 2600, have better graphics, work on the chips for the new system continued throughout 1978 and focused on much-improved video hardware known as the Color Television Interface Adaptor, or CTIA. During this gestation the home computer era began in earnest in the form of the TRS-80, Commodore PET, Warner Communications had purchased Atari from Nolan Bushnell for $28 million in 1976 in order to fund the launch of the 2600. Atari had recently sent Ray Kassar to act as the CEO of the company, Kassar felt the chipset should be used in a home computer to challenge Apple. In order to adapt the machine to this role, it would need to support character graphics, include some form of expansion for peripherals, and run the then-universal BASIC programming language. The CTIA, like the 2600s TIA, was designed to produce Player-Missile graphics, instead of expanding the CTIA to handle these tasks, the designers instead introduced an entirely new chip for this purpose, the Alphanumeric Television Interface Controller, or ANTIC
30.
Bolton
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Bolton is a town in Greater Manchester in North West England. A former mill town, Bolton has been a centre for textiles since Flemish weavers settled in the area in the 14th century, introducing a wool. The urbanisation and development of the town coincided with the introduction of textile manufacture during the Industrial Revolution. The British cotton industry declined sharply after the First World War, close to the West Pennine Moors, Bolton is 10 miles northwest of Manchester. It is surrounded by smaller towns and villages that together form the Metropolitan Borough of Bolton. The town of Bolton has a population of 139,403, historically part of Lancashire, Bolton originated as a small settlement in the moorland known as Bolton le Moors. In the English Civil War, the town was a Parliamentarian outpost in a staunchly Royalist region, in what became known as the Bolton Massacre,1,600 residents were killed and 700 were taken prisoner. Football club Bolton Wanderers play home games at the Macron Stadium, Cultural interests include the Octagon Theatre and the Bolton Museum and Art Gallery, as well as one of the earliest public libraries established after the Public Libraries Act 1850. Bolton is a common Northern English name derived from the Old English bothl-tun, the first recorded use of the name, in the form Boelton, dates from 1185 to describe Bolton le Moors, though this may not be in relation to a dwelling. It was recorded as Bothelton in 1212, Botelton in 1257, Boulton in 1288, later forms of Botheltun were Bodeltown, Botheltun-le-Moors, Bowelton, Boltune, Bolton-super-Moras, Bolton-in-ye-Moors, Bolton-le-Moors. The towns motto of Supera Moras means overcome difficulties, and is a pun on the Bolton-super-Moras version of the meaning literally. A Bronze Age mound was excavated in Victorian times outside Haulgh Hall, the Romans built roads from Manchester to Ribchester to the east and a road along what is now the A6 to the west. It is claimed that Agricola built a fort at Blackrod by clearing land above the forest, evidence of a Saxon settlement exists in the form of religious objects found when the Victorian parish church was built. In 1067 Great Bolton was the property of Roger de Poitou and after 1100 and it became the property of the Pilkingtons who forfeited it in the Civil War and after that the Stanleys who became Earls of Derby. Great Bolton and Little Bolton were part of the Marsey fee, in 1212 Little Bolton was held by Roger de Bolton as plough-land, a charter to hold a market in Churchgate was granted on 14 December 1251 by King Henry III of England. Bolton became a town and borough by a charter from the Earl of Derby, William de Ferrers, on 14 January 1253. Burgage plots were laid out on Churchgate and Deansgate in the centre of the town close to where Ye Olde Man & Scythe public house. In 1337 Flemish weavers settled and introduced the manufacture of woollen cloth, more Flemish weavers, fleeing the Huguenot persecutions, settled here in the 17th century
31.
Stockport
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Stockport /ˈstɒkpɔːrt/ is a large town in Greater Manchester, England,7 miles south-east of Manchester city centre, where the River Goyt and Tame merge to create the River Mersey. The town is the largest settlement in the borough of the same name. Historically, most of the town was in Cheshire, but the area to the north of the Mersey was in Lancashire. Stockport in the 16th century was a small town entirely on the bank of the Mersey. In the 18th century the town had one of the first mechanised factories in the British Isles. However, Stockports predominant industries of the 19th century were the cotton, Stockport was also at the centre of the countrys hatting industry, which by 1884 was exporting more than six million hats a year, the last hat works in Stockport closed in 1997. Dominating the western approaches to the town is the Stockport Viaduct, built in 1840, the viaducts 27 brick arches carry the mainline railways from Manchester to Birmingham and London over the River Mersey. This structure featured as the background in many paintings by L. S. Lowry, Stockport was recorded as Stokeport in 1170. The currently accepted etymology is Old English port, a place, with stoc, a hamlet, hence. Older derivations include stock, a place or castle, with port. The castle probably refers to Stockport Castle, a 12th-century motte-and-bailey first mentioned in 1173, other derivations are based on early variants such as Stopford and Stockford. There is evidence that a ford across the Mersey existed at the foot of Bridge Street Brow, Stopford retains a use in the adjectival form, Stopfordian, for Stockport-related items, and pupils of Stockport Grammar School style themselves Stopfordians. By contrast, former pupils of Stockport School are known as Old Stoconians, Stopfordian is used as the general term, or demonym used for people from Stockport, much as someone from London would be a Londoner. Stockport has never been a sea or river port as the Mersey is not navigable here, in the centre of Stockport it has been culverted and the main shopping street, Merseyway, built above it. The earliest evidence of occupation in the wider area are microliths from the hunter-gatherers of the Mesolithic period and weapons. Early Bronze Age remains include stone hammers, flint knives, palstaves, there is a gap in the age of finds between about 1200 BC and the start of the Roman period in about 70 AD, which may indicate depopulation, possibly due to a poorer climate. Despite a strong tradition, there is little evidence of a Roman military station at Stockport. It is assumed that roads from Cheadle to Ardotalia and Manchester to Buxton crossed close to the town centre
32.
Manchester Airport
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Manchester Airport is an international airport in Ringway, Manchester, England,7.5 nautical miles south west of Manchester city centre. In 2016, it was the third busiest airport in the United Kingdom in terms of passenger numbers, the airport comprises three terminals, a goods terminal and is the only British airport other than Londons Heathrow Airport to operate two runways over 3,280 yd in length. Manchester Airport covers an area of 560 hectares and has flights to 199 destinations, officially opened on 25 June 1938, it was initially known as Ringway Airport. In the Second World War, as RAF Ringway, it was a base for the Royal Air Force, Ringway, after which the airport was named, is a village with a few buildings and church at the southern edge of the airport. The airport handled 25.6 million passengers in 2016, a record total and this potential figure is limited by the airports restriction to 61 aircraft movements per hour. Manchester Airport started construction on 28 November 1935 and opened partly in June 1937 and completely on 25 June 1938, after the Second World War, the base reverted to a civilian airport and gradually expanded to its present size. Historically, Manchester Airport was consistently the busiest airport after London Heathrow for a number of following the war. In 1972, the M56 motorway opened to the airport, by 1993, the airport railway station opened. From 1997 to 2001 its second runway was built, causing protests in the area. In October 2008 the daily New York–JFK service was terminated and in March 2013. This leaves a daily high frequency BA Shuttle serving London Heathrow, in codeshare with British Airways Oneworld Alliance partner American Airlines operations remain in Terminal 3 with daily flights to both New York–JFK and Chicago–OHare. American Airlines has since merged with US Airways, which offers service to Philadelphia and operated a seasonal route to Charlotte. Since taking over BA Connects select routes, Flybe has gone on to add more destinations. In 2013 Virgin Atlantic introduced its Little Red short-haul brand to take-up some of the available Heathrow, Manchester was the inaugural destination, with services were operated by aircraft wet-leased from Aer Lingus. However, these ceased in March 2015 due to low popularity. As part of the Governments The Future of Air Transport White Paper, Manchester Airport published its Master Plan on its proposed expansions until 2030. A full-length parallel taxiway may be added to the second runway, the World Logistics Hub is also part of the Airport City Enterprise Developments in South Manchester. This development is designed to meet the demand for cargo handling space
33.
The 400 Blows
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The 400 Blows is a 1959 French drama film, the debut by director François Truffaut, it stars Jean-Pierre Léaud, Albert Rémy, and Claire Maurier. One of the films of the French New Wave, it displays many of the characteristic traits of the movement. Written by Truffaut and Marcel Moussy, the film is about Antoine Doinel, filmed on location in Paris and Honfleur, it is the first in a series of five films in which Léaud plays the semi-autobiographical character. The 400 Blows received numerous awards and nominations, including the Cannes Film Festival Award for Best Director, the OCIC Award, the film was also nominated for an Academy Award for Best Writing in 1960. The 400 Blows had a total of 4,092,970 admissions in France, making it Truffauts most successful film in his home country. The 400 Blows is widely considered one of the best French films in the history of cinema, in the 2012 Sight & Sound critics poll of the greatest films ever made, Antoine Doinel is a young boy growing up in Paris during the 1950s. Misunderstood by his parents for playing truant from school and stealing, the boy finally quits school after being caught plagiarizing Balzac by his teacher. He steals a typewriter from his stepfathers work place to finance his plans to leave home, the stepfather turns Antoine over to the police and Antoine spends the night in jail, sharing a cell with prostitutes and thieves. During an interview with the judge, Antoine’s mother confesses that her husband is not Antoine’s biological father, Antoine is placed in an observation center for troubled youths near the seashore. A psychologist at the center probes reasons for Antoines unhappiness, which the youth reveals in a series of monologues. One day, while playing football with the boys, Antoine escapes under a fence and runs away to the ocean. He reaches the shoreline of the sea and runs into it, the film concludes with a freeze-frame of Antoine, and the camera optically zooms in on his face, looking into the camera. The English title is a translation of the French but misses its meaning, as the French title refers to the idiom faire les quatre cents coups. On the first prints in the United States, subtitler and dubber Noelle Gillmor gave the film the title Wild Oats, before seeing it, some people thought the film covered the topic of corporal punishment. The semi-autobiographical film reflects events of Truffauts and his friends lives, in style, it expresses Truffauts personal history of French film, with references to other works—most notably a scene borrowed wholesale from Jean Vigos Zéro de conduite. Truffaut dedicated the film to the man who became his father, André Bazin. Besides being a study, the film is an exposé of the injustices of the treatment of juvenile offenders in France at the time. It was nominated for Best Original Screenplay at the 32nd Academy Awards, the film holds a very rare 100% Certified Fresh rating on Rotten Tomatoes based on 54 reviews
34.
400 (card game)
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400 is a Lebanese trick-taking card game played in two partnerships with a standard deck of 52 playing cards. The object of the game is to be the first team to reach forty-one points, the game somewhat resembles Spades, but with subtle differences. Historically, the game is played in Syria, Lebanon, Palestine, Jordan. It is similar to the game Tarneeb, which is played in the region. To accumulate the most points at or beyond 41, points are accrued by winning at least the number of tricks bid in each hand, hearts are always trump and other suits have no innate value. Cards rank, A K Q J1098765432 The first dealer is chosen by a draw for high card, the entire deck is dealt two cards at a time, face down, beginning on the dealers right. The players then pick up their cards and arrange them by suits. If one player runs out of cards, that is, either extra cards were dealt elsewhere or one or more cards are missing, the hand is considered void. Each player decides how many tricks he will be able to take, the player to the dealers right starts the bidding and, in turn, each player states how many tricks he expects to win. There is only one round of bidding, every player must make a bid, no player may pass. No suit is named in the bid, the minimum bid for each player is two, regardless if the player can or cannot take two tricks. Also, when a point total is 30-39, his minimum bid becomes three. When a player reaches 40 points, his minimum bid becomes 4, if the player reaches 50 points, his minimum bid becomes 5, and so on. Although 400 is played in teams, bids are not done in partnership, if partner A bids four tricks and partner B bids three tricks, bringing the total to seven, A and B are bound by their respective bids. Should partner A take five tricks and partner B take two, A will be credited with their bid, while B will not. )Unlike Spades. Should this occur, the deal goes to the players right. As noted above, the bids must equal 11 in order for a hand to begin. The same occurs when a player reaches 40 points, should a second player reach 30, the total bids in the hand should equal to 12
35.
Ontario
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Ontario, one of the 13 provinces and territories of Canada, is located in east-central Canada. It is Canadas most populous province by a margin, accounting for nearly 40 percent of all Canadians. Ontario is fourth-largest in total area when the territories of the Northwest Territories and it is home to the nations capital city, Ottawa, and the nations most populous city, Toronto. There is only about 1 km of land made up of portages including Height of Land Portage on the Minnesota border. Ontario is sometimes divided into two regions, Northern Ontario and Southern Ontario. The great majority of Ontarios population and arable land is located in the south, in contrast, the larger, northern part of Ontario is sparsely populated with cold winters and is heavily forested. The province is named after Lake Ontario, a thought to be derived from Ontarí, io, a Huron word meaning great lake, or possibly skanadario. Ontario has about 250,000 freshwater lakes, the province consists of three main geographical regions, The thinly populated Canadian Shield in the northwestern and central portions, which comprises over half the land area of Ontario. Although this area mostly does not support agriculture, it is rich in minerals and in part covered by the Central and Midwestern Canadian Shield forests, studded with lakes, Northern Ontario is subdivided into two sub-regions, Northwestern Ontario and Northeastern Ontario. The virtually unpopulated Hudson Bay Lowlands in the north and northeast, mainly swampy. Southern Ontario which is further sub-divided into four regions, Central Ontario, Eastern Ontario, Golden Horseshoe, the highest point is Ishpatina Ridge at 693 metres above sea level located in Temagami, Northeastern Ontario. In the south, elevations of over 500 m are surpassed near Collingwood, above the Blue Mountains in the Dundalk Highlands, the Carolinian forest zone covers most of the southwestern region of the province. A well-known geographic feature is Niagara Falls, part of the Niagara Escarpment, the Saint Lawrence Seaway allows navigation to and from the Atlantic Ocean as far inland as Thunder Bay in Northwestern Ontario. Northern Ontario occupies roughly 87 percent of the area of the province. Point Pelee is a peninsula of Lake Erie in southwestern Ontario that is the southernmost extent of Canadas mainland, Pelee Island and Middle Island in Lake Erie extend slightly farther. All are south of 42°N – slightly farther south than the border of California. The climate of Ontario varies by season and location, the effects of these major air masses on temperature and precipitation depend mainly on latitude, proximity to major bodies of water and to a small extent, terrain relief. In general, most of Ontarios climate is classified as humid continental, Ontario has three main climatic regions
36.
400-series highways (Ontario)
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The 400-series highways are a network of controlled-access highways throughout the southern portion of the Canadian province of Ontario, forming a special subset of the provincial highway system. Although Ontario had been constructing divided highways for two decades prior, 400-series designations were introduced in 1952, initially only Highways 400,401 and 402 were numbered, other designations followed in the subsequent decades. Modern 400-series highways have high standards, speed limits of 100 kilometres per hour. As a result, they experience the lowest accident and fatality rate comparative to traffic volume in North America. When the 400-series designations were first applied to Ontario freeways in 1952, originally inspired by German Autobahns, Thomas McQuesten planned a network of Dual Highways across the southern half of the province. The Queen Elizabeth Way was first, an upgrade to the partially constructed Middle Road in 1934, the construction boom that followed World War II resulted in a great number of new freeway construction projects in the province. Seeking a new way to distinguish the controlled-access freeways from the two lane Kings Highway networks, the Department of Highways created the 400-series designations in 1952. By the end of the year, Highway 400,401 and 402 were numbered, catharines, Highway 406 south from St. The first sections of freeways were opened in 1963,1977,1963,1965,1997,1974. Highway 420 was designated in Niagara Falls, though it had built as part of the QEW in 1941. Other major works included the skyway bridges along the QEW and the expansion of Highway 401 into twelve lane collector-express systems, by the mid-1980s, the network had more-or-less taken its current shape, with only Highways 407 and 416 not yet built. Instead, emphasis was placed on expanding existing routes to accommodate increasing traffic volumes, however, extensions of Highway 400 towards Parry Sound, Highway 403 between Woodstock and Hamilton, Highway 404 towards Newmarket, and Highway 427 towards Vaughan were underway. By the end of the decade, construction of Highway 407 and Highway 416 had begun, Highways 407 and 416 opened in the late 1990s. Until early 2015, Highways 407 and 416 were the most-recently designated freeways in Ontario and this has changed with the designation of Highways 412 and 418. Of note are the Ontario Tall Wall median barrier and the Parclo A-4 interchange design, the Institute of Traffic Engineers subsequently recommended this design to replace the cloverleaf interchange throughout North America. Highways in Ontario are among the safest in North America, with 0.63 fatalities per 10,000 licensed drivers in 2010, conforming with the Manual on Uniform Traffic Control Devices, Ontario utilizes green signs for guidance purposes. Generally, blue signage is used to list services and attractions at upcoming exits, however, several exceptions exist, notably blue guidance signage for toll highways like Highway 407 and Highway 412, in addition to the collector lanes of highways. The baseline standard for the construction of or expansion to a freeway in Ontario is a daily traffic count of 10,000 vehicles per day
37.
Twin Cities 400
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The 400 was a named passenger train operated by the Chicago and North Western Railway between Chicago and Saint Paul, with a final stop in Minneapolis. It was a train with limited stops between Chicago and the Twin Cities. It ran from 1935 to 1963 and spawned a number of 400 trains,1934 had seen the introduction of lightweight streamlined trains in the United States. The railroads hoped these futuristic trains would stem the tide of customers turning away from train travel, the Chicago and North Western Railway had not invested in this new technology, but decided to upgrade track and motive power for higher speeds with heavyweight, steam-powered trains. While C&NWs existing Chicago to St. Paul Viking train went through Madison, taking about 12 hours, the railroad also upgraded its locomotives and passenger cars. The passenger cars got air conditioning and improved suspension parts for a smoother ride, a test run was made on December 30,1934, but the regular train started on January 2,1935. Time dubbed the 400, the fastest train scheduled on the American Continent, while the 400 implied 400 miles in 400 minutes, Chicago to St. Paul was 408.6 miles in 420 minutes, with the last leg to Minneapolis taking another 30 minutes. The 400s had priority over all other trains, the employee timetable specified that Freight trains, transfer trains, other 400 trains would receive similar instructions in later years, and the rule remained in effect for most of the Twin Cities 400s existence. On the first day the train reached 91 miles per hour and this included a 75-minute schedule between Chicago and Milwaukee, averaging 68 mph there and 63 mph overall. One day in late 1935 the 400 needed to make up time, later, streamlined diesel trains were said to reach 112 mph. From 1950 to 1955 the train ran its shortest schedule, 6¼ hours between St. Paul and Chicago, an average of over 65 mph. In 1952 the railroad installed automatic train stop along the half of the route from Chicago to Wyeville due to regulations from the Interstate Commerce Commission. This allowed the train to run at 95 to 100 mph there, the pace reverted to a 6½-hour schedule in 1955 and in 1960 to the 7-hour pace established in 1935. C&NW ceased running the Twin Cities 400 in 1963 and all intercity service on C&NW ended with the formation of Amtrak in 1971. Today the only Twin Cities to Chicago train is the Amtrak Empire Builder, the 400 was notable for fast trains of its day in that it originally ran with rebuilt or upgraded, rather than new equipment. This stood in comparison to the Milwaukee Roads Hiawatha and the Burlington Zephyrs, each of which first ran with brand new locomotives. Each 400 train required two locomotives, which were swapped partway through the trip, primarily because some grease fittings on the train could not withstand the entire journey at high speed. The steam locomotives were upgraded to feature a 45° lamp on top of the boiler just ahead of the smokestack and these lights were intended to announce the approach of the train and could be seen for a great distance in rural areas
38.
Chicago and North Western Railway
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The Chicago and North Western Transportation Company was a Class I railroad in the Midwestern United States. It was also known as the North Western, the railroad operated more than 5,000 miles of track as of the turn of the 20th century, and over 12,000 miles of track in seven states before retrenchment in the late 1970s. Until 1972, when the company was sold to its employees, it was named the Chicago and North Western Railway. The C&NW became one of the longest railroads in the United States as a result of mergers with other railroads, such as the Chicago Great Western Railway, Minneapolis and St. Louis Railway and others. By 1995, track sales and abandonment had reduced the total back to about 5,000. The majority of the abandoned and sold lines were lightly trafficked branches in Iowa, Illinois, Minnesota, South Dakota and Wisconsin. Large line sales, such as those that resulted in the Dakota, Minnesota and Eastern Railroad further helped reduce the railroad to a core with several regional feeders. The company was purchased by Union Pacific Railroad in April 1995, the Chicago and North Western Railway was chartered on June 7,1859. It had purchased the assets of the bankrupt Chicago, St. Paul, on February 15,1865, it officially merged with the Galena and Chicago Union Railroad, which had been chartered on January 16,1836. The Winona and St. Peter Railroad was added to the network in 1867, the North Western had owned a majority of the stock of the Chicago, St. Paul, Minneapolis and Omaha Railway since 1882. On January 1,1957 it leased the company, and merged it into the North Western in 1972. The Omaha Roads main line ran from an interchange with the North Western at Elroy, Wisconsin, to the Twin Cities, down to Sioux City, Iowa, the North Western picked up several important short railroads during its later years. It finalized acquisition of the Litchfield and Madison Railway on January 1,1958, the Litchfield and Madison railroad was a 44-mile bridge road from East St. Louis to Litchfield, Illinois. On July 30,1968, the North Western acquired two former interurbans — the 36-mile Des Moines and Central Iowa Railway, and the 110-mile Fort Dodge, Des Moines and Southern Railway. The DM&CI gave access to the Firestone plant in Des Moines, Iowa, on November 1,1960, the North Western acquired the rail properties of the 1, 500-mile Minneapolis and St. Louis Railway. In spite of its name, it ran only from Minneapolis, Minnesota, to Peoria and this acquisition provided traffic and modern rolling stock, and eliminated competition. On July 1,1968 the 1,500 mi Chicago Great Western Railway was merged into the North Western and this railroad went from Chicago to Oelwein, Iowa. From there lines went to the Twin Cities, Omaha, Nebraska, a connection from Hayfield, Minnesota, to Clarion, Iowa, provided a Twin Cities to Omaha main line
39.
Minneapolis/St. Paul
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Minneapolis–Saint Paul is a major metropolitan area built around the Mississippi, Minnesota and St. Croix rivers in east central Minnesota. The area is known as the Twin Cities after its two largest cities, Minneapolis, the city with the largest population in the state, and Saint Paul. It is an example of twin cities in the sense of geographical proximity, Minnesotans living outside of Minneapolis and Saint Paul often refer to the two together as The Cities. There are several different definitions of the region, many refer to the Twin Cities as the seven-county region which is governed under the Metropolitan Council regional governmental agency and planning organization. The Office of Management and Budget officially designates 16 counties as the Minneapolis–St, paul–Bloomington MN-WI Metropolitan Statistical Area, the 16th largest in the United States. The entire region known as the Minneapolis–St, Paul MN-WI Combined Statistical Area, has a population of 3,866,768, the 14th largest, according to 2015 Census estimates. Despite the Twin moniker, both cities are independent municipalities with defined borders, Minneapolis was influenced by its early Scandinavian and Lutheran heritage and hosts the largest Somali population in North America. St. Paul was influenced by its early French, Irish, the Minneapolis-St. Paul metropolitan area includes 16 counties, of which 14 are in Minnesota and two in Wisconsin. Note, Counties that are bolded are under jurisdiction of the Metropolitan Council, numbers in parentheses are 2013 census estimates. Counties that are italicized were added to the area when the Office of Management. There are approximately 218 incorporated municipalities within the Twin Cities metropolitan region and this includes census-designated places along with villages in Wisconsin, but excludes unincorporated towns in Wisconsin, known as civil townships in other states. Estimates are as of 2013 for cities with 25,000 or more inhabitants, Paul, MN-WI Combined Statistical Area is made up of 19 counties in Minnesota and two counties in Wisconsin. The statistical area includes two areas and three micropolitan areas. As of the 2010 Census, the CSA had a population of 3,684,928, the CSA definition encompasses 11,132.44 sq mi of area. After St. Paul completed its elaborate Cathedral in 1915, Minneapolis quickly followed up with the equally ornate Basilica of St. Mary in 1926. In the late 19th and early 20th centuries the rivalry became so intense that an architect practicing in one city was often refused business in the other. The 1890 United States Census even led to the two cities arresting and/or kidnapping each others census takers, in an attempt to either city from outgrowing the other. The rivalry could occasionally erupt into inter-city violence, as happened at a 1923 game between the Minneapolis Millers and the St. Paul Saints, both teams of the American Association
40.
Chicago, Illinois
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Chicago, officially the City of Chicago, is the third-most populous city in the United States. With over 2.7 million residents, it is the most populous city in the state of Illinois, and it is the county seat of Cook County. In 2012, Chicago was listed as a global city by the Globalization and World Cities Research Network. Chicago has the third-largest gross metropolitan product in the United States—about $640 billion according to 2015 estimates, the city has one of the worlds largest and most diversified economies with no single industry employing more than 14% of the workforce. In 2016, Chicago hosted over 54 million domestic and international visitors, landmarks in the city include Millennium Park, Navy Pier, the Magnificent Mile, Art Institute of Chicago, Museum Campus, the Willis Tower, Museum of Science and Industry, and Lincoln Park Zoo. Chicagos culture includes the arts, novels, film, theater, especially improvisational comedy. Chicago also has sports teams in each of the major professional leagues. The city has many nicknames, the best-known being the Windy City, the name Chicago is derived from a French rendering of the Native American word shikaakwa, known to botanists as Allium tricoccum, from the Miami-Illinois language. The first known reference to the site of the current city of Chicago as Checagou was by Robert de LaSalle around 1679 in a memoir, henri Joutel, in his journal of 1688, noted that the wild garlic, called chicagoua, grew abundantly in the area. In the mid-18th century, the area was inhabited by a Native American tribe known as the Potawatomi, the first known non-indigenous permanent settler in Chicago was Jean Baptiste Point du Sable. Du Sable was of African and French descent and arrived in the 1780s and he is commonly known as the Founder of Chicago. In 1803, the United States Army built Fort Dearborn, which was destroyed in 1812 in the Battle of Fort Dearborn, the Ottawa, Ojibwe, and Potawatomi tribes had ceded additional land to the United States in the 1816 Treaty of St. Louis. The Potawatomi were forcibly removed from their land after the Treaty of Chicago in 1833, on August 12,1833, the Town of Chicago was organized with a population of about 200. Within seven years it grew to more than 4,000 people, on June 15,1835, the first public land sales began with Edmund Dick Taylor as U. S. The City of Chicago was incorporated on Saturday, March 4,1837, as the site of the Chicago Portage, the city became an important transportation hub between the eastern and western United States. Chicagos first railway, Galena and Chicago Union Railroad, and the Illinois, the canal allowed steamboats and sailing ships on the Great Lakes to connect to the Mississippi River. A flourishing economy brought residents from rural communities and immigrants from abroad, manufacturing and retail and finance sectors became dominant, influencing the American economy. The Chicago Board of Trade listed the first ever standardized exchange traded forward contracts and these issues also helped propel another Illinoisan, Abraham Lincoln, to the national stage
41.
RMS Olympic
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RMS Olympic was a transatlantic ocean liner, the lead ship of the White Star Lines trio of Olympic-class liners. Unlike her younger sister ships, Olympic had a long career and this included service as a troopship during the First World War, which gained her the nickname Old Reliable. Olympic was the largest ocean liner in the world for two periods during 1911–13, interrupted only by the tenure of the slightly larger Titanic. Olympic also retained the title of the largest British-built liner until RMS Queen Mary was launched in 1934, by contrast with Olympic, the other ships in the class, Titanic and Britannic, did not have long service lives. Built in Belfast, Ireland, the RMS Olympic was the first of the three Olympic-class ocean liners – the others were RMS Titanic and HMHS Britannic. They were by far the largest vessels of the British shipping company White Star Lines fleet, the company sought an upgrade in their fleet primarily in response to the Cunard giants but also to replace their largest and now outclassed ships from 1890, SS Teutonic and SS Majestic. The former was replaced by Olympic while Majestic was replaced by Titanic, Majestic would be brought back into her old spot on White Stars New York service after Titanics loss. The ships were constructed by the Belfast shipbuilders Harland and Wolff, cost considerations were relatively low on the agenda and Harland and Wolff was authorised to spend what it needed on the ships, plus a five percent profit margin. In the case of the Olympic-class ships, a cost of £3 million for the first two ships was agreed plus extras to contract and the five percent fee. Harland and Wolff put their leading designers to work designing the Olympic-class vessels, carlisles responsibilities included the decorations, equipment and all general arrangements, including the implementation of an efficient lifeboat davit design. On 29 July 1908, Harland and Wolff presented the drawings to J. Bruce Ismay, Ismay approved the design and signed three letters of agreement two days later authorising the start of construction. At this point the first ship – which was later to become Olympic – had no name, Titanic was based on a revised version of the same design and was given the number 401. Bruce Ismays father Thomas Henry Ismay had previously planned to build a ship named Olympic as a ship to Oceanic. The senior Ismay died in 1899 and the order for the ship was cancelled, construction of Olympic began three months before Titanic to ease pressures on the shipyard. Several years would pass before Britannic would be launched, in order to accommodate the construction of the class, Harland and Wolff upgraded their facility in Belfast, the most dramatic change was the combining of three slipways into two larger ones. Olympics keel was laid in December 1908 and she was launched on 20 October 1910 and her hull was repainted black following the launch. The first-class passengers enjoyed luxurious cabins, and some were equipped with private bathrooms, first-class passengers could have meals in the ships large and luxurious dining saloon or in the more intimate A La Carte Restaurant. The second-class facilities included a room, a library, a spacious dining room
42.
RMS Titanic
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Of the 2,224 passengers and crew aboard, more than 1,500 died, making it one of the deadliest commercial peacetime maritime disasters in modern history. Thomas Andrews, her architect, died in the disaster, the first class accommodation was designed to be the pinnacle of comfort and luxury, with an on-board gymnasium, swimming pool, libraries, high-class restaurants and opulent cabins. A high-power radiotelegraph transmitter was available for sending passenger marconigrams and for the operational use. Titanic only carried enough lifeboats for 1,178 people—slightly more than half of the number on board, after leaving Southampton on 10 April 1912, Titanic called at Cherbourg in France and Queenstown in Ireland before heading west to New York. On 14 April, four days into the crossing and about 375 miles south of Newfoundland, the collision caused the ships hull plates to buckle inwards along her starboard side and opened five of her sixteen watertight compartments to the sea, she could only survive four flooding. Meanwhile, passengers and some members were evacuated in lifeboats. A disproportionate number of men were left aboard because of a women and children first protocol for loading lifeboats, at 2,20 a. m. she broke apart and foundered—with well over one thousand people still aboard. Just under two hours after Titanic sank, the Cunard liner RMS Carpathia arrived at the scene, where she brought aboard an estimated 705 survivors. The disaster was greeted with shock and outrage at the huge loss of life. Public inquiries in Britain and the United States led to improvements in maritime safety. One of their most important legacies was the establishment in 1914 of the International Convention for the Safety of Life at Sea, which still governs maritime safety today. Additionally, several new regulations were passed around the world in an effort to learn from the many missteps in wireless communications—which could have saved many more passengers. The wreck of Titanic, first discovered over 70 years after the sinking, remains on the seabed, since her discovery in 1985, thousands of artifacts have been recovered and put on display at museums around the world. Titanic has become one of the most famous ships in history, her memory is kept alive by numerous works of culture, including books, folk songs, films, exhibits. Titanic is the second largest ocean liner wreck in the world, only beaten by her sister HMHS Britannic, the name Titanic was derived from Greek mythology and meant gigantic. They were by far the largest vessels of the British shipping company White Star Lines fleet, Teutonic was replaced by Olympic while Majestic was replaced by Titanic. Majestic would be back into her old spot on White Stars New York service after Titanics loss. The ships were constructed by the Belfast shipbuilders Harland and Wolff, cost considerations were relatively low on the agenda and Harland and Wolff was authorised to spend what it needed on the ships, plus a five percent profit margin
43.
Ted Williams
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Theodore Samuel Williams was an American professional baseball player and manager. He played his entire 19-year Major League Baseball career as a fielder for the Boston Red Sox from 1939 to 1942 and 1946 to 1960, excepting service time during World War II. Nicknamed The Kid, The Splendid Splinter, Teddy Ballgame, The Thumper and The Greatest Hitter Who Ever Lived, Williams was also an outstanding fielder, especially in the difficult left field of Fenway Park in Boston, where he played his entire Major League career at that position. Williams was a seventeen-time All-Star, a recipient of the American League Most Valuable Player Award, a six-time AL batting champion. He finished his career with a.344 batting average,521 home runs, and a 0.482 on-base percentage. His batting average is the highest of any MLB player with 302 or more home runs, born and raised in San Diego, Williams played baseball throughout his youth. Joining the Red Sox in 1939, he emerged as one of the sports best hitters. In 1941, Williams posted a.406 batting average, making him the last MLB player to bat over.400 in a season and he followed this up by winning his first Triple Crown in 1942. Williams interrupted his career in 1943 to serve three years in the US Navy and US Marine Corps during World War II. Upon returning to MLB in 1946, Williams won his first AL MVP Award, in 1947, he won his second Triple Crown. Williams was returned to military duty for portions of the 1952 and 1953 seasons to serve as a Marine combat aviator in the Korean War. In 1957 and 1958 at the ages of 39 and 40, respectively, Williams retired from playing in 1960. He was inducted into the Baseball Hall of Fame in 1966, Williams managed the Washington Senators/Texas Rangers franchise from 1969 to 1972. An avid sport fisherman, he hosted a program about fishing. Williams involvement in the Jimmy Fund helped raise millions in dollars for cancer care, in 1991 President George H. W. Bush presented Williams with the Presidential Medal of Freedom, the highest civilian award bestowed by the United States government. He was selected for the Major League Baseball All-Time Team in 1997, Ted Williams was born Theodore Samuel Williams in San Diego, California. At some later date he amended his birth certificate, removing his name, which he claimed originated from a maternal uncle. His father was a soldier, sheriff, and photographer from New York, while his mother, May Venzor, Williams resented his mothers long hours working in the Salvation Army, and Williams and his brother cringed when she took them to the Armys street-corner revivals
44.
Gregorian calendar
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The Gregorian calendar is internationally the most widely used civil calendar. It is named after Pope Gregory XIII, who introduced it in October 1582, the calendar was a refinement to the Julian calendar involving a 0. 002% correction in the length of the year. The motivation for the reform was to stop the drift of the calendar with respect to the equinoxes and solstices—particularly the northern vernal equinox, transition to the Gregorian calendar would restore the holiday to the time of the year in which it was celebrated when introduced by the early Church. The reform was adopted initially by the Catholic countries of Europe, the last European country to adopt the reform was Greece, in 1923. Many countries that have used the Islamic and other religious calendars have come to adopt this calendar for civil purposes. The reform was a modification of a made by Aloysius Lilius. His proposal included reducing the number of years in four centuries from 100 to 97. Lilius also produced an original and practical scheme for adjusting the epacts of the moon when calculating the date of Easter. For example, the years 1700,1800, and 1900 are not leap years, but the years 1600 and 2000 are. The canonical Easter tables were devised at the end of the third century, when the vernal equinox fell either on 20 March or 21 March depending on the years position in the leap year cycle. As the rule was that the full moon preceding Easter was not to precede the equinox, the date was fixed at 21 March for computational purposes, the Gregorian calendar reproduced these conditions by removing ten days. To unambiguously specify a date, dual dating or Old Style, dual dating gives two consecutive years for a given date, because of differences in the starting date of the year, and/or to give both the Julian and the Gregorian dates. The Gregorian calendar continued to use the calendar era, which counts years from the traditional date of the nativity. This year-numbering system, also known as Dionysian era or Common Era, is the predominant international standard today, the Gregorian calendar is a solar calendar. A regular Gregorian year consists of 365 days, but as in the Julian calendar, in a leap year, in the Julian calendar a leap year occurs every 4 years, but the Gregorian calendar omits 3 leap days every 400 years. In the Julian calendar, this day was inserted by doubling 24 February. In the modern period, it has become customary to number the days from the beginning of the month, some churches, notably the Roman Catholic Church, delay February festivals after the 23rd by one day in leap years. Gregorian years are identified by consecutive year numbers, the cycles repeat completely every 146,097 days, which equals 400 years
45.
Intertestamental period
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It is known by members of the Protestant community as the 400 Silent Years because it is believed to have been a span where God revealed nothing new to his people. It is said many of the Deuterocanonical or Anagignoskomena books, accepted as scripture by Roman Catholicism. This is also the time when many pseudepigraphal works were produced, an understanding of the events of the intertestamental period provides context for the New Testament. Archived from the original on August 7,2015, what happened in the intertestamental period
46.
Kaph
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Kaf is the eleventh letter of the Semitic abjads, including Phoenician Kāp, Hebrew Kāf כ, Aramaic Kāp, Syriac Kāp̄ ܟܟ, and Arabic Kāf ک/ك. The Phoenician letter gave rise to the Greek kappa, Latin K, kaph is thought to have been derived from a pictogram of a hand. The letter is named kāf, and it is written in several ways depending on its position in the word, the long s-shaped variant form, al-kāf al-mabsūṭah, which is only used in Arabic texts and for writing Quran. In Moroccan Arabic its pronounced as k, g or ch, in literary Arabic, kāf is used as a prefix meaning like, as, or as though. For example, كَطَائِر, meaning like a bird or as though a bird, the prefix كَـ ka is one of the Arabic words for like or as. The /ka/ prefix sometimes has added to other words to create fixed constructions. For instance, it is prefixed to ﺫَلِك /ðaːlik/ this, that to form the fixed word كَذَلِك /kaðaːlik/ like so, Kāf is used as a possessive suffix for second-person singular nouns, for instance, كِتَاب kitāb becomes كِتَابُكَ kitābuka كِتَابُكِ kitābuki. At the ends of sentences and often in conversation the final vowel is suppressed, Hebrew spelling, כָּף The letter kaf is one of the six letters which can receive a dagesh kal. The other five are bet, gimel, daleth, pe, there are two orthographic variants of this letter which alter the pronunciation, When the kaph has a dot in its center, known as a dagesh, it represents a voiceless velar plosive. There are various rules in Hebrew grammar that stipulate when and why a dagesh is used, when this letter appears as כ without the dagesh in its center it represents, like the ch in German Bach. In modern Israeli Hebrew the letter heth is often pronounced as a, if the letter is at the end of a word the symbol is drawn differently. However, it does not change the pronunciation or transliteration in any way, the name for the letter is final kaf. Four additional Hebrew letters take final forms, tsadi, mem, nun, kaf/khaf is the only Hebrew letter that can take a vowel in its word-final form which is pronounced after the consonant, that vowel being the qamatz. In gematria, kaph represents the number 20 and its final form represents 500, but this is rarely used, tav and qoph being used instead. As a prefix, kaph is a preposition, It can mean like or as, as in literary Arabic, in colloquial Hebrew, kaph and shin together have the meaning of when. This is a contraction of כאשר, kaasher
47.
Nun
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A nun is a member of a religious community of women, typically one living under vows of poverty, chastity, and obedience. The term nun is applicable to Catholics, Orthodox Christians, Anglicans, Lutherans, Jains, Buddhists, Taoists, Hindus, Mother Teresas Missionaries of Charity, lives an active vocation of both prayer and service, often to the needy, ill, poor, and uneducated. All Buddhist traditions have nuns, although their status is different among Buddhist countries, fully ordained Buddhist nuns have more Patimokkha rules than the monks. The important vows are the same, however, as with monks, there is quite a lot of variation in nuns dress and social conventions between Buddhist cultures in Asia. Chinese nuns possess the full ordination, Tibetan nuns do not. In Thailand, a country never had a tradition of fully ordained nuns. However, some of them have played an important role in dhamma-practitioners community. There are in Thai Forest Tradition foremost nuns such as Mae Ji Kaew Sianglam, the founder of the Nunnery of Baan Huai Saai, who is believed by some to be enlightened as well as Upāsikā Kee Nanayon. At the beginning of the 21st century, some Buddhist women in Thailand have started to introduce the bhikkhuni sangha in their country as well, dhammananda Bhikkhuni, formerly the successful academic scholar Dr. Chatsumarn Kabilsingh, established a controversial monastery for the training of Buddhist nuns in Thailand. The relatively active roles of Taiwanese nuns were noted by some studies, researcher Charles Brewer Jones estimates that from 1952 to 1999, when the Buddhist Association of the ROC organized public ordination, female applicants have outnumbered males by about three to one. He adds, All my informants in the areas of Taipei and Sanhsia considered nuns at least as respectable as monks, in contrast, however, Shiu-kuen Tsung found in Taipei county that female clergy were viewed with some suspicion by society. She reports that while outsiders did not necessarily regard their vocation as unworthy of respect, wei-yi Cheng studied Luminary order in southern Taiwan. Based on studies of Luminary order, Cheng concluded that the order in Taiwan was still young and gave nuns more rooms of development. Gelongma ordination requires the presence of ten fully ordained people keeping exactly the same vows, because ten nuns are required to ordain a new one, the effort to establish the Dharmaguptaka bhikkhu tradition has taken a long time. It is permissible for a Tibetan nun to receive ordination from another living tradition. Based on this, Western nuns ordained in Tibetan tradition, like Thubten Chodron, the ordination of monks and nuns in Tibetan Buddhism distinguishes three stages, rabjung-ma, getshül-ma and gelong-ma. The clothes of the nuns in Tibet are basically the same as those of monks, hokke-ji in 747 was established by the consort of the Emperor. It took charge of provincial convents, performed ceremonies for the protection of the state, aristocratic Japanese women often became Buddhist nuns in the premodern period
48.
Pe (letter)
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Pe is the seventeenth letter of the Semitic abjads, including Phoenician Pē, Hebrew Pē פ, Aramaic Pē, Syriac Pē ܦ, and Arabic Fāʼ ف and also Persian Peʼ پ. The Phoenician letter gave rise to the Greek Pi, Latin P, Pe is usually assumed to come from a pictogram of a mouth. The letter ﻑ is named ﻓﺎء fāʾ. g and it may be used interchangeably with the modified letter ﭪ - ve in this case. In the process of developing from Proto-Semitic, Proto-Semitic /p/ became Arabic /f/, examples on usage in Modern Standard Arabic, Fāʾ-fatḥah is a multi-function prefix most commonly equivalent to so or so that. For example, نَكْتُب naktub → فَنَكْتُب fanaktub, in Persian, it uses پ to represent the phoneme Voiceless bilabial stop /p/ The Persian alphabet has taken the shape of ba’ but it has three dots below instead. In the Maghreb, the dot in fāʼ is written underneath, once the prevalent style, it is now only used in Maghribi countries for writing Quran, with the exception of Libya and Algeria, which adopted the Mashriqi form. The Maghrebi alphabet has taken the shape of fa’ to mean qāf instead and it is also romanized pey, especially when used in Yiddish. The letter Pe is one of the six letters which can receive a Dagesh Kal, the six are Bet, Gimel, Daleth, Kaph, Pe, and Tav. There are two variants of this letter which indicate a different pronunciation, When the Pe has a dot in its center, known as a dagesh, it represents a voiceless bilabial plosive. There are various rules in Hebrew grammar that stipulate when and why a dagesh is used, when Pe appears without the dagesh dot in its center, then it usually represents a voiceless labiodental fricative /f/. At the end of words, the written form changes to a Pe/Fe Sophit. When a word in modern Hebrew borrowed from another language ends with /p/ and this is because native Hebrew words, which always use the final form at the end, cannot end in /p/. In gematria, Pe represents the number 80 and its final form represents 800 but this is rarely used, Tav written twice being used instead
49.
Tzade
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Ṣade is the eighteenth letter of the Semitic abjads, including Phoenician Çādē, Hebrew Ṣādi צ, Aramaic Ṣāḏē, Syriac Ṣāḏē ܨ, Geez Ṣädäy ጸ, and Arabic Ṣād ص. Its oldest sound value is probably /sˤ/, although there is a variety of pronunciation in different modern Semitic languages and it represents the coalescence of three Proto-Semitic emphatic consonants in Canaanite. Arabic, which kept the separate, introduced variants of ṣād. In Aramaic, these emphatic consonants coalesced instead with ʿayin and ṭēt, respectively, the Phoenician letter is continued in the Greek San and possibly Sampi, and in Etruscan
50.
Prime number
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A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a number is called a composite number. For example,5 is prime because 1 and 5 are its only positive integer factors, the property of being prime is called primality. A simple but slow method of verifying the primality of a number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and n, algorithms much more efficient than trial division have been devised to test the primality of large numbers. Particularly fast methods are available for numbers of forms, such as Mersenne numbers. As of January 2016, the largest known prime number has 22,338,618 decimal digits, there are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no simple formula that separates prime numbers from composite numbers. However, the distribution of primes, that is to say, many questions regarding prime numbers remain open, such as Goldbachs conjecture, and the twin prime conjecture. Such questions spurred the development of branches of number theory. Prime numbers give rise to various generalizations in other domains, mainly algebra, such as prime elements. A natural number is called a number if it has exactly two positive divisors,1 and the number itself. Natural numbers greater than 1 that are not prime are called composite, among the numbers 1 to 6, the numbers 2,3, and 5 are the prime numbers, while 1,4, and 6 are not prime. 1 is excluded as a number, for reasons explained below. 2 is a number, since the only natural numbers dividing it are 1 and 2. Next,3 is prime, too,1 and 3 do divide 3 without remainder, however,4 is composite, since 2 is another number dividing 4 without remainder,4 =2 ·2. 5 is again prime, none of the numbers 2,3, next,6 is divisible by 2 or 3, since 6 =2 ·3. The image at the right illustrates that 12 is not prime,12 =3 ·4, no even number greater than 2 is prime because by definition, any such number n has at least three distinct divisors, namely 1,2, and n
51.
Eisenstein prime
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In mathematics, an Eisenstein prime is an Eisenstein integer z = a + b ω that is irreducible in the ring-theoretic sense, its only Eisenstein divisors are the units, a + bω itself and its associates. The associates and the conjugate of any Eisenstein prime are also prime. It follows that the absolute value squared of every Eisenstein prime is a prime or the square of a natural prime. The first few Eisenstein primes that equal a natural prime 3n −1 are,2,5,11,17,23,29,41,47,53,59,71,83,89,101. Natural primes that are congruent to 0 or 1 modulo 3 are not Eisenstein primes, some non-real Eisenstein primes are 2 + ω,3 + ω,4 + ω,5 + 2ω,6 + ω,7 + ω,7 + 3ω. Up to conjugacy and unit multiples, the primes listed above, as of March 2017, the largest known Eisenstein prime is the seventh largest known prime 10223 ×231172165 +1, discovered by Péter Szabolcs and PrimeGrid. All larger known primes are Mersenne primes, discovered by GIMPS, real Eisenstein primes are congruent to 2 mod 3, and Mersenne primes are congruent to 1 mod 3, thus no Mersenne prime is an Eisenstein prime
52.
Mertens function
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In number theory, the Mertens function is defined for all positive integers n as M = ∑ k =1 n μ where μ is the Möbius function. The function is named in honour of Franz Mertens and this definition can be extended to positive real numbers as follows, M = M. Less formally, M is the count of square-free integers up to x that have a number of prime factors. Because the Möbius function only takes the values −1,0, and +1, the Mertens conjecture went further, stating that there would be no x where the absolute value of the Mertens function exceeds the square root of x. The Mertens conjecture was proven false in 1985 by Andrew Odlyzko, however, the Riemann hypothesis is equivalent to a weaker conjecture on the growth of M, namely M = O. Since high values for M grow at least as fast as the root of x. Here, O refers to Big O notation, the true rate of growth of M is not known. An unpublished conjecture of Steve Gonek states that 0 < lim sup x → ∞ | M | x 5 /4 < ∞, probabilistic evidence towards this conjecture is given by Nathan Ng. Using the Euler product one finds that 1 ζ = ∏ p = ∑ n =1 ∞ μ n s where ζ is the Riemann zeta function and the product is taken over primes. Then, using this Dirichlet series with Perrons formula, one obtains,12 π i ∫ c − i ∞ c + i ∞ x s s ζ d s = M where c >1. Conversely, one has the Mellin transform 1 ζ = s ∫1 ∞ M x s +1 d x which holds for R e >1. A curious relation given by Mertens himself involving the second Chebyshev function is ψ = M log + M log + M log + ⋯. Assuming that there are not multiple non-trivial roots of ζ we have the formula by the residue theorem. Weyl conjectured that the Mertens function satisfied the approximate functional-differential equation y 2 − ∑ r =1 N B2 r. Another formula for the Mertens function is M = ∑ a ∈ F n e 2 π i a where F n is the Farey sequence of order n and this formula is used in the proof of the Franel–Landau theorem. M is the determinant of the n × n Redheffer matrix, using sieve methods similar to those used in prime counting, the Mertens function has been computed for all integers up to an increasing range of x. The Mertens function for all values up to x may be computed in O time. Combinatorial based algorithms can compute isolated values of M in O time, see A084237 for values of M at powers of 10
53.
HTTP 401
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This is a list of Hypertext Transfer Protocol response status codes. It includes codes from IETF Request for Comments, other specifications, the first digit of the status code specifies one of five standard classes of responses. The message phrases shown are typical, but any human-readable alternative may be provided, unless otherwise stated, the status code is part of the HTTP/1.1 standard. The Internet Assigned Numbers Authority maintains the registry of HTTP status codes. An informational response indicates that the request was received and understood and it is issued on a provisional basis while request processing continues. It alerts the client to wait for a final response, the message consists only of the status line and optional header fields, and is terminated by an empty line. As the HTTP/1.0 standard did not define any 1xx status codes,100 Continue The server has received the request headers and the client should proceed to send the request body. Sending a large request body to a server after a request has been rejected for inappropriate headers would be inefficient. To have a check the requests headers, a client must send Expect, 100-continue as a header in its initial request. The response 417 Expectation Failed indicates the request should not be continued,101 Switching Protocols The requester has asked the server to switch protocols and the server has agreed to do so. 102 Processing A WebDAV request may contain many sub-requests involving file operations and this code indicates that the server has received and is processing the request, but no response is available yet. This prevents the client from timing out and assuming the request was lost and this class of status codes indicates the action requested by the client was received, understood, accepted, and processed successfully. 200 OK Standard response for successful HTTP requests, the actual response will depend on the request method used. In a GET request, the response will contain an entity corresponding to the requested resource, in a POST request, the response will contain an entity describing or containing the result of the action. 201 Created The request has been fulfilled, resulting in the creation of a new resource,202 Accepted The request has been accepted for processing, but the processing has not been completed. The request might or might not be acted upon. 203 Non-Authoritative Information The server is a proxy that received a 200 OK from its origin. 204 No Content The server successfully processed the request and is not returning any content,205 Reset Content The server successfully processed the request, but is not returning any content
54.
Rhode Island
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Rhode Island, officially the State of Rhode Island and Providence Plantations, is a state in the New England region of the northeastern United States. Rhode Island is the smallest in area, the eighth least populous, and its official name is also the longest of any state in the Union. Rhode Island is bordered by Connecticut to the west, Massachusetts to the north and east, the state also shares a short maritime border with New York. It boycotted the 1787 convention that drew up the United States Constitution, on May 29,1790, Rhode Island became the 13th and last state to ratify the Constitution. Rhode Islands official nickname is The Ocean State, a reference to the fact that the state has several large bays, Rhode Island covers 1,214 square miles, of which 1,045 square miles are land. Despite its name, most of Rhode Island is located on the mainland of the United States, the official name of the state is State of Rhode Island and Providence Plantations, which is derived from the merger of four settlements. Rhode Island is now commonly called Aquidneck Island, the largest of several islands in Narragansett Bay, Providence Plantation was the name of the colony founded by Roger Williams in the area now known as the city of Providence. This was adjoined by the settlement of Warwick, hence the plural Providence Plantations and it is unclear how Aquidneck Island came to be known as Rhode Island, although there are two popular theories. Explorer Giovanni da Verrazzano noted the presence of an island near the mouth of Narragansett Bay in 1524, subsequent European explorers were unable to precisely identify the island that Verrazzano had named, but the Pilgrims who later colonized the area assumed that it was Aquidneck. A second theory concerns the fact that Adriaen Block passed by Aquidneck during his expeditions in the 1610s, historians have theorized that this reddish appearance resulted from either red autumn foliage or red clay on portions of the shore. The earliest documented use of the name Rhode Island for Aquidneck was in 1637 by Roger Williams, the name was officially applied to the island in 1644 with these words, Aquethneck shall be henceforth called the Isle of Rodes or Rhode-Island. The name Isle of Rodes is used in a document as late as 1646. Dutch maps as early as 1659 call the island Red Island, Williams was a theologian forced out of the Massachusetts Bay Colony. Seeking religious and political tolerance, he and others founded Providence Plantation as a proprietary colony. Providence referred to the concept of providence, and plantation was an English term for a colony. State of Rhode Island and Providence Plantations is the longest official name of any state in the Union, advocates for excising plantation asserted that the word specifically referred to the British colonial practice of establishing settlements which disenfranchised native people. Advocates for retaining the name argued that plantation was simply an archaic English synonym for colony, the referendum election was held on November 2,2010, and the people voted overwhelmingly to retain the entire original name. It shares a maritime border with New York State between Block Island and Long Island
55.
Stephen Colbert
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Stephen Tyrone Colbert is an American comedian, television host, and author. Colbert has hosted The Late Show with Stephen Colbert, a television talk show on CBS. Colbert originally studied to be an actor, but became interested in improvisational theatre while attending Northwestern University. He wrote and performed on the short-lived Dana Carvey Show before collaborating with Sedaris and he gained considerable attention for his role on the latter as closeted gay history teacher Chuck Noblet. His work as a correspondent on Comedy Centrals news-parody series The Daily Show gained him wide recognition, in 2005, he left The Daily Show to host a spin-off series, The Colbert Report. The series became one of Comedy Centrals highest-rated series, earning Colbert an invitation to perform as featured entertainer at the White House Correspondents Association Dinner in 2006, Colbert has won nine Primetime Emmy Awards, two Grammy Awards, and two Peabody Awards. Colbert was named one of Times 100 Most Influential People in 2006 and 2012 and his book, I Am America, was #1 on The New York Times Best Seller list in 2007. Colbert was born in Washington, D. C. the youngest of 11 children in a Catholic family and he grew up on James Island, South Carolina. Colbert and his siblings, in descending order by age, are James, Edward, Mary, William, Margo, Thomas, Jay, Elizabeth, Paul, Peter, stephens mother, Lorna Elizabeth Colbert, was a homemaker. In interviews, Colbert has described his parents as people who also strongly valued intellectualism and taught their children that it was possible to question the church. The emphasis his family placed on intelligence and his observation of negative stereotypes of Southerners led Colbert to train himself to suppress his Southern accent while he was quite young. While Colbert sometimes comedically claims his surname is French, he is of 15/16ths Irish ancestry, many of his ancestors emigrated from Ireland to North America in the 19th century before and during the Great Famine. He offered his children the option to pronounce the name whichever way they preferred, Stephen started using /koʊlˈbɛər/ later in life when he transferred to Northwestern University, taking advantage of the opportunity to reinvent himself in a new place where no one knew him. Ed responded /ˈkoʊlbərt/, to which Stephen jokingly replied, See you in Hell and they were en route to enroll the two boys at Canterbury School in New Milford, Connecticut. Lorna Colbert relocated the family downtown to the urban environment of East Bay Street in Charleston. Colbert found the transition difficult and did not easily make new friends in his new neighborhood, Colbert later described himself during this time as detached, lacking a sense of importance regarding the things with which other children concerned themselves. He developed a love of science fiction and fantasy novels, especially the works of J. R. R. Tolkien, Colbert attended Charlestons Episcopal Porter-Gaud School, where he participated in several school plays and contributed to the school newspaper but was not highly motivated academically. During his adolescence, he briefly fronted A Shot in the Dark, when he was younger, he had hoped to study marine biology, but surgery intended to repair a severely perforated eardrum caused him inner ear damage
56.
The Colbert Report
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The show focused on a fictional anchorman character named Stephen Colbert, played by his real-life namesake. The character, described by Colbert as a well-intentioned, poorly informed, furthermore, the show satirized conservative personality-driven political talk programs, particularly Fox Newss The OReilly Factor. The Colbert Report is a spin-off of Comedy Centrals The Daily Show, the program was created by Colbert, Jon Stewart, and Ben Karlin. The shows writing was grounded in improvisation, and often lampooned current events stories, the shows structure also included a guest interview, in which the Colbert character attempts to deconstruct his opponents argument. The show was taped in New York Citys Hells Kitchen neighborhood, the show was taped and broadcast Monday through Thursday, with weeks taken off at multiple points in a given year for breaks. The Colbert Report saw immediate critical and ratings successes, leading to various awards, the shows cultural influence—which occasionally would require a fair degree of participation from the show’s audience, dubbed the Colbert Nation—extended beyond the program a number of times. This impact included the running for U. S. In addition, the show inspired various forms of multimedia, including music, the Colbert Report satirized conservative personality-driven political pundit programs, and focused on a fictional anchorman character named Stephen Colbert, played by his real-life namesake. Colbert joined Comedy Centrals The Daily Show in 1997, a year following its launch, when Jon Stewart became the programs host in 1999, The Daily Show developed a markedly different style, bringing a sharper political focus to the humor than the show previously exhibited. Colbert recalled that Stewart specifically asked him to have a political viewpoint, Colbert became a fixture on The Daily Show, occasionally hosting in Stewarts absence. In 2003, the program began running advertisements for a program titled The Colbert Réport. When fellow Daily Show star Steve Carell left to pursue a film and television career and he pitched The Colbert Report to the channel in 2004. Stewart pushed Comedy Central to pick up the show, and Colbert was given an eight-week tryout, following the shows immediate success, the show quickly became a fixture in the late-night lineup. At its peak, the show averaged 1.5 million viewers each evening, the fictional Colbert anchorman character became gradually toned down over the course of the shows run, as the host believed he would eventually need to move beyond it. He began to regard it as an act of discipline to perform as the character, he remarked, to model behavior. It became very hard to watch punditry of any kind, of whatever political stripe. With his contract set to end in December 2014, he had decided to leave the show when he was contacted by CBS to replace David Letterman as the host of its Late Show franchise. The shows ending was announced concurrently with Colberts jump to CBS in April 2014, the last episode aired on December 18,2014
57.
Ontario Highway 401
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It stretches 828.0 kilometres from Windsor in the west to the Ontario–Quebec border in the east. The part of Highway 401 that passes through Toronto is North Americas busiest highway, the route is maintained by the Ministry of Transportation of Ontario and patrolled by the Ontario Provincial Police. The speed limit is 100 km/h throughout its length, unless posted otherwise and these three sections of highway were 11.8,54.7 and 41.2 km, respectively. In 1964, the route became fully navigable from Windsor to the Ontario–Quebec border, in 1965 it was given a second designation, the Macdonald–Cartier Freeway, in honour of the Fathers of Confederation. At the end of 1968, the Gananoque–Brockville section was bypassed, in 2011, construction began on a westward extension called the Right Honourable Herb Gray Parkway. This new route follows, but does not replace, former Highway 3 between the end of the freeway and the E. C. Row Expressway, at which point it turns and parallels that route towards the site of the future Gordie Howe International Bridge, an 8-kilometre section of the parkway, east of the E. C. Row interchange, opened on June 28,2015, with the remaining section completed and opened on November 21, the expansive twelve-plus-lane collector–express system will also be extended west through Mississauga to Milton and east through Ajax and Whitby. Highway 401 extends across Southwestern, Central and Eastern Ontario, in anticipation of the future expansion of the highway, the transportation ministry purchased a 91. 4-metre-wide right-of-way along the entire length. Generally, the highway occupies only a portion of this allotment and this makes it North Americas busiest roadway, surpassing the Santa Monica Freeway in Los Angeles and I-75 in Atlanta. Highway 401 also features North Americas busiest multi-structure bridge, located at Hoggs Hollow in Toronto, the four bridges, two for each direction with the collector and express lanes, carried an average of 373,700 vehicles daily in 2006. The highway is one of the backbones of a network in the Great Lakes region, connecting the populous Quebec City–Windsor corridor with Michigan, New York. It is the connection between Toronto and Montreal, becoming Autoroute 20 at the Ontario–Quebec border. At present, Highway 401 begins as a freeway at the west end of the E. C. At the Dougall Parkway, the highway turns east and exits Windsor, from here, Highway 401 mostly parallels the former route of Highway 98 from Windsor to Tilbury. Southwestern Ontario is flat, primarily land, that takes advantage of the fertile clay soil deposited throughout the region. Here the highways flat and straight route is notorious for leading to driver inattention, the section from Windsor to London has become known for deadly car accidents and pile-ups, earning it the nickname Carnage Alley. As the highway approaches London, Highway 402 merges in, resulting in a six-lane cross-section, within London, it intersects the citys two municipal expressways, Highbury Avenue and the Veterans Memorial Parkway
58.
Windsor, Ontario
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Windsor is a city in Ontario and the southernmost city in Canada. It is located on the shore of the Detroit River, directly across the river from Detroit. Windsor is a contributor to Canadas automotive industry and has a storied history. Prior to European exploration and settlement, the Windsor area was inhabited by the First Nations, a French agricultural settlement was established at the site of Windsor in 1749. It is the oldest continually inhabited European-founded settlement in Canada west of Montreal, the area was first named la Petite Côte. Later it was called La Côte de Misère because of the sandy soils near LaSalle, Windsors French-Canadian heritage is reflected in French street names such as Ouellette, Pelissier, François, Pierre, Langlois, Marentette, and Lauzon. The current street system of Windsor reflects the Canadien method of land division. Today, the street name often indicates the name of the family that at one time farmed the land where the street is now located. The street system of outlying areas is consistent with the British system for granting land concessions, there is a significant French-speaking minority in Windsor and the surrounding area, particularly in the Lakeshore, Tecumseh and LaSalle areas. In 1794, after the American Revolution, the settlement of Sandwich was founded and it was later renamed Windsor, after the town in Berkshire, England. The Sandwich neighbourhood on Windsors west side is home to some of the oldest buildings in the city, including Mackenzie Hall, today, this building functions as a community centre. The oldest building in the city is the Duff-Baby House built in 1792 and it is owned by Ontario Heritage Trust and houses government offices. The François Baby House in downtown Windsor was built in 1812 and houses Windsors Community Museum, Windsor was the site of a battle during the Upper Canada Rebellion in 1838, and also served as a theatre for the Patriot War, later that year. Windsor was established as a village in 1854, then became a town in 1858, the Windsor Police Service was established on July 1,1867. A fire consumed much of Windsors downtown core on October 12,1871, Sandwich, Ford City and Walkerville were separate legal entities in their own right until 1935. They are now historic neighbourhoods of Windsor, Ford City was officially incorporated as a village in 1912, it became a town in 1915, and a city in 1929. Walkerville was incorporated as a town in 1890, Sandwich was established in 1817 as a town with no municipal status. It was incorporated as a town in 1858 and these three towns were annexed by Windsor in 1935
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Toronto
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Toronto is the most populous city in Canada and the provincial capital of Ontario. With a population of 2,731,571, Toronto is the fourth most populous city in North America after Mexico City, New York City, and Los Angeles. A global city, Toronto is a centre of business, finance, arts, and culture. Aboriginal peoples have inhabited the area now known as Toronto for thousands of years, the city itself is situated on the southern terminus of an ancient Aboriginal trail leading north to Lake Simcoe, used by the Wyandot, Iroquois, and the Mississauga. Permanent European settlement began in the 1790s, after the broadly disputed Toronto Purchase of 1787, the British established the town of York, and later designated it as the capital of Upper Canada. During the War of 1812, the town was the site of the Battle of York, York was renamed and incorporated as the city of Toronto in 1834, and became the capital of the province of Ontario during the Canadian Confederation in 1867. The city proper has since expanded past its original borders through amalgamation with surrounding municipalities at various times in its history to its current area of 630.2 km2. While the majority of Torontonians speak English as their primary language, Toronto is a prominent centre for music, theatre, motion picture production, and television production, and is home to the headquarters of Canadas major national broadcast networks and media outlets. Toronto is well known for its skyscrapers and high-rise buildings, in particular the tallest free-standing structure in the Western Hemisphere, the name Toronto is likely derived from the Iroquois word tkaronto, meaning place where trees stand in the water. This refers to the end of what is now Lake Simcoe. A portage route from Lake Ontario to Lake Huron running through this point, in the 1660s, the Iroquois established two villages within what is today Toronto, Ganatsekwyagon on the banks of the Rouge River and Teiaiagonon the banks of the Humber River. By 1701, the Mississauga had displaced the Iroquois, who abandoned the Toronto area at the end of the Beaver Wars, French traders founded Fort Rouillé on the current Exhibition grounds in 1750, but abandoned it in 1759. During the American Revolutionary War, the region saw an influx of British settlers as United Empire Loyalists fled for the British-controlled lands north of Lake Ontario, the new province of Upper Canada was in the process of creation and needed a capital. Dorchester intended the location to be named Toronto, in 1793, Governor John Graves Simcoe established the town of York on the Toronto Purchase lands, instead naming it after Prince Frederick, Duke of York and Albany. Simcoe decided to move the Upper Canada capital from Newark to York, the York garrison was constructed at the entrance of the towns natural harbour, sheltered by a long sandbar peninsula. The towns settlement formed at the end of the harbour behind the peninsula, near the present-day intersection of Parliament Street. In 1813, as part of the War of 1812, the Battle of York ended in the towns capture, the surrender of the town was negotiated by John Strachan. US soldiers destroyed much of the garrison and set fire to the parliament buildings during their five-day occupation, the sacking of York was a primary motivation for the Burning of Washington by British troops later in the war
60.
Quebec Autoroute 20
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At 585 km, it is the longest Autoroute in Quebec. It is one of two links between Montreal and Quebec City, the other is the A-40. There are two sections of the A-20, separated by a 57 km gap, the mainline extends for 540 km from the Ontario border to its current terminus at Trois-Pistoles. The second, more northerly section is far shorter, constructed as a super two autoroute, this section of the A-20 bypasses Rimouski to the south and ends at a roundabout junction with Highway 132 in Mont-Joli. While the Quebec government has completed environmental and economic reviews of the impact of linking the two sections of Autoroute 20, it has not committed the necessary for construction. The A-20 begins at the Ontario-Quebec border near Rivière-Beaudette as the continuation of Ontario Highway 401, the westernmost section of the A-20 was named the Autoroute du Souvenir in 2007 to honour Canadian veterans. Road marker signs on this stretch of the feature a poppy. At km 29, the A-20 crosses A-30 before becoming an urban boulevard for approximately eight kilometers in Vaudreuil-Dorion and this stretch of highway takes the A-20 across the Ottawa River. The speed limit is 50 km/h in Vaudreuil-Dorion and 70 km/h in LÎle-Perrot, the A-20 once again becomes a limited-access highway at km 38, just before crossing the Sainte-Anne-de-Bellevue Canal onto the Island of Montreal. The A-20 then traverses the West Island along the shore of Lac Saint-Louis to an interchange with the A-520. Commonly called the Dorval Interchange, this exit is the access to Montreals Trudeau International Airport. Further east, the A-20 crosses the A-13 at its southern terminus, just west of downtown Montreal, the A-20, A-15, and A-720 meet at the Turcot Interchange. From this interchange, A-15 continues north to Laval while A-20 east is multiplexed with A-15 south on the approach to the Champlain Bridge, traffic bound for the city centre continues as the A-720. Multiplexed with the A-10 and A-15, all three cross the Saint Lawrence River via the Champlain Bridge to the South Shore. The multiplex splits south of the bridge, the A-20 parallels the south shore of the river through suburban Longueuil. The junction with the A-25 affords a direct connection to the Louis Hippolyte Lafontaine Bridge-Tunnel, the Trans-Canada Highway joins the A-20 at this junction. The largest section of the A-20 is named after Jean Lesage, a shorter section that serves as a bypass of Rimouski and extends east to a final terminus at Route 132 in Mont-Joli. From the junction with A-25, the A-20 travels east, away from the St. Lawrence River, at kilometer 98, the A-20 intersects the A-30 near Mont Saint-Bruno, crossing the Richelieu River just north of Mont-Saint-Hilaire
61.
Montreal
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Montreal, officially Montréal, is the most populous municipality in the Canadian province of Quebec and the 2nd-most populous in Canada as a whole. Originally called Ville-Marie, or City of Mary, it is believed to be named after Mount Royal, the city has a distinct four-season continental climate, with warm-to-hot summers and cold, snowy winters. In 2016, Montreal had a population of 1,704,694, Montreals metropolitan area had a population of 4,098,927 and a population of 1,958,257 in the urban agglomeration, with all of the municipalities on the Island of Montreal included. Legally a French-speaking city,60. 5% of Montrealers speak French at home,21. 2% speak English and 19. 8% speak neither, Montreal is one of the most bilingual cities in Quebec and Canada, with 56% of the population able to speak both official languages. Montreal is the second-largest primarily French-speaking city in the world after Paris, historically the commercial capital of Canada, it was surpassed in population and economic strength by Toronto in the 1970s. It remains an important centre of commerce, aerospace, finance, pharmaceuticals, technology, design, education, culture, tourism, gaming, film, Montreal was also named a UNESCO City of Design. In 2009, Montreal was named North Americas leading host city for international events, according to the 2009 preliminary rankings of the International Congress. According to the 2015 Global Liveability Ranking by the Economist Intelligence Unit, in the 2017 edition of their Best Student Cities ranking, Quacquarelli Symonds ranked Montreal as the worlds best city to study abroad. Also, Montreal has 11 universities with 170,000 students enrolled, the Greater Montréal region has the highest number of university students per capita among all metropolitan areas in North America. It is the only Canadian city to have held the Summer Olympics, currently, the city hosts the Canadian Grand Prix of Formula One, the Montreal International Jazz Festival and the Just for Laughs festival. In 2012, Montreal was ranked as a Beta+ world city, in Kanien’kéha, or Mohawk language, the island is called Tiohtià, ke Tsi or Ka-wé-no-te. In Anishinaabemowin, or Ojibwe language, the land is called Mooniyaang, though the city was first named by French colonizers Ville Marie, or City of Mary, its current name comes from Mount Royal, the triple-peaked hill in the heart of the city. The most popular theory is that the name derives from Mont Réal, Cartiers 1535 diary entry, naming the mountain, according to the Commission de toponymie du Québec and the Geographical Names Board of Canada, Canadian place names have only one official form. Thus, Montreal is officially spelled with an accent over the e in both English and French. In practice, this is limited to governmental uses. English-speaking Montrealers, including English-language media, regularly omit the accent when writing in English, archaeological evidence demonstrates that First Nations native people occupied the island of Montreal as early as 4,000 years ago. By the year AD1000, they had started to cultivate maize, within a few hundred years, they had built fortified villages. Archeologists have found evidence of their habitation there and at locations in the valley since at least the 14th century
62.
Quebec City
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Quebec City, French, Ville de Québec, officially Québec) is the capital city of the Canadian province of Quebec. Founded in 1608 by Samuel de Champlain, Quebec City is one of the oldest cities in North America. The citys landmarks include the Château Frontenac, a hotel which dominates the skyline, and La Citadelle, the National Assembly of Quebec, the Musée national des beaux-arts du Québec, and the Musée de la civilisation are found within or near Vieux-Québec. Thus, Québec is officially spelled with an accented é in both Canadian English and French, although the accent is not used in common English usage. Quebec City is one of the oldest European settlements in North America, while many of the major cities in Latin America date from the sixteenth century, among cities in Canada and the U. S. few were created earlier than Quebec City. Also, Quebecs Old Town is the only North American fortified city north of Mexico whose walls still exist, French explorer Jacques Cartier built a fort at the site in 1535, where he stayed for the winter before going back to France in spring 1536. He came back in 1541 with the goal of building a permanent settlement, Quebec was founded by Samuel de Champlain, a French explorer and diplomat on 3 July 1608, and at the site of a long abandoned St. Lawrence Iroquoian settlement called Stadacona. Champlain, also called The Father of New France, served as its administrator for the rest of his life, the name Canada refers to this settlement. Although called the cradle of the Francophone population in North America, the place seemed favourable to the establishment of a permanent colony. In 1629 there was the surrender of Quebec, without battle, however, Samuel de Champlain argued that the English seizing of the lands was illegal as the war had already ended, he worked to have the lands returned to France. As part of the negotiations of their exit from the Anglo-French War. These terms were signed into law with the Treaty of Saint-Germain-en-Laye, the lands in Quebec and Acadia were returned to the French Company of One Hundred Associates. In 1665, there were 550 people in 70 houses living in the city, one-quarter of the people were members of religious orders, secular priests, Jesuits, Ursulines nuns and the order running the local hospital, Hotel-Dieu. Quebec City was the headquarters of many raids against New England during the four French, in the last war, the French and Indian War, Quebec City was captured by the British in 1759 and held until the end of the war in 1763. France ceded New France, including the city, to Britain in 1763, at the end of French rule in 1763, forests, villages, fields and pastures surrounded the town of 8,000 inhabitants. The town distinguished itself by its architecture, fortifications, affluent homes of masonry and shacks in the suburbs of Saint-Jean. Despite its urbanity and its status as capital, Quebec City remained a small city with close ties to its rural surroundings. Nearby inhabitants traded their farm surpluses and firewood for imported goods from France at the two city markets, during the American Revolution revolutionary troops from the southern colonies assaulted the British garrison in an attempt to liberate Quebec City, in a conflict now known as the Battle of Quebec
63.
Sphenic number
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In number theory, a sphenic number is a positive integer that is the product of three distinct prime numbers. A sphenic number is a product pqr where p, q and this definition is more stringent than simply requiring the integer to have exactly three prime factors. For instance,60 =22 ×3 ×5 has exactly 3 prime factors, the smallest sphenic number is 30 =2 ×3 ×5, the product of the smallest three primes. The first few numbers are 30,42,66,70,78,102,105,110,114,130,138,154,165. As of January 2016 the largest known number is × ×. It is the product of the three largest known primes, all sphenic numbers have exactly eight divisors. If we express the number as n = p ⋅ q ⋅ r, where p, q. For example,24 is not a number, but it has exactly eight divisors. All sphenic numbers are by definition squarefree, because the factors must be distinct. The Möbius function of any number is −1. The cyclotomic polynomials Φ n, taken over all sphenic numbers n, the first case of two consecutive sphenic integers is 230 = 2×5×23 and 231 = 3×7×11. The first case of three is 1309 = 7×11×17,1310 = 2×5×131, and 1311 = 3×19×23, there is no case of more than three, because every fourth consecutive positive integer is divisible by 4 = 2×2 and therefore not squarefree. The numbers 2013,2014, and 2015 are all sphenic, the next three consecutive sphenic years will be 2665,2666 and 2667. Semiprimes, products of two prime numbers