1.
Integer
–
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
Integer
–
Algebraic structure → Group theory
Group theory
2.
Negative number
–
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
Negative number
–
This thermometer is indicating a negative
Fahrenheit temperature (−4°F).
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
100 (number)
–
The
U.S. hundred-dollar bill, Series 2009.
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
Factorization
–
A visual representation of the factorization of cubes using volumes. For a sum of cubes, simply substitute z=-y.
5.
Prime number
–
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
Prime number
–
The number 12 is not a prime, as 12 items can be placed into 3 equal-size columns of 4 each (among other ways). 11 items cannot be all placed into several equal-size columns of more than 1 item each without some extra items leftover (a remainder). Therefore, the number 11 is a prime.
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
Greek numerals
–
Numeral systems
Greek numerals
–
A
Constantinopolitan map of the British Isles from
Ptolemy 's
Geography (c. 1300), using Greek numerals for its
graticule: 52–63°N of the
equator and 6–33°E from Ptolemy's
Prime Meridian at the
Fortunate Isles.
7.
Roman numerals
–
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
Roman numerals
–
Entrance to section LII (52) of the
Colosseum, with numerals still visible
Roman numerals
–
Numeral systems
Roman numerals
–
A typical
clock face with Roman numerals in
Bad Salzdetfurth, Germany
Roman numerals
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An inscription on
Admiralty Arch, London. The number is 1910, for which MCMX would be more usual
8.
Binary number
–
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
Binary number
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Numeral systems
Binary number
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Arithmetic values represented by parts of the Eye of Horus
Binary number
–
Gottfried Leibniz
Binary number
–
George Boole
9.
Ternary numeral system
–
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
Ternary numeral system
–
Numeral systems
10.
Quaternary numeral system
–
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
Quaternary numeral system
–
Numeral systems
11.
Quinary
–
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
Quinary
–
Numeral systems
12.
Senary
–
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
Senary
–
Numeral systems
Senary
–
34 senary = 22 decimal, in senary finger counting
Senary
13.
Octal
–
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
Octal
–
Numeral systems
14.
Duodecimal
–
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
Duodecimal
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Numeral systems
Duodecimal
–
A duodecimal multiplication table
15.
Hexadecimal
–
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
Hexadecimal
–
Numeral systems
Hexadecimal
–
Bruce Alan Martin's hexadecimal notation proposal
Hexadecimal
–
Hexadecimal finger-counting scheme.
16.
Vigesimal
–
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
Vigesimal
–
Numeral systems
Vigesimal
–
The
Maya numerals are a base-20 system.
17.
Base 36
–
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
Base 36
–
Numeral systems
Base 36
–
34 senary = 22 decimal, in senary finger counting
Base 36
18.
Natural number
–
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
Natural number
–
The
Ishango bone (on exhibition at the
Royal Belgian Institute of Natural Sciences) is believed to have been used 20,000 years ago for natural number arithmetic.
Natural number
–
Natural numbers can be used for counting (one
apple, two apples, three apples, …)
19.
Parity (mathematics)
–
Parity is a mathematical term that describes the property of an integers inclusion in one of two categories, even or odd. An integer is even if it is divisible by two and odd if it is not even. For example,6 is even there is no remainder when dividing it by 2. By contrast,3,5,7,21 leave a remainder of 1 when divided by 2, examples of even numbers include −4,0,8, and 1738. In particular, zero is an even number, some examples of odd numbers are −5,3,9, and 73. Parity does not apply to non-integer numbers and this classification applies only to integers, i. e. non-integers like 1/2,4.201, or infinity are neither even nor odd. The sets of even and odd numbers can be defined as following and that is, if the last digit is 1,3,5,7, or 9, then it is odd, otherwise it is even. The same idea will work using any even base, in particular, a number expressed in the binary numeral system is odd if its last digit is 1 and even if its last digit is 0. In an odd base, the number is according to the sum of its digits – it is even if. The following laws can be verified using the properties of divisibility and they are a special case of rules in modular arithmetic, and are commonly used to check if an equality is likely to be correct by testing the parity of each side. As with ordinary arithmetic, multiplication and addition are commutative and associative in modulo 2 arithmetic, however, subtraction in modulo 2 is identical to addition, so subtraction also possesses these properties, which is not true for normal integer arithmetic. The structure is in fact a field with just two elements, the division of two whole numbers does not necessarily result in a whole number. For example,1 divided by 4 equals 1/4, which is neither even nor odd, since the concepts even, but when the quotient is an integer, it will be even if and only if the dividend has more factors of two than the divisor. The ancient Greeks considered 1, the monad, to be neither odd nor fully even. It is this, that two relatively different things or ideas there stands always a third, in a sort of balance. Thus, there is here between odd and even numbers one number which is neither of the two, similarly, in form, the right angle stands between the acute and obtuse angles, and in language, the semi-vowels or aspirants between the mutes and vowels. A thoughtful teacher and a pupil taught to think for himself can scarcely help noticing this, integer coordinates of points in Euclidean spaces of two or more dimensions also have a parity, usually defined as the parity of the sum of the coordinates. For instance, the cubic lattice and its higher-dimensional generalizations
Parity (mathematics)
–
Rubik's Revenge in solved state
Parity (mathematics)
20.
Deficient number
–
In number theory, a deficient or deficient number is a number n for which the sum of divisors σ<2n, or, equivalently, the sum of proper divisors s<n. The value 2n − σ is called the numbers deficiency, as an example, consider the number 21. Its proper divisors are 1,3 and 7, and their sum is 11, because 11 is less than 21, the number 21 is deficient. Its deficiency is 2 ×21 −32 =10, since the aliquot sums of prime numbers equal 1, all prime numbers are deficient. An infinite number of even and odd deficient numbers exist. All odd numbers with one or two prime factors are deficient. All proper divisors of deficient or perfect numbers are deficient, there exists at least one deficient number in the interval for all sufficiently large n. Closely related to deficient numbers are perfect numbers with σ = 2n, the natural numbers were first classified as either deficient, perfect or abundant by Nicomachus in his Introductio Arithmetica. Almost perfect number Amicable number Sociable number Sándor, József, Mitrinović, Dragoslav S. Crstici, Borislav, the Prime Glossary, Deficient number Weisstein, Eric W. Deficient Number
Deficient number
–
Overview
21.
Thue-Morse sequence
–
The first few steps of this procedure yield the strings 0 then 01,0110,01101001,0110100110010110, and so on, which are prefixes of the Thue–Morse sequence. There are several equivalent ways of defining the Thue–Morse sequence, to compute the nth element tn, write the number n in binary. If the number of ones in this expansion is odd then tn =1. For this reason John H. Conway et al. call numbers n satisfying tn =1 odious numbers and numbers for which tn =0 evil numbers. In other words, tn =0 if n is an evil number, if this bit is at an even index, tn differs from tn −1, and otherwise it is the same as tn −1. The resulting algorithm takes constant time to each sequence element. The Thue–Morse sequence is the sequence tn satisfying the relation for all non-negative integers n. So, the first element is 0, then once the first 2n elements have been specified, forming a string s, then the next 2n elements must form the bitwise negation of s. Now we have defined the first 2n+1 elements, and we recurse, spelling out the first few steps in detail, We start with 0. The bitwise negation of 0 is 1, combining these, the first 2 elements are 01. The bitwise negation of 01 is 10, combining these, the first 4 elements are 0110. The bitwise negation of 0110 is 1001, combining these, the first 8 elements are 01101001. The sequence can also be defined by, ∏ i =0 ∞ = ∑ j =0 ∞ t j x j and that is, there are many instances of XX, where X is some string. For instance, with k =0, we have A = T0 =0, however, there are no cubes, instances of XXX. There are also no overlapping squares, instances of 0X0X0 or 1X1X1, notice that T2n is palindrome for any n >1. Further, let qn be a word obtain from T2n by counting ones between consecutive zeros, for instance, q1 =2 and q2 =2102012 and so on. The words Tn do not contain overlapping squares in consequence, the words qn are palindrome squarefree words, the easiest way to make a recurrent sequence is to form a periodic sequence, one where the sequence repeats entirely after a given number m of steps. Then nX can be set to any multiple of m that is larger than twice the length of X, but the Morse sequence is uniformly recurrent without being periodic, not even eventually periodic
Thue-Morse sequence
–
5
logical matrices that give the beginning of the T.-M. sequence, when read line by line
Either in set A (vertical index)
or in set B (horizontal index) is an odd number of elements.
Thue-Morse sequence
–
This graphic demonstrates the repeating and complementary makeup of the Thue–Morse sequence.
22.
Eisenstein prime
–
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
Eisenstein prime
–
Small Eisenstein primes. Those on the green axes are associate to a natural prime of the form 3 n − 1. All others have an absolute value squared equal to a natural prime.
23.
Gaussian integer
–
In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with addition and multiplication of complex numbers, form an integral domain. This integral domain is a case of a commutative ring of quadratic integers. It does not have an ordering that respects arithmetic. Formally, the Gaussian integers are the set Z =, where i 2 = −1, note that when they are considered within the complex plane the Gaussian integers may be seen to constitute the 2-dimensional integer lattice. The norm of a Gaussian integer is the square of its value as a complex number. It is the natural number defined as N = a 2 + b 2 = ¯ =, the norm is multiplicative, since the absolute value of complex numbers is multiplicative, i. e. one has N = N N. The latter can also be verified by a straightforward check, the units of Z are precisely those elements with norm 1, i. e. the set. The Gaussian integers form a principal ideal domain with units, for x ∈ Z, the four numbers ±x, ±ix are called the associates of x. As for every principal ideal domain, Z is also a unique factorization domain and it follows that a Gaussian integer is prime if and only if it is irreducible. The prime elements of Z are also known as Gaussian primes, an associate of a Gaussian prime is also a Gaussian prime. The Gaussian primes are symmetric about the real and imaginary axes, the positive integer Gaussian primes are the prime numbers that are congruent to 3 modulo 4. One should not refer to only these numbers as the Gaussian primes, which refers to all the Gaussian primes, many of which do not lie in Z. In other words, a Gaussian integer is a Gaussian prime if and only if either its norm is a prime number, for example,5 = · and 13 = ·. If p =2, we have 2 = = i2, the ring of Gaussian integers is the integral closure of Z in the field of Gaussian rationals Q consisting of the complex numbers whose real and imaginary part are both rational. It is easy to see graphically that every number is no farther than a distance of 22 from some Gaussian integer. Put another way, every number has a maximal distance of 22 N units to some multiple of z, where z is any Gaussian integer, this turns Z into a Euclidean domain. The ring of Gaussian integers was introduced by Carl Friedrich Gauss in his monograph on quartic reciprocity
Gaussian integer
–
Gaussian integers as
lattice points in the
complex plane
24.
2 (number)
–
2 is a number, numeral, and glyph. It is the number following 1 and preceding 3. The number two has many properties in mathematics, an integer is called even if it is divisible by 2. For integers written in a system based on an even number, such as decimal and hexadecimal. If it is even, then the number is even. In particular, when written in the system, all multiples of 2 will end in 0,2,4,6. In numeral systems based on an odd number, divisibility by 2 can be tested by having a root that is even. Two is the smallest and first prime number, and the only prime number. Two and three are the two consecutive prime numbers. 2 is the first Sophie Germain prime, the first factorial prime, the first Lucas prime, the first Ramanujan prime, and it is an Eisenstein prime with no imaginary part and real part of the form 3n −1. It is also a Stern prime, a Pell number, the first Fibonacci prime, and it is the third Fibonacci number, and the second and fourth Perrin numbers. Despite being prime, two is also a highly composite number, because it is a natural number which has more divisors than any other number scaled relative to the number itself. The next superior highly composite number is six, vulgar fractions with only 2 or 5 in the denominator do not yield infinite decimal expansions, as is the case with all other primes, because 2 and 5 are factors of ten, the decimal base. Two is the number x such that the sum of the reciprocals of the powers of x equals itself. In symbols ∑ k =0 ∞12 k =1 +12 +14 +18 +116 + ⋯ =2. This comes from the fact that, ∑ k =0 ∞1 n k =1 +1 n −1 for all n ∈ R >1, powers of two are central to the concept of Mersenne primes, and important to computer science. Two is the first Mersenne prime exponent, the square root of 2 was the first known irrational number. The smallest field has two elements, in the set-theoretical construction of the natural numbers,2 is identified with the set
2 (number)
–
The twos of all four suits in
playing cards
25.
Asteroid belt
–
The asteroid belt is the circumstellar disc in the Solar System located roughly between the orbits of the planets Mars and Jupiter. It is occupied by numerous irregularly shaped bodies called asteroids or minor planets, the asteroid belt is also termed the main asteroid belt or main belt to distinguish it from other asteroid populations in the Solar System such as near-Earth asteroids and trojan asteroids. About half the mass of the belt is contained in the four largest asteroids, Ceres, Vesta, Pallas, the total mass of the asteroid belt is approximately 4% that of the Moon, or 22% that of Pluto, and roughly twice that of Plutos moon Charon. Ceres, the belts only dwarf planet, is about 950 km in diameter, whereas Vesta, Pallas. The remaining bodies range down to the size of a dust particle, the asteroid material is so thinly distributed that numerous unmanned spacecraft have traversed it without incident. Nonetheless, collisions between large asteroids do occur, and these can form a family whose members have similar orbital characteristics. Individual asteroids within the belt are categorized by their spectra. The asteroid belt formed from the solar nebula as a group of planetesimals. Planetesimals are the precursors of the protoplanets. Between Mars and Jupiter, however, gravitational perturbations from Jupiter imbued the protoplanets with too much energy for them to accrete into a planet. Collisions became too violent, and instead of fusing together, the planetesimals, as a result,99. 9% of the asteroid belts original mass was lost in the first 100 million years of the Solar Systems history. Some fragments eventually found their way into the inner Solar System, Asteroid orbits continue to be appreciably perturbed whenever their period of revolution about the Sun forms an orbital resonance with Jupiter. At these orbital distances, a Kirkwood gap occurs as they are swept into other orbits. Classes of small Solar System bodies in other regions are the objects, the centaurs, the Kuiper belt objects, the scattered disc objects, the sednoids. On 22 January 2014, ESA scientists reported the detection, for the first definitive time, of water vapor on Ceres, the detection was made by using the far-infrared abilities of the Herschel Space Observatory. The finding was unexpected because comets, not asteroids, are considered to sprout jets. According to one of the scientists, The lines are becoming more and more blurred between comets and asteroids. This pattern, now known as the Titius–Bode law, predicted the semi-major axes of the six planets of the provided one allowed for a gap between the orbits of Mars and Jupiter
Asteroid belt
–
By far the largest object within the belt is
Ceres. The total mass of the asteroid belt is significantly less than
Pluto 's, and approximately twice that of Pluto's moon
Charon.
Asteroid belt
–
Sun Jupiter trojans Orbits of
planets
Asteroid belt
–
Giuseppe Piazzi, discoverer of
Ceres, the largest object in the asteroid belt. For several decades after its discovery Ceres was known as a planet, after which it was reclassified as asteroid number 1. In 2006 it was recognized to be a dwarf planet.
Asteroid belt
–
951 Gaspra, the first asteroid imaged by a spacecraft, as viewed during
Galileo ' s 1991 flyby; colors are exaggerated
26.
Asteroid
–
Asteroids are minor planets, especially those of the inner Solar System. The larger ones have also been called planetoids and these terms have historically been applied to any astronomical object orbiting the Sun that did not show the disc of a planet and was not observed to have the characteristics of an active comet. As minor planets in the outer Solar System were discovered and found to have volatile-based surfaces that resemble those of comets, in this article, the term asteroid refers to the minor planets of the inner Solar System including those co-orbital with Jupiter. There are millions of asteroids, many thought to be the remnants of planetesimals. The large majority of known asteroids orbit in the belt between the orbits of Mars and Jupiter, or are co-orbital with Jupiter. However, other orbital families exist with significant populations, including the near-Earth objects, individual asteroids are classified by their characteristic spectra, with the majority falling into three main groups, C-type, M-type, and S-type. These were named after and are identified with carbon-rich, metallic. The size of asteroids varies greatly, some reaching as much as 1000 km across, asteroids are differentiated from comets and meteoroids. In the case of comets, the difference is one of composition, while asteroids are composed of mineral and rock, comets are composed of dust. In addition, asteroids formed closer to the sun, preventing the development of the aforementioned cometary ice, the difference between asteroids and meteoroids is mainly one of size, meteoroids have a diameter of less than one meter, whereas asteroids have a diameter of greater than one meter. Finally, meteoroids can be composed of either cometary or asteroidal materials, only one asteroid,4 Vesta, which has a relatively reflective surface, is normally visible to the naked eye, and this only in very dark skies when it is favorably positioned. Rarely, small asteroids passing close to Earth may be visible to the eye for a short time. As of March 2016, the Minor Planet Center had data on more than 1.3 million objects in the inner and outer Solar System, the United Nations declared June 30 as International Asteroid Day to educate the public about asteroids. The date of International Asteroid Day commemorates the anniversary of the Tunguska asteroid impact over Siberia, the first asteroid to be discovered, Ceres, was found in 1801 by Giuseppe Piazzi, and was originally considered to be a new planet. In the early half of the nineteenth century, the terms asteroid. Asteroid discovery methods have improved over the past two centuries. This task required that hand-drawn sky charts be prepared for all stars in the band down to an agreed-upon limit of faintness. On subsequent nights, the sky would be charted again and any moving object would, hopefully, the expected motion of the missing planet was about 30 seconds of arc per hour, readily discernible by observers
Asteroid
–
253 Mathilde, a
C-type asteroid measuring about 50 kilometres (30 mi) across, covered in craters half that size. Photograph taken in 1997 by the
NEAR Shoemaker probe.
Asteroid
–
2013 EC, shown here in radar images, has a provisional designation
Asteroid
–
⚵
Asteroid
–
243 Ida and its moon Dactyl. Dactyl is the first satellite of an asteroid to be discovered.
27.
Quasar
–
A quasar is an active galactic nucleus of very high luminosity. A quasar consists of a black hole surrounded by an orbiting accretion disk of gas. As gas in the accretion disk falls toward the black hole, quasars emit energy across the electromagnetic spectrum and can be observed at radio, infrared, visible, ultraviolet, and X-ray wavelengths. The most powerful quasars have luminosities exceeding 1041 W, thousands of greater than the luminosity of a large galaxy such as the Milky Way. Quasars are found over a broad range of distances. The peak epoch of quasar activity in the Universe corresponds to redshifts around 2, as of 2011, the most distant known quasar is at redshift z=7.085, light observed from this quasar was emitted when the Universe was only 770 million years old. Because quasars are distant objects, any light which reaches the Earth is redshifted due to the expansion of space. In early optical images, quasars appeared as point sources, indistinguishable from stars, with infrared telescopes and the Hubble Space Telescope, the host galaxies surrounding the quasars have been detected in some cases. These galaxies are normally too dim to be seen against the glare of the quasar, most quasars, with the exception of 3C273 whose average apparent magnitude is 12.9, cannot be seen with small telescopes. The luminosity of some quasars changes rapidly in the optical range, because these changes occur very rapidly they define an upper limit on the volume of a quasar, quasars are not much larger than the Solar System. This implies a high power density. The mechanism of brightness changes probably involves relativistic beaming of astrophysical jets pointed nearly directly toward Earth, the highest redshift quasar known is ULAS J1120+0641, with a redshift of 7.085, which corresponds to a comoving distance of approximately 29 billion light-years from Earth. Since light cannot escape the black holes, the energy is actually generated outside the event horizon by gravitational stresses. Central masses of 105 to 109 solar masses have been measured in quasars by using reverberation mapping. The matter accreting onto the hole is unlikely to fall directly in. Quasars may also be ignited or re-ignited when normal galaxies merge, in fact, it has been suggested that a quasar could form as the Andromeda Galaxy collides with our own Milky Way galaxy in approximately 3–5 billion years. More than 200,000 quasars are known, most from the Sloan Digital Sky Survey, all observed quasar spectra have redshifts between 0.056 and 7.085. Applying Hubbles law to these redshifts, it can be shown that they are between 600 million and 28.85 billion light-years away
Quasar
–
Artist's rendering of
ULAS J1120+0641, a very distant quasar powered by a black hole with a mass two billion times that of the Sun. Credit:
ESO /M. Kornmesser
Quasar
–
A
Hubble picture showing a quasar core
Quasar
–
Quasar QSO-160913+653228 is so distant its light has taken nine billion years to reach us, two thirds of the time that has elapsed since the
Big Bang.
Quasar
–
The
Chandra X-ray image is of the quasar PKS 1127-145, a highly luminous source of X-rays and visible light about 10 billion light years from Earth. An enormous X-ray jet extends at least a million light years from the quasar. Image is 60 arcsec on a side.
RA 11h 30m 7.10s
Dec -14° 49' 27" in Crater. Observation date: May 28, 2000. Instrument: ACIS.
28.
Constellation
–
A constellation is formally defined as a region of the celestial sphere, with boundaries laid down by the International Astronomical Union. The constellation areas mostly had their origins in Western-traditional patterns of stars from which the constellations take their names, in 1922, the International Astronomical Union officially recognized the 88 modern constellations, which cover the entire sky. They began as the 48 classical Greek constellations laid down by Ptolemy in the Almagest, Constellations in the far southern sky are late 16th- and mid 18th-century constructions. 12 of the 88 constellations compose the zodiac signs, though the positions of the constellations only loosely match the dates assigned to them in astrology. The term constellation can refer to the stars within the boundaries of that constellation. Notable groupings of stars that do not form a constellation are called asterisms, when astronomers say something is “in” a given constellation they mean it is within those official boundaries. Any given point in a coordinate system can unambiguously be assigned to a single constellation. Many astronomical naming systems give the constellation in which an object is found along with a designation in order to convey a rough idea in which part of the sky it is located. For example, the Flamsteed designation for bright stars consists of a number, the word constellation seems to come from the Late Latin term cōnstellātiō, which can be translated as set of stars, and came into use in English during the 14th century. It also denotes 88 named groups of stars in the shape of stellar-patterns, the Ancient Greek word for constellation was ἄστρον. Colloquial usage does not draw a distinction between constellation in the sense of an asterism and constellation in the sense of an area surrounding an asterism. The modern system of constellations used in astronomy employs the latter concept, the term circumpolar constellation is used for any constellation that, from a particular latitude on Earth, never sets below the horizon. From the North Pole or South Pole, all constellations south or north of the equator are circumpolar constellations. In the equatorial or temperate latitudes, the term equatorial constellation has sometimes been used for constellations that lie to the opposite the circumpolar constellations. They generally include all constellations that intersect the celestial equator or part of the zodiac, usually the only thing the stars in a constellation have in common is that they appear near each other in the sky when viewed from the Earth. In galactic space, the stars of a constellation usually lie at a variety of distances, since stars also travel on their own orbits through the Milky Way, the star patterns of the constellations change slowly over time. After tens to hundreds of thousands of years, their familiar outlines will become unrecognisable, the terms chosen for the constellation themselves, together with the appearance of a constellation, may reveal where and when its constellation makers lived. The earliest direct evidence for the constellations comes from inscribed stones and it seems that the bulk of the Mesopotamian constellations were created within a relatively short interval from around 1300 to 1000 BC
Constellation
Constellation
Constellation
–
Babylonian tablet recording
Halley's comet in 164 BC.
Constellation
–
Chinese star map with a cylindrical projection (
Su Song)
29.
Emergency telephone number
–
In many countries the public switched telephone network has a single emergency telephone number that allows a caller to contact local emergency services for assistance. The emergency number differs from country to country, it is typically a number so that it can be easily remembered and dialed quickly. Some countries have a different emergency number for each of the different emergency services, see List of emergency telephone numbers. The emergency telephone number is a case in the countrys telephone number plan. In the past, calls to the telephone number were often routed over special dedicated circuits. Though with the advent of electronic exchanges these calls are now mixed with ordinary telephone traffic. Often the system is set up so that once a call is made to a telephone number. Should the caller abandon the call, the line may still be held until the emergency service answers, an emergency telephone number call may be answered by either a telephone operator or an emergency service dispatcher. The nature of the emergency is then determined, if the call has been answered by a telephone operator, they then connect the call to the appropriate emergency service, who then dispatches the appropriate help. In the case of services being needed on a call. Emergency dispatchers are trained to control the call in order to help in an appropriate manner. The emergency dispatcher may find it necessary to give urgent advice in life-threatening situations, some dispatchers have special training in telling people how to perform first aid or CPR. In many parts of the world, a service can identify the telephone number that a call has been placed from. This is normally done using the system that the company uses to bill calls. For an individual fixed landline telephone, the number can often be associated with the callers address. However, with phones and business telephones, the address may be a mailing address rather than the callers location. The latest enhanced systems, such as Enhanced 911, are able to provide the location of mobile telephones. This is often specifically mandated in a countrys legislation, when an emergency happened in the pre-dial telephone era, the user simply picked up the telephone receiver and waited for the operator to answer number, please
Emergency telephone number
–
9-1-1 is an emergency telephone number used in the
United States,
Canada, as well as in some Latin American countries - for example,
Costa Rica,
El Salvador,
Paraguay
30.
Brazil
–
Brazil, officially the Federative Republic of Brazil, is the largest country in both South America and Latin America. As the worlds fifth-largest country by area and population, it is the largest country to have Portuguese as an official language. Its Amazon River basin includes a vast tropical forest, home to wildlife, a variety of ecological systems. This unique environmental heritage makes Brazil one of 17 megadiverse countries, Brazil was inhabited by numerous tribal nations prior to the landing in 1500 of explorer Pedro Álvares Cabral, who claimed the area for the Portuguese Empire. Brazil remained a Portuguese colony until 1808, when the capital of the empire was transferred from Lisbon to Rio de Janeiro, in 1815, the colony was elevated to the rank of kingdom upon the formation of the United Kingdom of Portugal, Brazil and the Algarves. Independence was achieved in 1822 with the creation of the Empire of Brazil, a state governed under a constitutional monarchy. The ratification of the first constitution in 1824 led to the formation of a bicameral legislature, the country became a presidential republic in 1889 following a military coup détat. An authoritarian military junta came to power in 1964 and ruled until 1985, Brazils current constitution, formulated in 1988, defines it as a democratic federal republic. The federation is composed of the union of the Federal District, the 26 states, Brazils economy is the worlds ninth-largest by nominal GDP and seventh-largest by GDP as of 2015. A member of the BRICS group, Brazil until 2010 had one of the worlds fastest growing economies, with its economic reforms giving the country new international recognition. Brazils national development bank plays an important role for the economic growth. Brazil is a member of the United Nations, the G20, BRICS, Unasul, Mercosul, Organization of American States, Organization of Ibero-American States, CPLP. Brazil is a power in Latin America and a middle power in international affairs. One of the worlds major breadbaskets, Brazil has been the largest producer of coffee for the last 150 years and it is likely that the word Brazil comes from the Portuguese word for brazilwood, a tree that once grew plentifully along the Brazilian coast. In Portuguese, brazilwood is called pau-brasil, with the word brasil commonly given the etymology red like an ember, formed from Latin brasa and the suffix -il. As brazilwood produces a red dye, it was highly valued by the European cloth industry and was the earliest commercially exploited product from Brazil. The popular appellation eclipsed and eventually supplanted the official Portuguese name, early sailors sometimes also called it the Land of Parrots. In the Guarani language, a language of Paraguay, Brazil is called Pindorama
Brazil
–
Megaliths in the
Solstice Archaeological Park, in
Amapá, erected between 500 and 2000 years ago, probably to carry out
astronomical observations.
Brazil
–
Flag
Brazil
–
Representation of the landing of
Pedro Álvares Cabral in
Porto Seguro, 1500.
Brazil
–
Painting showing the arrest of
Tiradentes; he was sentenced to death for his involvement in the best known
movement for independence in Colonial Brazil.
31.
Federal Highway Police
–
The title patrolman given to the members was abolished in 1998, replaced by the title police. Members of the PRF are divided into four classes, Third, Second, First, since 2009, entry into the PRF already required a university education degree recognized by the Ministry of Education. Condition now described in Law 9,654, the Federal Highway Police was created in 1928 during the administration of President Washington Luís Pereira de Sousa, under the name Roadway Police. It is present in all units of the federation and is managed by the Federal Highway Police Department, the states are divided into administrative units known as regions. A region can be a superintendency, in the case of larger states, some regions encompass more than one Brazilian state. Regions are divided into delegations, which coordinate the patrol posts, currently the PRF has over four hundred patrol posts in the most diverse Brazilian municipalities, providing a capillarity to the structure of the agency that few national institutions possess. Despite the uniformed work, the PRF is not a military institution, the entire hierarchy is based on the functions of supervision, which can be occupied by any police officer, for example a special agent may be supervisor of an inspector. The PRF has one of the most innovative systems to combat vehicular theft, after reporting a theft, the vehicles owner, stuck in the bureaucratic system, must wait 24 hours in most cases for the report to be entered into the vehicular theft system. Sometimes this information takes over 24 hours to enter the Integrated Traffic System, therefore, if the thief were to be stopped before this point, there would be no record of a stolen vehicle and the thief would not be prosecuted. To eliminate this deficiency, the Federal Highway Police Department created the Alert System, the theft victim enters his or her vehicles license plate number and all PRF patrol posts will be immediately notified. The system is not well known, as it has had little coverage by the press. The ability to interact with the PRF becomes instantaneous and free of bureaucracy and this Alert System was created by PRF members with informatics degrees, who formed a programs development center to facilitate and improve the interactivity between police officers and vehicle owners. Registry of robbery in Alert System The Federal Highway Police Department makes available a statistical survey updated daily, the press, as well as the public, can access the registry of apprehension of drugs and recovery of stolen vehicles. Through this system, checking the information available on one day and comparing it to what is published on the next day, any federal highway police officer has access to an accident reported in this system, even if it was in another region. This system allows accidents of national relevance to be investigated by the General Command in Brasília in real time, the information is not only instantaneous for commanders, but also for any PRF officer who would like to consult this information. The information in the PRFs data network not only circulates freely among regions and agents, now, not only PRF officers can view and print the BATs, but also vehicle owners, insurance companies, drivers, and victims. Anyone involved in the accident can print the bulletin, free of charge, directly from the PRFs website, the PRF presented sufficient argument to the Brazilian Army for that caliber to be allowed for PRF use. The 38 caliber, lacking in stopping power, was retired by the Federal Highway Police and this means that for every 100 people hit by this caliber,92 will become unable to continue fighting with only one shot of the firearm
Federal Highway Police
–
Patch of the Federal Highway Police
Federal Highway Police
–
Polícia Rodoviária Federal in the new livery
Federal Highway Police
–
Brazilian Federal Highway Police at work.
Federal Highway Police
–
A Federal Highway Police truck, on Highway BR-040, near
Valparaíso,
Goiás.
32.
Ghana
–
Ghana, officially the Republic of Ghana, is a unitary presidential constitutional democracy, located along the Gulf of Guinea and Atlantic Ocean, in the subregion of West Africa. Spanning a land mass of 238,535 km², Ghana is bordered by the Ivory Coast in the west, Burkina Faso in the north, Togo in the east, Ghana means Warrior King in the Soninke language. The territory of present-day Ghana has been inhabited for a millennium, numerous kingdoms and empires emerged over the centuries, of which the most powerful was the Kingdom of Ashanti. Beginning in the 15th century, numerous European powers contested the area for trading rights, following over a century of native resistance, Ghanas current borders were established by the 1900s as the British Gold Coast. On 6 March 1957, it became the first sub-Saharan African nation to become independent of European colonisation, a multicultural nation, Ghana has a population of approximately 27 million, spanning a variety of ethnic, linguistic and religious groups. Five percent of the population practices traditional faiths,71. 2% adhere to Christianity and 17. 6% are Muslim and its diverse geography and ecology ranges from coastal savannahs to tropical jungles. Ghana is a country led by a president who is both head of state and head of the government. Ghanas economy is one of the strongest and most diversified in Africa, following a century of relative stability. Ghanas growing economic prosperity and democratic political system have made it a power in West Africa. It is a member of the Non-Aligned Movement, the African Union, the Economic Community of West African States, Group of 24, Ghana was already recognized as one of the great kingdoms in Bilad el-Sudan by the ninth century. Ghana was inhabited in the Middle Ages and the Age of Discovery by a number of ancient predominantly Akan kingdoms in the Southern and this included the Ashanti Empire, the Akwamu, the Bonoman, the Denkyira, and the Mankessim Kingdom. Until the 11th century, the majority of modern Ghanas territorial area was unoccupied and uninhabited by humans. Although the area of present-day Ghana in West Africa has experienced many population movements, by the early 11th century, the Akans were firmly established in the Akan state called Bonoman, for which the Brong-Ahafo Region is named. From the 13th century, Akans emerged from what is believed to have been the Bonoman area, to create several Akan states of Ghana and these states included Bonoman, Ashanti, Denkyira, Mankessim Kingdom, and Akwamu Eastern region. By the 19th century, the territory of the part of Ghana was included in the Kingdom of Ashanti. The Kingdom of Ashanti government operated first as a loose network, prior to Akan contact with Europeans, the Akan Ashanti people created an advanced economy based on principally gold and gold bar commodities then traded with the states of Africa. The earliest known kingdoms to emerge in modern Ghana were the Mole-Dagbani states, the Mole-Dagombas came on horseback from present-day Burkina Faso under a single leader, Naa Gbewaa. The death of Naa Gbewaa caused civil war among his children, some of whom broke off and founded separate states including Dagbon, Mamprugu, Mossi, Nanumba, Akan trade with European states began after contact with Portuguese in the 15th century
Ghana
–
1925 map of pre–existing Ghana
Ghana
Ghana
–
16th – 17th century
Akan Terracotta,
Metropolitan Museum of Art
Ghana
–
A 1850 map showing the
Akan Kingdom of Ashanti within the
Guinea region and surrounding regions in West Africa.
33.
Greece
–
Greece, officially the Hellenic Republic, historically also known as Hellas, is a country in southeastern Europe, with a population of approximately 11 million as of 2015. Athens is the capital and largest city, followed by Thessaloniki. Greece is strategically located at the crossroads of Europe, Asia, situated on the southern tip of the Balkan peninsula, it shares land borders with Albania to the northwest, the Republic of Macedonia and Bulgaria to the north, and Turkey to the northeast. Greece consists of nine regions, Macedonia, Central Greece, the Peloponnese, Thessaly, Epirus, the Aegean Islands, Thrace, Crete. The Aegean Sea lies to the east of the mainland, the Ionian Sea to the west, the Cretan Sea and the Mediterranean Sea to the south. Greece has the longest coastline on the Mediterranean Basin and the 11th longest coastline in the world at 13,676 km in length, featuring a vast number of islands, eighty percent of Greece is mountainous, with Mount Olympus being the highest peak at 2,918 metres. From the eighth century BC, the Greeks were organised into various independent city-states, known as polis, which spanned the entire Mediterranean region and the Black Sea. Greece was annexed by Rome in the second century BC, becoming a part of the Roman Empire and its successor. The Greek Orthodox Church also shaped modern Greek identity and transmitted Greek traditions to the wider Orthodox World, falling under Ottoman dominion in the mid-15th century, the modern nation state of Greece emerged in 1830 following a war of independence. Greeces rich historical legacy is reflected by its 18 UNESCO World Heritage Sites, among the most in Europe, Greece is a democratic and developed country with an advanced high-income economy, a high quality of life, and a very high standard of living. A founding member of the United Nations, Greece was the member to join the European Communities and has been part of the Eurozone since 2001. Greeces unique cultural heritage, large industry, prominent shipping sector. It is the largest economy in the Balkans, where it is an important regional investor, the names for the nation of Greece and the Greek people differ from the names used in other languages, locations and cultures. The earliest evidence of the presence of human ancestors in the southern Balkans, dated to 270,000 BC, is to be found in the Petralona cave, all three stages of the stone age are represented in Greece, for example in the Franchthi Cave. Neolithic settlements in Greece, dating from the 7th millennium BC, are the oldest in Europe by several centuries and these civilizations possessed writing, the Minoans writing in an undeciphered script known as Linear A, and the Mycenaeans in Linear B, an early form of Greek. The Mycenaeans gradually absorbed the Minoans, but collapsed violently around 1200 BC and this ushered in a period known as the Greek Dark Ages, from which written records are absent. The end of the Dark Ages is traditionally dated to 776 BC, the Iliad and the Odyssey, the foundational texts of Western literature, are believed to have been composed by Homer in the 7th or 8th centuries BC. With the end of the Dark Ages, there emerged various kingdoms and city-states across the Greek peninsula, in 508 BC, Cleisthenes instituted the worlds first democratic system of government in Athens
Greece
–
Fresco displaying the Minoan ritual of "bull leaping", found in
Knossos,
Crete.
Greece
–
Flag
Greece
–
The
Lion Gate,
Mycenae
Greece
–
The
Parthenon on the
Acropolis of Athens is one of the best known symbols of
classical Greece.
34.
Wildfire
–
A wildfire or wildland fire is a fire in an area of combustible vegetation that occurs in the countryside or rural area. Fossil charcoal indicates that wildfires began soon after the appearance of terrestrial plants 420 million years ago, wildfire’s occurrence throughout the history of terrestrial life invites conjecture that fire must have had pronounced evolutionary effects on most ecosystems flora and fauna. Earth is an intrinsically flammable planet owing to its cover of vegetation, seasonally dry climates, atmospheric oxygen. Wildfires can be characterized in terms of the cause of ignition, their properties, the combustible material present. Wildfires can cause damage to property and human life, but they have beneficial effects on native vegetation, animals. Many plant species depend on the effects of fire for growth, however, wildfire in ecosystems where wildfire is uncommon or where non-native vegetation has encroached may have negative ecological effects. Wildfire behaviour and severity result from the combination of such as available fuels, physical setting. Strategies of wildfire prevention, detection, and suppression have varied over the years, one common and inexpensive technique is controlled burning, permitting or even igniting smaller fires to minimize the amount of flammable material available for a potential wildfire. Vegetation may be burned periodically to maintain species diversity and frequent burning of surface fuels limits fuel accumulation. Wildland fire use is the cheapest and most ecologically appropriate policy for many forests, fuels may also be removed by logging, but fuels treatments and thinning have no effect on severe fire behavior. Wildfires can also be started in communities experiencing shifting cultivation, where land is cleared quickly and farmed until the soil loses fertility, forested areas cleared by logging encourage the dominance of flammable grasses, and abandoned logging roads overgrown by vegetation may act as fire corridors. The most common cause of wildfires throughout the world. In Canada and northwest China, for example, lightning operates as the source of ignition. In other parts of the world, human involvement is a major contributor, in China and in the Mediterranean Basin, human carelessness is a major cause of wildfires. In the United States and Australia, the source of wildfires can be traced both to lightning strikes and to human activities. Coal seam fires burn in the thousands around the world, such as those in Burning Mountain, New South Wales, Centralia, Pennsylvania and they can also flare up unexpectedly and ignite nearby flammable material. The spread of wildfires based on the flammable material present, its vertical arrangement and moisture content. Fuel arrangement and density is governed in part by topography, as land shape determines factors such as available sunlight, overall, fire types can be generally characterized by their fuels as follows, Ground fires are fed by subterranean roots, duff and other buried organic matter
Wildfire
–
A
wildfire in California on September 5, 2008
Wildfire
–
A surface fire in the western desert of
Utah, U.S.
Wildfire
–
Charred landscape following a crown fire in the
North Cascades, U.S.
Wildfire
–
Torching of Juniper Tree on the Palisade Wildfire in Nevada
35.
Thailand
–
Thailand, officially the Kingdom of Thailand, formerly known as Siam, is a country at the centre of the Indochinese peninsula in Southeast Asia. With a total area of approximately 513,000 km2, Thailand is the worlds 51st-largest country and it is the 20th-most-populous country in the world, with around 66 million people. The capital and largest city is Bangkok, Thailand is a constitutional monarchy and has switched between parliamentary democracy and military junta for decades, the latest coup being in May 2014 by the National Council for Peace and Order. Its capital and most populous city is Bangkok and its maritime boundaries include Vietnam in the Gulf of Thailand to the southeast, and Indonesia and India on the Andaman Sea to the southwest. The Thai economy is the worlds 20th largest by GDP at PPP and it became a newly industrialised country and a major exporter in the 1990s. Manufacturing, agriculture, and tourism are leading sectors of the economy and it is considered a middle power in the region and around the world. The country has always been called Mueang Thai by its citizens, by outsiders prior to 1949, it was usually known by the exonym Siam. The word Siam has been identified with the Sanskrit Śyāma, the names Shan and A-hom seem to be variants of the same word. The word Śyâma is possibly not its origin, but a learned, another theory is the name derives from Chinese, Ayutthaya emerged as a dominant centre in the late fourteenth century. The Chinese called this region Xian, which the Portuguese converted into Siam, the signature of King Mongkut reads SPPM Mongkut King of the Siamese, giving the name Siam official status until 24 June 1939 when it was changed to Thailand. Thailand was renamed Siam from 1945 to 11 May 1949, after which it reverted to Thailand. According to George Cœdès, the word Thai means free man in the Thai language, ratcha Anachak Thai means kingdom of Thailand or kingdom of Thai. Etymologically, its components are, ratcha, -ana- -chak, the Thai National Anthem, written by Luang Saranupraphan during the extremely patriotic 1930s, refers to the Thai nation as, prathet Thai. The first line of the anthem is, prathet thai ruam lueat nuea chat chuea thai, Thailand is the unity of Thai flesh. There is evidence of habitation in Thailand that has been dated at 40,000 years before the present. Similar to other regions in Southeast Asia, Thailand was heavily influenced by the culture and religions of India, Thailand in its earliest days was under the rule of the Khmer Empire, which had strong Hindu roots, and the influence among Thais remains even today. Voretzsch believes that Buddhism must have been flowing into Siam from India in the time of the Indian Emperor Ashoka of the Maurya Empire, later Thailand was influenced by the south Indian Pallava dynasty and north Indian Gupta Empire. The Menam Basin was originally populated by the Mons, and the location of Dvaravati in the 7th century, the History of the Yuan mentions an embassy from the kingdom of Sukhothai in 1282
Thailand
–
The ruins of
Wat Chaiwatthanaram at
Ayutthaya.
Thailand
–
Flag
Thailand
–
Stupas,
Ayutthaya Historical Park.
Thailand
–
Pottery discovered near
Ban Chiang in Udon Thani Province, the earliest dating to 2100 BCE.
36.
France
–
France, officially the French Republic, is a country with territory in western Europe and several overseas regions and territories. The European, or metropolitan, area of France extends from the Mediterranean Sea to the English Channel and the North Sea, Overseas France include French Guiana on the South American continent and several island territories in the Atlantic, Pacific and Indian oceans. France spans 643,801 square kilometres and had a population of almost 67 million people as of January 2017. It is a unitary republic with the capital in Paris. Other major urban centres include Marseille, Lyon, Lille, Nice, Toulouse, during the Iron Age, what is now metropolitan France was inhabited by the Gauls, a Celtic people. The area was annexed in 51 BC by Rome, which held Gaul until 486, France emerged as a major European power in the Late Middle Ages, with its victory in the Hundred Years War strengthening state-building and political centralisation. During the Renaissance, French culture flourished and a colonial empire was established. The 16th century was dominated by civil wars between Catholics and Protestants. France became Europes dominant cultural, political, and military power under Louis XIV, in the 19th century Napoleon took power and established the First French Empire, whose subsequent Napoleonic Wars shaped the course of continental Europe. Following the collapse of the Empire, France endured a succession of governments culminating with the establishment of the French Third Republic in 1870. Following liberation in 1944, a Fourth Republic was established and later dissolved in the course of the Algerian War, the Fifth Republic, led by Charles de Gaulle, was formed in 1958 and remains to this day. Algeria and nearly all the colonies became independent in the 1960s with minimal controversy and typically retained close economic. France has long been a centre of art, science. It hosts Europes fourth-largest number of cultural UNESCO World Heritage Sites and receives around 83 million foreign tourists annually, France is a developed country with the worlds sixth-largest economy by nominal GDP and ninth-largest by purchasing power parity. In terms of household wealth, it ranks fourth in the world. France performs well in international rankings of education, health care, life expectancy, France remains a great power in the world, being one of the five permanent members of the United Nations Security Council with the power to veto and an official nuclear-weapon state. It is a member state of the European Union and the Eurozone. It is also a member of the Group of 7, North Atlantic Treaty Organization, Organisation for Economic Co-operation and Development, the World Trade Organization, originally applied to the whole Frankish Empire, the name France comes from the Latin Francia, or country of the Franks
France
–
One of the
Lascaux paintings: a horse –
Dordogne, approximately 18,000 BC
France
–
Flag
France
–
The
Maison Carrée was a temple of the
Gallo-Roman city of Nemausus (present-day
Nîmes) and is one of the best preserved vestiges of the
Roman Empire.
France
–
With
Clovis ' conversion to Catholicism in 498, the
Frankish monarchy,
elective and
secular until then, became
hereditary and of
divine right.
37.
Australia
–
Australia, officially the Commonwealth of Australia, is a country comprising the mainland of the Australian continent, the island of Tasmania and numerous smaller islands. It is the worlds sixth-largest country by total area, the neighbouring countries are Papua New Guinea, Indonesia and East Timor to the north, the Solomon Islands and Vanuatu to the north-east, and New Zealand to the south-east. Australias capital is Canberra, and its largest urban area is Sydney, for about 50,000 years before the first British settlement in the late 18th century, Australia was inhabited by indigenous Australians, who spoke languages classifiable into roughly 250 groups. The population grew steadily in subsequent decades, and by the 1850s most of the continent had been explored, on 1 January 1901, the six colonies federated, forming the Commonwealth of Australia. Australia has since maintained a liberal democratic political system that functions as a federal parliamentary constitutional monarchy comprising six states. The population of 24 million is highly urbanised and heavily concentrated on the eastern seaboard, Australia has the worlds 13th-largest economy and ninth-highest per capita income. With the second-highest human development index globally, the country highly in quality of life, health, education, economic freedom. The name Australia is derived from the Latin Terra Australis a name used for putative lands in the southern hemisphere since ancient times, the Dutch adjectival form Australische was used in a Dutch book in Batavia in 1638, to refer to the newly discovered lands to the south. On 12 December 1817, Macquarie recommended to the Colonial Office that it be formally adopted, in 1824, the Admiralty agreed that the continent should be known officially as Australia. The first official published use of the term Australia came with the 1830 publication of The Australia Directory and these first inhabitants may have been ancestors of modern Indigenous Australians. The Torres Strait Islanders, ethnically Melanesian, were originally horticulturists, the northern coasts and waters of Australia were visited sporadically by fishermen from Maritime Southeast Asia. The first recorded European sighting of the Australian mainland, and the first recorded European landfall on the Australian continent, are attributed to the Dutch. The first ship and crew to chart the Australian coast and meet with Aboriginal people was the Duyfken captained by Dutch navigator, Willem Janszoon. He sighted the coast of Cape York Peninsula in early 1606, the Dutch charted the whole of the western and northern coastlines and named the island continent New Holland during the 17th century, but made no attempt at settlement. William Dampier, an English explorer and privateer, landed on the north-west coast of New Holland in 1688, in 1770, James Cook sailed along and mapped the east coast, which he named New South Wales and claimed for Great Britain. The first settlement led to the foundation of Sydney, and the exploration, a British settlement was established in Van Diemens Land, now known as Tasmania, in 1803, and it became a separate colony in 1825. The United Kingdom formally claimed the part of Western Australia in 1828. Separate colonies were carved from parts of New South Wales, South Australia in 1836, Victoria in 1851, the Northern Territory was founded in 1911 when it was excised from South Australia
Australia
–
Aboriginal rock art in the
Kimberley region of Western Australia
Australia
Australia
–
Portrait of Captain
James Cook, the first European to map the eastern coastline of Australia in 1770
Australia
–
Tasmania's
Port Arthur penal settlement is one of eleven UNESCO World Heritage-listed
Australian Convict Sites.
38.
191 Peachtree Tower
–
One Ninety One Peachtree Tower is a 235 m 50-story skyscraper in Atlanta, Georgia. Throughout the 1990s 191 Peachtree was considered Atlantas premier business address, however, when two of its largest tenants, law firm King & Spalding, and Wachovia moved to Midtowns new 1180 Peachtree and Atlantic Station respectively in 2006, most of the building was left vacant. That same year, Cousins Properties purchased the building from Equity Office Properties, the building is located on the former site of the Hotel Majestic, which in the early 20th century was one of the citys major hotels. The building was proposed in July 1987 at 48 floors. The buildings facade is made of flame finished Rosa Dante granite, each tower possesses a rooftop crown that is illuminated at night. The lighted double crown figured prominently in night footage taken by helicopter during the 1996 Olympics, the primary entrance to the building is through a soaring 102-foot tall atrium adjacent to Peachtree Street in Downtown Atlanta. Architecture of Atlanta List of tallest buildings in Atlanta List of tallest buildings in the United States One Ninety One Peachtree Tower at Cousins Properties
191 Peachtree Tower
–
191 Peachtree Tower
191 Peachtree Tower
191 Peachtree Tower
39.
Peachtree Street
–
Peachtree Street is one of several major streets running through the city of Atlanta. Beginning at Five Points in downtown Atlanta, it runs North through Midtown, upon entering Buckhead, Atlanta grew on a site occupied by the Creek people, which included a major village called Standing Peachtree. There is some dispute whether the Creek settlement was called Standing Peachtree or Standing Pitch Tree. Pine trees, common to the area, were known as pitch trees due to their sap. A trail known as the Peachtree Trail stretched from northeast Georgia to Standing Pitch Tree along the Chattahoochee River, the original Peachtree Road began in 1812 at Fort Daniel located at Hog Mountain in present-day Gwinnett County and ran along the course of the trail to the Chattahoochee. Some portions of the present road trace this route, after the American Civil War a shantytown named Tight Squeeze developed at Peachtree at what is now 10th Street in Midtown Atlanta. It was infamous for vagrancy, desperation, robberies of merchants transiting the settlement, the Peachtree name is common throughout the Atlanta area. In fact, it is often joked by natives that half of the streets in Atlanta are named Peachtree, while Peachtree alone always refers to this street, there are 71 streets in Atlanta with a variant of Peachtree in their name. Peachtree City is a golf community located south of the city. Peachtree Corners is also a suburb located north of the city. West Peachtree divides the northeast and northwest quadrants of the city and county for street addressing purposes, where the current Peachtree Street turns to Peachtree Road and briefly heads northwest, it actually crosses West Peachtree, leaving it on the east side. It is at point that the Buford-Spring Connector begins, taking the route of old I-85. The studios of WSB-TV are located on section of West Peachtree Street. Through this section north of 17th Street in Midtown, and in south of North Avenue to Peachtree Street. Between the two, it no more than a block to the east. From the Buford-Spring Connector north to Roswell Road, Peachtree Street and Peachtree Road carry U. S.19 and Georgia 9. At a five-way intersection with East/West Paces Ferry Road at the center of the original Buckhead Village, these continue north onto Roswell Road, south of the connector,9 and 19 continue on two one-way streets, West Peachtree Street northbound and Spring Street southbound. Peachtree meets Piedmont Road between Buckhead Village and Lenox Square
Peachtree Street
–
People celebrating on Peachtree Street
Peachtree Street
–
Peachtree Street,
downtown Atlanta, 1974
Peachtree Street
–
Peachtree Street as it travels through
Midtown
Peachtree Street
–
Atlanta St. Patrick's Day Parade on Peachtree Street, 2013
40.
Skyscraper
–
A skyscraper is a tall, continuously habitable building having multiple floors. When the term was used in the 1880s it described a building of 10 to 20 floors. Mostly designed for office, commercial and residential uses, a skyscraper can also be called a high-rise, for buildings above a height of 300 m, the term supertall can be used, while skyscrapers reaching beyond 600 m are classified as megatall. One common feature of skyscrapers is having a steel framework that supports curtain walls and these curtain walls either bear on the framework below or are suspended from the framework above, rather than resting on load-bearing walls of conventional construction. Some early skyscrapers have a frame that enables the construction of load-bearing walls taller than of those made of reinforced concrete. Modern skyscrapers walls are not load-bearing, and most skyscrapers are characterized by surface areas of windows made possible by steel frames. However, skyscrapers can have curtain walls that mimic conventional walls with a surface area of windows. Modern skyscrapers often have a structure, and are designed to act like a hollow cylinder to resist wind, seismic. To appear more slender, allow less wind exposure, and transmit more daylight to the ground, many skyscrapers have a design with setbacks, a relatively big building may be considered a skyscraper if it protrudes well above its built environment and changes the overall skyline. The maximum height of structures has progressed historically with building methods and technologies, the Burj Khalifa is currently the tallest building in the world. High-rise buildings are considered shorter than skyscrapers, the first steel-frame skyscraper was the Home Insurance Building in Chicago, Illinois in 1885. Even the scholars making the argument find it to be purely academic and this definition was based on the steel skeleton—as opposed to constructions of load-bearing masonry, which passed their practical limit in 1891 with Chicagos Monadnock Building. What is the characteristic of the tall office building. The force and power of altitude must be in it, the glory and it must be every inch a proud and soaring thing, rising in sheer exaltation that from bottom to top it is a unit without a single dissenting line. Some structural engineers define a highrise as any vertical construction for which wind is a significant load factor than earthquake or weight. Note that this criterion fits not only high-rises but some other tall structures, the word skyscraper often carries a connotation of pride and achievement. A loose convention of some in the United States and Europe draws the limit of a skyscraper at 150 m or 490 ft. The tallest building in ancient times was the 146 m Great Pyramid of Giza in ancient Egypt and it was not surpassed in height for thousands of years, the 14th century AD Lincoln Cathedral being conjectured by many to have exceeded it
Skyscraper
–
The
Burj Khalifa, in
Dubai (
United Arab Emirates), has been the
tallest skyscraper in the world since 2009, with a height of 829.8 m.
Skyscraper
–
The 16th-century city of
Shibam consisted entirely of over 500 high-rise tower houses.
Skyscraper
–
The
Two Towers of Bologna in the 12th century reached 97.2 m (319 ft) in height.
Skyscraper
–
Oriel Chambers, Liverpool. The world's first glass curtain walled building. The stone
mullions are decorative.
41.
Atlanta
–
Atlanta is the capital of and the most populous city in the U. S. state of Georgia, with an estimated 2015 population of 463,878. Atlanta is the cultural and economic center of the Atlanta metropolitan area, home to 5,710,795 people, Atlanta is the county seat of Fulton County, and a small portion of the city extends eastward into DeKalb County. In 1837, Atlanta was founded at the intersection of two lines, and the city rose from the ashes of the American Civil War to become a national center of commerce. Atlantas economy is considered diverse, with dominant sectors that include logistics, professional and business services, media operations, Atlanta has topographic features that include rolling hills and dense tree coverage. Revitalization of Atlantas neighborhoods, initially spurred by the 1996 Olympics in Atlanta, has intensified in the 21st century, altering the demographics, politics. Prior to the arrival of European settlers in north Georgia, Creek Indians inhabited the area, standing Peachtree, a Creek village located where Peachtree Creek flows into the Chattahoochee River, was the closest Indian settlement to what is now Atlanta. As part of the removal of Native Americans from northern Georgia from 1802 to 1825, the Creek ceded the area in 1821. In 1836, the Georgia General Assembly voted to build the Western, the initial route was to run southward from Chattanooga to a terminus east of the Chattahoochee River, which would then be linked to Savannah. After engineers surveyed various possible locations for the terminus, the zero milepost was driven into the ground in what is now Five Points. A year later, the area around the milepost had developed into a settlement, first known as Terminus, and later as Thrasherville after a merchant who built homes. By 1842, the town had six buildings and 30 residents and was renamed Marthasville to honor the Governors daughter, later, J. Edgar Thomson, Chief Engineer of the Georgia Railroad, suggested the town be renamed Atlantica-Pacifica, which was shortened to Atlanta. The residents approved, and the town was incorporated as Atlanta on December 29,1847, by 1860, Atlantas population had grown to 9,554. During the American Civil War, the nexus of multiple railroads in Atlanta made the city a hub for the distribution of military supplies, in 1864, the Union Army moved southward following the capture of Chattanooga and began its invasion of north Georgia. On the next day, Mayor James Calhoun surrendered Atlanta to the Union Army, on November 11,1864, Sherman prepared for the Union Armys March to the Sea by ordering Atlanta to be burned to the ground, sparing only the citys churches and hospitals. After the Civil War ended in 1865, Atlanta was gradually rebuilt, due to the citys superior rail transportation network, the state capital was moved from Milledgeville to Atlanta in 1868. In the 1880 Census, Atlanta surpassed Savannah as Georgias largest city, by 1885, the founding of the Georgia School of Technology and the citys black colleges had established Atlanta as a center for higher education. In 1895, Atlanta hosted the Cotton States and International Exposition, during the first decades of the 20th century, Atlanta experienced a period of unprecedented growth. In three decades time, Atlantas population tripled as the city expanded to include nearby streetcar suburbs
Atlanta
–
From top to bottom left to right: Atlanta skyline seen from
Buckhead, the
Fox Theatre, the
Georgia State Capitol,
Centennial Olympic Park,
Millennium Gate, the
Canopy Walk, the
Georgia Aquarium,
The Phoenix statue, and the
Midtown skyline
Atlanta
–
Marietta Street, 1864
Atlanta
–
Atlanta in ruins during the Civil War, 1864
Atlanta
–
In 1907, Peachtree Street, the main street of Atlanta, was busy with streetcars and automobiles.
42.
Chicago
–
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
Chicago
–
Clockwise from top:
Downtown Chicago, the
Chicago Theatre, the
'L',
Navy Pier,
Millennium Park, the
Field Museum, and the
Willis Tower.
Chicago
–
Traditional
Potawatomi costume on display at the
Field Museum
Chicago
–
A 1903 painting of Chicago in 1833
Chicago
–
An artist's rendering of the
Great Chicago Fire of 1871
43.
Saskatchewan
–
Saskatchewan is a prairie and boreal province in west-central Canada, the only province without natural borders. It has an area of 651,900 square kilometres, nearly 10 percent of which is water, composed mostly of rivers, reservoirs. As of December 2013, Saskatchewans population was estimated at 1,114,170, residents primarily live in the southern prairie half of the province, while the northern boreal half is mostly forested and sparsely populated. Of the total population, roughly half live in the provinces largest city, Saskatoon, or the provincial capital, other notable cities include Prince Albert, Moose Jaw, Yorkton, Swift Current, North Battleford, and the border city Lloydminster. Saskatchewan is a province with large distances to moderating bodies of waters. As a result, its climate is continental, rendering severe winters throughout the province. Southern areas have very warm or hot summers, Midale and Yellow Grass near the U. S. border are tied for the highest ever recorded temperatures in Canada with 45 °C observed at both locations on July 5,1937. In winter, temperatures below −45 °C are possible even in the south during extreme cold snaps, Saskatchewan has been inhabited for thousands of years by various indigenous groups, and first explored by Europeans in 1690 and settled in 1774. It became a province in 1905, carved out from the vast North-West Territories, in the early 20th century the province became known as a stronghold for Canadian social democracy, North Americas first social-democratic government was elected in 1944. The provinces economy is based on agriculture, mining, and energy, Saskatchewans current premier is Brad Wall and its lieutenant-governor is Vaughn Solomon Schofield. In 1992, the federal and provincial governments signed a land claim agreement with First Nations in Saskatchewan. The First Nations received compensation and were permitted to buy land on the market for the tribes, they have acquired about 3,079 square kilometres. Some First Nations have used their settlement to invest in urban areas and its name derived from the Saskatchewan River. The river was known as kisiskāciwani-sīpiy in the Cree language, as Saskatchewans borders largely follow the geographic coordinates of longitude and latitude, the province is roughly a quadrilateral, or a shape with four sides. However the 49th parallel boundary and the 60th northern border appear curved on globes, additionally, the eastern boundary of the province is partially crooked rather than following a line of longitude, as correction lines were devised by surveyors prior to the homestead program. S. States of Montana and North Dakota, Saskatchewan has the distinction of being the only Canadian province for which no borders correspond to physical geographic features. Along with Alberta, Saskatchewan is one of only two land-locked provinces, the overwhelming majority of Saskatchewans population is located in the southern third of the province, south of the 53rd parallel. Saskatchewan contains two natural regions, the Canadian Shield in the north and the Interior Plains in the south
Saskatchewan
–
Henry Kelsey sees the
buffalo on the western plains.
Saskatchewan
–
Flag
Saskatchewan
–
Cree Pipe Stem Carrier, a painting of a Plains Cree warrior by
Paul Kane.
Saskatchewan
–
The
Battle of Batoche, 1885
44.
191st Air Refueling Squadron
–
The 191st Air Refueling Squadron is a unit of the Utah Air National Guard 151st Air Refueling Wing located at Salt Lake City Air National Guard Base, Utah. The 191st is equipped with the KC-135R Stratotanker, activated in October 1943 as the 407th Fighter Squadron at Hamilton Field, California. During World War II, the squadron was an Operational Training Unit, equipped with second-line P-39 Airacobras and its mission was to train newly graduated pilots from Training Command in combat tactics and maneuvers before being assigned to their permanent combat unit. Initially assigned to IV Fighter Command, then transferred to III Fighter Command in 1944 and it took part in air-ground maneuvers and demonstrations, participating in the Louisiana Maneuvers in the summer of 1944 and in similar activities in the US until after V-J Day. The wartime 407th Fighter Squadron was re-activated and re-designated as the 191st Fighter Squadron and it was organized at Salt Lake City Municipal Airport, Utah and was extended federal recognition on 18 November 1946 by the National Guard Bureau. The 191st Fighter Squadron was entitled to the history, honors, during its early years with the F-51D, the unit earned prominence as one of the Air Forces most respected aerial gunnery competitors. As a result of the Korean War, the 191st Fighter Squadron was federalized and brought to duty on 1 April 1951. The unit was ordered to the new Clovis Air Force Base, New Mexico, the federalized 140th was a composite organization of activated Air National Guard units, composed of the 191st, the 187th Fighter Squadron and the 120th Fighter Squadron. The 140th and its components were equipped with F-51D Mustangs, and were re-designated as Fighter-Bomber squadrons on 12 April 1951. During their period of service, many pilots were sent to Japan and South Korea to reinforce active-duty units,10 pilots flew over 100 missions. Clifford Jolley, flying an F-86 Sabrejet, shot down seven soviet made MIG-15 aircraft, at Clovis, elements of the 140th FBW took part in Operation Tumbler-Snapper –1952, a nuclear bomb test in Nevada. On 15 November 1952, the elements of the 140th returned to Air National Guard control in their respective states, upon return to Utah state control, the 191st was re-equipped by Tactical Air Command with F-51D Mustangs. On 1 July 1958, the 191st was authorized to expand to a level. The 191st FIS becoming the flying squadron. Other squadrons assigned into the group were the 151st Headquarters, 151st Material Squadron, 151st Combat Support Squadron, also, in 1958, the 151st FIW implemented the ADC Runway Alert Program, in which interceptors of the 191st Fighter-Interceptor Squadron were committed to a five-minute runway alert. The F-86s were replaced by the F-86L Sabre Interceptor, an aircraft designed to be integrated into the ADC SAGE interceptor direction. On 1 April 1961, the 151st was transferred from Air Defense Command to the Military Air Transport Service, the 151st Air Transport Group expanded its military airlift role to worldwide mission capabilities. In January 1966, the became the 151st Military Airlift Group
191st Air Refueling Squadron
–
KC-135R Stratotanker, 191st Air Refueling Squadron
191st Air Refueling Squadron
–
191st Air Refueling Squadron
45.
Utah Air National Guard
–
The Utah Air National Guard is the aerial militia of the U. S. State of Utah. Along with the Utah Army National Guard it is an element of the Utah National Guard, as state militia units, the units in the Utah Air National Guard are not in the normal United States Air Force chain of command. They are under the jurisdiction of the Governor of Utah though the office of the Utah Adjutant General unless they are federalized by order of the President of the United States. The Utah Air National Guard is headquartered in Salt Lake City, under the Total Force concept, Utah Air National Guard units are considered to be Air Reserve Components of the United States Air Force. Utah ANG units are trained and equipped by the Air Force and are gained by a Major Command of the USAF if federalized. State missions include disaster relief in times of earthquakes, hurricanes, floods and forest fires, search and rescue, protection of public services. The Utah Air National Guard is located on over 33.200 qm in the Northeast corner of the Salt Lake City International Airport, in 2007, over 1.450 trained men and women served in the Utah Air National Guard. To employ and administer reliable and secure command and control, data link, truman, allocated inactive unit designations to the National Guard Bureau for the formation of an Air Force National Guard. These unit designations were allotted and transferred to various State National Guard bureaus to provide them unit designations to re-establish them as Air National Guard units. The Utah Air National Guard was founded on 18 November 1946 with the recognition of the 191st Fighter Squadron at Salt Lake City Municipal Airport. It was equipped with F-51D Mustangs and its mission was the air defense of the state, flying F-51D Mustang fighter aircraft,10 pilots flew over 100 missions. Two Utah ANG pilots were killed in this conflict, one Utah Air National Guard pilot, Capt. Cliff Jolley, flying a North American F-86 Sabre, shot down seven soviet-made MiG-15 aircraft, during the Vietnam War, Utah Air Guard crews flew 6,600 hours of support missions for US forces. On 1 July 1958, the 191st Fighter-Interceptor Squadron was authorized to expand to a level. In 1990-91, Utah Air National Guard crews were some of the first to volunteer to support Operation Desert Shield, Utah Air National Guards support of this operation continued well into 1991. In 1999, many members were deployed to Europe in support of Operation Allied Force, members have also supported US drug interdiction activities and have provided air refueling for tactical and transportation aircraft supporting military activities involving Bosnia and Iraq. The Utah Air National Guard has participated in several Air Expeditionary Force missions, most recently at Andersen Air Force Base, in Utah, local communities can have benefits from the Utah Air National Guard. Activities included Sub-for-Santa, blood drives, Adopt a School Program, highway cleanup, the Utah Air National Guard also maintains a state of readiness to meet the needs to support the State of Utah during an earthquake, flood, civil disturbance or major disaster
Utah Air National Guard
–
191st Air Refueling Squadron KC-135 landing at Salt Lake City Air National Guard Base. The 191st ARS is the oldest unit in the Utah Air National Guard, having over 60 years of service to the state and nation.
Utah Air National Guard
–
F-51D Mustangs of the Nevada, California and Utah Air National Guards fly in formation, 1948. The 191st Fighter Squadron was assigned to the CA ANG
61st Fighter Wing during the postwar years
46.
191st Airlift Group
–
The 127th Air Refueling Group is a unit of the Michigan Air National Guard, assigned to the 127th Wing, Selfridge Air National Guard Base, Michigan. Established in 1962 when the Michigan ANG 171st Tactical Reconnaissance Squadron was expanded to a Group, was primarily a training unit flying second-line RF-84F Thundersteak reconnaissance aircraft for Tactical Air Command, upgrading to the newer RF-101 Voodoo in 1971. Reassigned to Aerospace Defense Command in 1973, equipped with F-106 Delta Dart interceptors, performed air defense duties of the Great Lakes and Detroit area until 1978 when ADCOM was merged into Tactical Air Command. Continued air defense mission for ADTAC component of TAC with F-4 Phantom IIs, upgraded to F-16A Fighting Falcons in 1990. Transferred to Air Mobility Command in 1993 when the became a C-130 Hercules Tactical Airlift unit. Inactivated in April 1996 when the 127th Fighter Wing and 191st Airlift Group were merged due to the One-Base, reactivated in May 1999 as a group under the 127th Wing, operating the C-130 airlift element of the composite wing. Inactivated in September 2007 with the realignment of Selfridge and transfer of the C-130s, 127th Wing Interview with a pilot who flew for the 171st
191st Airlift Group
–
A KC-135 Stratotanker lifts off at Selfridge Air National Guard Base, Mich., Nov. 4, 2012.
191st Airlift Group
–
171st Airlift Group C-130 Hercules
191st Airlift Group
–
191st Fighter Group F-16A interceptor, 1991
191st Airlift Group
–
F-4C in ADCOM interceptor liverly, 1980
47.
Michigan Air National Guard
–
The Michigan Air National Guard is the air force militia of the State of Michigan, United States of America. It is, along with the Michigan Army National Guard, an element of the Michigan National Guard, the Michigan Air National Guard is also an Air Reserve Component of the United States Air Force. As a state militia, the Michigan Air National Guard are not in the United States Air Force chain of command unless it is federalized. They are under the jurisdiction of the Governor of Michigan though the office of the Michigan Adjutant General unless they are federalized by order of the President of the United States. The Michigan Air National Guard is headquartered at the Joint Forces Headquarters compound, located in Lansing, Michigan, Michigan ANG units are trained and equipped by the Air Force and are operationally gained by a Major Command of the USAF if federalized. State missions include disaster relief in times of earthquakes, hurricanes, floods and forest fires, search and rescue, protection of public services. At the time the C-27J was the newest cargo aircraft in the Air Force inventory, the missions of the C-27 would have included direct support of Army units, homeland security, disaster response, and medical evacuation, as well as multiple other Federal and State requirements. Due to political decisions, the C-27 mission was replaced with a new Remotely Piloted Aircraft MQ-9 Reaper mission, the Wing also supports the Air Force Special Operations Command with its 107th Weather Flight. Support Unit Functions and Capabilities, Alpena Combat Readiness Training Center Houses the Combat Readiness Training Center which trains various units from National Guard, the origins of the Michigan Air National Guard can be traced back to the 107th Aero Squadron, which was organized on 27 August 1917. The squadron assembled, serviced, and repaired aircraft during World War I and it was re-designated 801st Aero Squadron on 1 February 1918 and inactivated after the end of the war on 18 March 1919. The Militia Act of 1903 established the present National Guard system, units raised by the states but paid for by the Federal Government, if federalized by Presidential order, they fall under the regular military chain of command. On 1 June 1920, the Militia Bureau issued Circular No.1 on organization of National Guard air units and it was reformed on 7 May 1926, as the 107th Observation Squadron and is oldest unit of the Michigan Air National Guard. It is one of the 29 original National Guard Observation Squadrons of the United States Army National Guard formed before World War II. The 116th Observation Squadron was ordered into service on 15 October 1940 as part of the buildup of the Army Air Corps prior to the United States entry into World War II. The unit was activated again on 15 October 1940, being redesignated 107th Observation Squadron with Douglas O-38 and it was sent to the airfield at Camp Beauregard, Louisiana for unit training on 28 October 1940. In 1941, the 107th was joined by two other National Guard observation units to form the 67th Observation Group, the 67th Group did anti-submarine patrolling off the East Coast of the US from mid-December 1941 to March 1942, when it returned to Louisiana for training in fighter aircraft. Under War Department policy, many of Michigans National Guard units were detached from their former organizations, such was the case for the 107th Observation Squadron, which entered service with the 32nd Division. The squadron was attached to the 67th Fighter Reconnaissance Group
Michigan Air National Guard
–
107th Fighter Squadron - A-10 Thunderbolt II taking off from Selfridge AGB, Detroit. The 107th FS is the oldest unit in the Michigan Air National Guard, having over 80 years of service to the state and nation
Michigan Air National Guard
–
Michigan Air National Guard North American P-51D Mustang 44-73227, 1946, prior to the formal establishment of the Air National Guard in September 1947.
48.
Selfridge ANGB
–
Selfridge Air National Guard Base or Selfridge ANGB is an Air National Guard installation located in Harrison Township, Michigan, near Mount Clemens. Selfridge Field was one of thirty-two Air Service training camps established after the United States entry into World War I in April 1917. In 1971, Selfridge ANGB became the largest and most complex joint Reserves Forces base in the United States, U. S. Army Garrison-Selfridge serves the Tank-automotive and Armaments Command supporting tank construction in the Detroit area. Civil Air Patrol civilian organizations at Selfridge are the 176th Selfridge Composite Squadron, Selfridge Air National Guard Base is named after 1st Lieutenant Thomas E. Selfridge. Selfridge was detailed for duty in April 1908 after being an assistant to Professor Alexander Graham Bell who was conducting aeronautical experiments in Nova Scotia. He was killed on 17 September 1908 while flying as a passenger with Orville Wright at Fort Myer, Selfridge was the first person to be killed in a crash of a powered aircraft. Joy, who took a great interest in aviation and led the company to begin developing aircraft engines for use in aircraft engaged in World War I combat in Europe. In the spring of 1917, lobbying began in Washington to locate an airfield at the site of the Joy Aviation Field on Lake St. Clair. The United States had just officially entered World War I on 7 April, proponents of the site pointed out the advantages of the fields proximity to the auto capital of the nation and the availability of the lake for practice bombing. The United States Army leased the 640 acres of land, and construction commenced immediately to provide the necessary road and rail access to the site. Within a month, the newspaper was reporting that 1,000 men were at work at the field constructing hangars, barracks, supply depots, machine shops and a school building. On 9 July, the first training aircraft, a Curtiss JN-4D arrived at the new airfield, the first pilots were members of the 8th and 9th Aero Squadrons, and Captain Byron Q. Jones was the first commander at Selfridge. Actual training of pilots began on 16 July 1917, three months after war was declared. Some of these students, a few of them from Mount Clemens area, were given a few flights and then, during the summer of 1917,72 men won aviator ratings and logged over 3,700 flying hours. From that time on, hundreds of men passed through Selfridge Air Pilot School for the four weeks of training which qualified them for a commission. Then they were on their way as instructors to the front or to the flying schools. From this school, which lasted until the end of March 1918,700 qualified mechanics were graduated, six squadrons from Kelly Field, Texas, were sent to Selfridge for study in the shops. The training center suffered a setback in March 1918, as the Clinton River flooded the entire site and all personnel were evacuated to schools
Selfridge ANGB
–
107th Fighter Squadron A-10 Thunderbolt II
Selfridge ANGB
–
A patch (and the insignia) of the Naval Air Facility Detroit
Selfridge ANGB
–
Airfields
49.
Michigan
–
Michigan /ˈmɪʃᵻɡən/ is a state in the Great Lakes and Midwestern regions of the United States. The name Michigan is the French form of the Ojibwa word mishigamaa, Michigan is the tenth most populous of the 50 United States, with the 11th most extensive total area. Its capital is Lansing, and its largest city is Detroit, Michigan is the only state to consist of two peninsulas. The Lower Peninsula, to which the name Michigan was originally applied, is noted to be shaped like a mitten. The Upper Peninsula is separated from the Lower Peninsula by the Straits of Mackinac, the two peninsulas are connected by the Mackinac Bridge. The state has the longest freshwater coastline of any political subdivision in the world, being bounded by four of the five Great Lakes, as a result, it is one of the leading U. S. states for recreational boating. Michigan also has 64,980 inland lakes and ponds, a person in the state is never more than six miles from a natural water source or more than 85 miles from a Great Lakes shoreline. What is now the state of Michigan was first settled by Native American tribes before being colonized by French explorers in the 17th century, the area was organized as part of the larger Northwest Territory until 1800, when western Michigan became part of the Indiana Territory. Eventually, in 1805, the Michigan Territory was formed, which lasted until it was admitted into the Union on January 26,1837, the state of Michigan soon became an important center of industry and trade in the Great Lakes region and a popular immigrant destination. Though Michigan has come to develop an economy, it is widely known as the center of the U. S. automotive industry. When the first European explorers arrived, the most populous tribes were Algonquian peoples, which include the Anishinaabe groups of Ojibwe, Odaawaa/Odawa, the three nations co-existed peacefully as part of a loose confederation called the Council of Three Fires. The Ojibwe, whose numbers are estimated to have been between 25,000 and 35,000, were the largest, French voyageurs and coureurs des bois explored and settled in Michigan in the 17th century. The first Europeans to reach what became Michigan were those of Étienne Brûlés expedition in 1622, the first permanent European settlement was founded in 1668 on the site where Père Jacques Marquette established Sault Ste. Marie, Michigan as a base for Catholic missions, missionaries in 1671–75 founded outlying stations at Saint Ignace and Marquette. Jesuit missionaries were received by the areas Indian populations, with relatively few difficulties or hostilities. In 1679, Robert Cavelier, Sieur de la Salle built Fort Miami at present-day St. Joseph, in 1691, the French established a trading post and Fort St. Joseph along the St. Joseph River at the present day city of Niles. The hundred soldiers and workers who accompanied Cadillac built a fort enclosing one arpent, cadillacs wife, Marie Thérèse Guyon, soon moved to Detroit, becoming one of the first European women to settle in the Michigan wilderness. The town quickly became a major fur-trading and shipping post, the Église de Saint-Anne was founded the same year
Michigan
–
Père Marquette and the Indians (1869), Wilhelm Lamprecht
Michigan
–
Flag
Michigan
–
Approximate area of Michigan highlighted in
Guillaume de L'Isle 's 1718 map
Michigan
–
Lumbering pines in the late 1800s