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.
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.
6.
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
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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
7.
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
8.
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
9.
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
10.
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
11.
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
12.
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
13.
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
–
Numeral systems
Duodecimal
–
A duodecimal multiplication table
14.
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.
15.
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.
16.
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
17.
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, …)
18.
NASCAR
–
The National Association for Stock Car Auto Racing is an American family-owned and operated business venture that sanctions and governs multiple auto-racing sports events. Bill France Sr. founded the company in 1948 and his grandson Brian France became its CEO in 2003, NASCAR is motorsports preeminent stock-car racing organization. The three largest racing-series sanctioned by this company are the Monster Energy NASCAR Cup Series, the Xfinity Series, the company also oversees NASCAR Local Racing, the Whelen Modified Tour, the Whelen All-American Series, and the NASCAR iRacing. com Series. NASCAR sanctions over 1,500 races at over 100 tracks in 39 of the 50 US states as well as in Canada. NASCAR has presented exhibition races at the Suzuka and Motegi circuits in Japan, the Autódromo Hermanos Rodríguez in Mexico, NASCAR has its official headquarters in Daytona Beach, Florida, and also maintains offices in the North Carolina cities of Charlotte, Concord, and Conover. Regional offices are located in New York City and Los Angeles, with offices in Mexico City. Owing to NASCARs Southern roots, all but a handful of NASCAR teams are based in North Carolina. NASCAR is second to the National Football League among professional sports franchises in terms of television viewers, internationally, its races are broadcast on television in over 150 countries. In 2004, NASCARs Director of Security stated that the company holds 17 of the Top 20 regularly attended single-day sporting events in the world, fortune 500 companies sponsor NASCAR more than any other motor sport, although this sponsorship has declined since the early-2000s. By the time the Bonneville Salt Flats became the location for pursuit of land speed records. Drivers raced on a 4. 1-mile course, consisting of a 1. 5–2. 0-mile stretch of beach as one straightaway, the two straights were connected by two tight, deeply rutted and sand covered turns at each end. Stock car racing in the United States has its origins in bootlegging during Prohibition, bootleggers needed to distribute their illicit products, and they typically used small, fast vehicles to better evade the police. Many of the drivers would modify their cars for speed and handling, as well as increased cargo capacity, the cars continued to improve, and by the late 1940s, races featuring these cars were being run for pride and profit. These races were popular entertainment in the rural Southern United States, most races in those days were of modified cars. Street vehicles were lightened and reinforced, mechanic William France Sr. moved to Daytona Beach, Florida, from Washington, D. C. in 1935 to escape the Great Depression. He was familiar with the history of the area from the speed record attempts. France entered the 1936 Daytona event, finishing fifth and he took over running the course in 1938. He promoted a few races before World War II, France had the notion that people would enjoy watching stock cars race
NASCAR
–
Nextel Cup Series (now Sprint Cup Series) race cars at Infineon Raceway (now Sonoma Raceway) in 2005
NASCAR
–
Current NASCAR President
Mike Helton (left) being presented a
Commandant Coin by Admiral
Thomas H. Collins (right) in 2005.
NASCAR
–
Junior Johnson, seen here in 1985, was a popular NASCAR driver from the 1950s who began as a bootlegging driver from
Wilkes County, North Carolina.
NASCAR
–
Richard Petty 's 1970 426 C.I.
Plymouth Superbird on display.
19.
Daytona 500
–
The Daytona 500 is a 500-mile-long Monster Energy NASCAR Cup Series motor race held annually at Daytona International Speedway in Daytona Beach, Florida. It is the first of two Cup races held every year at Daytona, the second being the Coke Zero 400 and it is one of the four restrictor plate races on the Cup schedule. The inaugural Daytona 500 was held in 1959 coinciding with the opening of the speedway and since 1982, the Daytona 500 is regarded as the most important and prestigious race on the NASCAR calendar, carrying by far the largest purse. Championship points awarded are equal to that of any other Monster Energy NASCAR Cup Series race. It is also the series first race of the year, this phenomenon is unique in sports. The 2006 Daytona 500 attracted the sixth largest average live global TV audience of any sporting event that year with 20 million viewers, the race serves as the final event of Speedweeks and is sometimes known as The Great American Race or the Super Bowl of Stock Car Racing. All 59 runnings of the race have been held in the month of February, from 1971 to 2011, it was associated with Presidents Day weekend, taking place on the Sunday before the third Monday in February. Beginning in 2012, the race was pushed up a week, because of inclement weather conditions on February 26, the 2012 Daytona 500 was postponed until the evening of Monday, February 27. The 2013 Daytona 500 was held on February 24, the first time the race was held on the last Sunday of February, the race is the direct successor of shorter races held on the Daytona Beach Road Course. This long square was partially on the sand and also on the highway near the beach, earlier events featured 200-mile races with stock cars. Eventually, a 500-mile stock car race was held at Daytona International Speedway in 1959 and it was the second 500-mile NASCAR race, following the annual Southern 500, and has been held every year since. By 1961, it began to be referred to as the Daytona 500, Daytona International Speedway is 2.5 miles long and a 500-mile race requires 200 laps to complete. However, the race is considered official after half its distance has been completed, the race has been shortened four times due to rain and once in response to the energy crisis of 1974. Since the adaptation of the green–white–checker finish rule in 2004, the race has gone past 500 miles on seven occasions,1959, Lee Petty, patriarch of the racing family, won the inaugural Daytona 500 on February 22,1959, defeating Johnny Beauchamp. 1965, The first rain-shortened Daytona 500 was the 1965 event, fred Lorenzen was in the lead when the race was called on lap 133 of 200. 1966, Richard Petty becomes the first two-time winner, having won the 1964 race. Through 2015, only 11 drivers have won 2 or more Daytona 500s,1967, Mario Andretti led 112 of the 200 laps including the last 33 to capture his first and only win in the Cup Series. 1968, For much of race, both Cale Yarborough and LeeRoy Yarbrough traded the lead
Daytona 500
–
Daytona 500
Daytona 500
–
Trevor Bayne, driving the No. 21
Motorcraft -sponsored
Ford for
Wood Brothers Racing, won the
2011 Daytona 500.
Daytona 500
–
Prerace ceremonies before the
2008 Daytona 500.
20.
Mile
–
The mile is an English unit of length of linear measure equal to 5,280 feet, or 1,760 yards, and standardised as exactly 1,609.344 metres by international agreement in 1959. The Romans divided their mile into 5,000 feet but the importance of furlongs in pre-modern England meant that the statute mile was made equivalent to 8 furlongs or 5,280 feet in 1593. This form of the mile then spread to the British-colonized nations who continue to employ the mile, the US Geological Survey now employs the metre for official purposes but legacy data from its 1927 geodetic datum has meant that a separate US survey mile continues to see some use. Derived units such as miles per hour and miles per gallon, however, continue to be abbreviated as mph, mpg. The modern English word mile derives from Middle English myl and Old English mīl, the present international mile is usually what is understood by the unqualified term mile. When this distance needs to be distinguished from the nautical mile, in British English, the statute mile may refer to the present international miles or to any other form of English mile since the 1593 Act of Parliament which set it as a distance of 1,760 yards. Under American law, however, the statute mile refers to the US survey mile, the mile has been variously abbreviated—with and without a trailing period—as m, M, ml, and mi. The American National Institute of Standards and Technology now uses and recommends mi in order to avoid confusion with the SI metre and millilitre. Derived units such as miles per hour and miles per gallon, however, continue to be abbreviated in the United States, United Kingdom, the BBC style holds that There is no acceptable abbreviation for ‘miles’ and so it should be spelt out when used in describing areas. The Roman mile consisted of a thousand paces as measured by every other step—as in the distance of the left foot hitting the ground 1,000 times. The ancient Romans, marching their armies through uncharted territory, would push a carved stick in the ground after each 1000 paces. Well-fed and harshly driven Roman legionaries in good weather thus created longer miles, the distance was indirectly standardised by Agrippas establishment of a standard Roman foot in 29 BC, and the definition of a pace as 5 feet. An Imperial Roman mile thus denoted 5,000 Roman feet, surveyors and specialized equipment such as the decempeda and dioptra then spread its use. In modern times, Agrippas Imperial Roman mile was empirically estimated to have been about 1,481 metres in length, in Hellenic areas of the Empire, the Roman mile was used beside the native Greek units as equivalent to 8 stadia of 600 Greek feet. The mílion continued to be used as a Byzantine unit and was used as the name of the zero mile marker for the Byzantine Empire. The Roman mile also spread throughout Europe, with its local variations giving rise to the different units below, also arising from the Roman mile is the milestone. All roads radiated out from the Roman Forum throughout the Empire –50,000 miles of stone-paved roads, at every mile was placed a shaped stone, on which was carved a Roman numeral, indicating the number of miles from the center of Rome – the Forum. Hence, one knew how far one was from Rome
Mile
–
A
milestone in
Westminster showing the distance from
Knightsbridge to
Hounslow and
Hyde Park Corner in miles.
Mile
–
The remains of the
Golden Milestone, the
zero mile marker of the
Roman road network, in the
Roman Forum.
Mile
–
Edinburgh 's "
Royal Mile "—running from
the castle to
Holyrood Abbey —is roughly a Scots mile long.
21.
Kilometers
–
The kilometre or kilometer is a unit of length in the metric system, equal to one thousand metres. K is occasionally used in some English-speaking countries as an alternative for the kilometre in colloquial writing. A slang term for the kilometre in the US military is klick, there are two common pronunciations for the word. It is generally preferred by the British Broadcasting Corporation and the Australian Broadcasting Corporation, many scientists and other users, particularly in countries where the metric system is not widely used, use the pronunciation with stress on the second syllable. The latter pronunciation follows the pattern used for the names of measuring instruments. The problem with this reasoning, however, is that the meter in those usages refers to a measuring device. The contrast is more obvious in countries using the British rather than American spelling of the word metre. When Australia introduced the system in 1975, the first pronunciation was declared official by the governments Metric Conversion Board. However, the Australian prime minister at the time, Gough Whitlam, by the 8 May 1790 decree, the Constituent assembly ordered the French Academy of Sciences to develop a new measurement system. In August 1793, the French National Convention decreed the metre as the length measurement system in the French Republic. The first name of the kilometre was Millaire, although the metre was formally defined in 1799, the myriametre was preferred to the kilometre for everyday use. The term myriamètre appeared a number of times in the text of Develeys book Physique dEmile, ou, Principes de la de la nature. French maps published in 1835 had scales showing myriametres and lieues de Poste, the Dutch, on the other hand, adopted the kilometre in 1817 but gave it the local name of the mijl. It was only in 1867 that the term became the only official unit of measure in the Netherlands to represent 1000 metres. In the US, the National Highway System Designation Act of 1995 prohibits the use of highway funds to convert existing signs or purchase new signs with metric units. Although the State DOTs had the option of using metric measurements or dual units, all of them abandoned metric measurements, the Manual on Uniform Traffic Control Devices since 2000 is published in both metric and American Customary Units. Some sporting disciplines feature 1000 m races in major events, but in other disciplines, even though records are catalogued
Kilometers
–
"km" redirects here. For other uses, see
KM (disambiguation).
Kilometers
–
Chinese expressway distances
road sign in eastern Beijing. Although the primary text is in Chinese, the distances use internationally recognised characters.
22.
Indy Racing League
–
INDYCAR is an American-based auto racing sanctioning body for Championship auto racing. The trade name INDYCAR was officially adopted on January 1,2011, INDYCAR is owned by Hulman & Company, which also owns the Indianapolis Motor Speedway complex and the Clabber Girl brand. The Leagues premier series was named the Indy Racing League IndyCar Series in 2003, in 2013, IZOD announced that they would be leaving the series. Verizon took over as sponsor in 2014, and the name became the Verizon IndyCar Series. The series initially raced exclusively on oval tracks, as the series was founded partly in response to the prominence of road. In 2005, the series abandoned its unofficial ovals-only stance, by 2009, the series had a roughly 50/50 split of ovals and road/street courses. Presently, the series currently runs one-third of its schedule on ovals, Indy Lights is the development series for the IndyCar series. It originally started in 2002, as the IRL Infiniti Pro Series coincidentally in the year as CARTs own Indy Lights series came to an end. Since the 2008 reunification, the Indy Lights name returned, the Indy Lights run as support races to IndyCar Series races. In the past, a round during the United States Grand Prix was also apart of the schedule, the series is now promoted by Andersen Promotions. The Pro Mazda Championship presented by Goodyear is a racecar driver development series in North America. Competitors use spec Formula Mazda race cars built by Star Race Cars, the original series, using first-generation tube-frame cars started in the early 1990s, with the current, high-tech, carbon-fiber car released in 2004. The series has historically included road courses, street courses, the series primary sponsors are Mazda and Cooper Tire and the cars, while purpose built for the track with carbon fiber monocoques, are powered by 250 horsepower Mazda Renesis rotary engines. The series stated goal is to develop new race driving talent, in 2010, the series became a part of The Road to Indy. In 2013 the series promotion was taken over by Andersen Promotions, uSF2000 is a series the organisation started sanctioning in 2010. Originally started in 1991 and folded in 2006, it was restarted in 2010 as part of the Road to Indy ladder series promoted by Andersen Promotions. The series utilizes tube frame Formula Ford chassis fitted with larger Mazda MZR four cylinder engines and wings, like other governing bodies, IndyCar awards points based upon where a driver finishes in a race. The top three drivers are separated by ten and five points respectively, the fourth through tenth-place finishers are separated by two points each
Indy Racing League
–
Hélio Castroneves practicing at the
2007 Indianapolis 500.
Indy Racing League
–
Indy Racing League, LLC
dba INDYCAR
Indy Racing League
–
Roberto Moreno practicing the
2007 Indianapolis 500.
Indy Racing League
–
Marco Andretti (left) practicing with father
Michael at Indy in 2007.
23.
Indianapolis 500
–
The Indianapolis 500 is an automobile race held annually at Indianapolis Motor Speedway in Speedway, Indiana, an enclave suburb of Indianapolis, Indiana. The event is held over Memorial Day weekend, which is typically the last weekend in May and it is contested as part of the Verizon IndyCar Series, the top level of American Championship Car racing, an open-wheel formula colloquially known as Indy Car Racing. The name of the race is often shortened to Indy 500, the event, billed as The Greatest Spectacle in Racing, is considered part of the Triple Crown of Motorsport, which comprises three of the most prestigious motorsports events in the world. The official attendance is not disclosed by Speedway management, but the permanent seating capacity is upwards of 250,000, the inaugural running was won by Ray Harroun in 1911. The race celebrated its 100th anniversary in 2011, and the 100th running was held in 2016, alexander Rossi is the defending champion. The most successful drivers are A. J. Foyt, Al Unser, the active driver with the most victories is Hélio Castroneves, with three. Rick Mears holds the record for most career pole positions with six, the most successful car owner is Roger Penske, owner of Team Penske, which has 16 total wins and 17 poles. For a list of races and winners, see List of Indianapolis 500 winners, the Indianapolis 500 is held annually at the Indianapolis Motor Speedway, a 2.5 mile oval circuit. Drivers race 200 laps, counterclockwise around the circuit, for a distance of 500 miles, since its inception in 1911, the race has always been scheduled on or around Memorial Day. Since 1974, the race has been scheduled for the Sunday of Memorial Day weekend, practice and time trials are held in the two weeks leading up to the race. Traditionally, the field consists of 33 starters, aligned in a grid of eleven rows of three cars apiece. The event is contested by Indy cars, a formula of professional-level, single-seat, open cockpit, open-wheel, as of 2015, all entrants utilize 2.2 L V6, twin-turbocharged engines, tuned to produce a range of 550–700 horsepower. Chevrolet and Honda are the current engine manufacturers involved in the sport, firestone, which has a deep history in the sport, dating back to the first 500, is the exclusive tire provider. The race is the most prestigious event of the IndyCar calendar and it has been avouched to be the largest single-day sporting event in the entire world. Likewise, the Indianapolis Motor Speedway itself is regarded as the worlds largest sporting facility in terms of capacity, the total purse exceeded $13 million in 2011, with over $2.5 million awarded to the winner, making it one of the richest cash prize funds in sports. Due to safety issues, the race is not held in wet conditions, in the event of a rain delay, the race will be postponed until rain showers cease, and the track is sufficiently dried. If rain falls during the race, officials can end the race, the Indianapolis Motor Speedway complex was built in 1909 as a gravel-and-tar track and hosted a smattering of small events, including ones for motorcycles. The first long distance event, in conditions, was the 100-lap Prest-O-Lite Trophy in 1909
Indianapolis 500
–
Joe Dawson winning the
1912 Indianapolis 500
Indianapolis 500
–
The
Mercedes-Benz W154 entered by Don Lee at the
1947 Indianapolis 500 with
Duke Nalon as driver
Indianapolis 500
–
Emerson Fittipaldi driving the
Penske PC-23 at the
1994 event
Indianapolis 500
–
The
Indianapolis Motor Speedway
24.
Fiat 500
–
Launched as the Nuova 500 in July 1957, it was a cheap and practical town car. Measuring 2.97 metres long, and originally powered by a 479 cc two-cylinder, air-cooled engine, the 500 is considered one of the first city cars. In 2007, the 50th anniversary of the Nuova 500s launch, Fiat launched another new 500, stylistically inspired by the 1957 Nuova 500, featuring a front-mounted engine and front-wheel drive. To meet the demands of the market which called for economy cars. It had a 2-door coupe body with sun-roof, which was complemented by an Estate version. Both continued until 1954 when they were replaced by an all-new, the new car had a rear-mounted engine, on the pattern of the Volkswagen Beetle, just like its bigger brother the 1955 Fiat 600. Several car makers followed the now uncommon rear engine configuration at the time and were quite successful, the Neckar version of the 500 was manufactured in Heilbronn under a complicated deal involving NSU, and was introduced in October 1961. Steyr-Puch produced cars based on the Fiat 500 under license in Graz, despite its diminutive size, the 500 proved to be an enormously practical and popular vehicle throughout Europe. Sports models were produced by Abarth, as well as by Giannini. An Austrian variant, produced by Steyr-Daimler-Puch, the 1957–1973 Steyr-Puch 500, had a motorcycle-derived Puch boxer twin motor, production of the 500 ended in 1975, although its replacement, the Fiat 126, was launched two years earlier. The 126 was never as popular as its predecessor in Italy, but was popular in the former Eastern Bloc countries. The Fiat 500 has a Cx of 0,38, a good performance for its time. The 500 features a 479 cc two-cylinder engine, hence the name, producing just 13 horsepower. This model also features a roof, foldable to the rear of the vehicle, like that of a Citroën 2CV — rather than the later roof design. The Nuova 500 is one of three models featuring suicide doors, including the Sport model, in total 181,036 examples of the Nuova 500 were produced from 1957 to 1960. In mid-1958 Fiat introduced the Nuova 500 Sport, featuring a powerful engine. Unique to the Sport was a rigid roof with three longitudinal grooves. A short-open-roof model was added a later, in 1959
Fiat 500
–
1970 Fiat 500 L
Fiat 500
–
Fiat 500 Giardiniera
Fiat 500
–
Fiat 500 Furgoncino
Fiat 500
–
Fiat 500 F
25.
Ford Five Hundred
–
The Ford Five Hundred is a full-size sedan that was produced by Ford Motor Company from the 2005 to the 2007 model years. Deriving its name from the Ford Fairlane 500 and Ford Galaxie 500 popularized during the 1960s, the larger of the two vehicles, the Five Hundred would also serve as an unofficial replacement for the Ford Crown Victoria in non-fleet markets. The Lincoln-Mercury Division marketed the Ford Five Hundred as the Mercury Montego, as the Five Hundred was sold solely as a four-door sedan, the role of the Ford Taurus station wagon was taken over by the Ford Freestyle, repackaged as a crossover SUV. The Ford Five Hundred/Mercury Montego were based upon the Volvo-derived Ford D3 platform, for the first time ever, a Ford full-size sedan was produced without rear-wheel drive. The Five Hundred/Montego utilize a standard front-wheel drive configuration, an electro-hydraulic Haldex all-wheel drive system is optional, the Five Hundred was produced alongside the Montego and Freestyle at Chicago Assembly in Chicago, Illinois. Outside of the United States and Canada, the Ford Five Hundred was marketed in Mexico, South Korea, while the Five Hundred name would remain in Mexico and the Middle East, the fifth-generation Ford Taurus was produced from 2008 to 2009. The Ford Freestyle crossover SUV was merged into the Taurus line, as part of the 1999 acquisition of Volvo Cars and its addition to Premier Automotive Group, Ford Motor Company expanded on its vehicle safety technology capabilities. In 2000, the Ford Prodigy concept car was shown, the Ford Five Hundred entered production on July 12,2004 at Chicago Assembly, and became available to the public in September 2004. The Ford Five Hundred/Mercury Montego were engineered with a quality control system named Total Vehicle Geometry, designed by Volvo, TVG is heavily computer-based, allowing for designers, engineers, and suppliers access for all data and results related to prototypes at all stages of the design process. With improved participation and access, fit and finish increased on prototype parts, decreasing the time needed for production vehicles. The Ford Five Hundred is based on the Ford D3 platform, shared with the Mercury Montego, alongside standard dual front airbags, the Five Hundred was available with both side airbags and curtain airbags as an option. As with the Ford Crown Victoria, the Five Hundred was configured with four-wheel anti-lock disc brakes. The Ford Five Hundred/Mercury Montego were powered by an engine, shared with the Ford Taurus. A distinguishing feature of the Ford Five Hundred is its tall exterior height, at 61.5 inches tall, it is over 5 inches taller than the Ford Taurus sold alongside it. A key feature driving the use of the body design was the upward movement of the H-point. In addition, the seat was positioned higher than the front seats. While visibility was one factor behind the seating position, safety was another as well. Under the front seats, a hydroformed cross-car steel beam is welded in between the B-pillars, designed as part of an side-impact safety design derived from Side Impact Protection System from Volvo
Ford Five Hundred
–
2005 Ford Five Hundred Limited AWD
Ford Five Hundred
–
2000
Ford Prodigy diesel-electric concept, which partly influenced the body design of the Five Hundred/Montego
Ford Five Hundred
–
2005 Five Hundred SE
Ford Five Hundred
–
Ford Mondeo
26.
Ford Galaxie
–
The Ford Galaxie was a full-sized car that was built in the United States of America by Ford for model years 1959 through to 1974. The name was used for the top models in Fords full-size range from 1958 until 1961, for 1962, all full-size Fords wore the Galaxie badge, with 500 and 500/XL denoting the higher series. The Galaxie 500/LTD was introduced for 1965 followed by the Galaxie 500 7-Litre for 1966, the Galaxie 500 part was dropped from the LTD in 1966, and from the XL in 1967, however the basic series structuring levels were maintained. The regular Galaxie 500 continued below the LTD as Fords mid-level full-size model from 1965 until its demise at the end of the 1974 model year, the Galaxie was the high volume counterpart to the Chevrolet Impala. The similarly named Ford Galaxy is a large car/minivan available in the European market, the vehicles name is derived from the original Ford Galaxie. The 1959 Ford range was introduced in late 1958 with the Fairlane 500 as the top trim level, during the 1959 model year the Galaxie was added to the range as an additional trim level, assuming the top position from the Fairlane 500. The Galaxie was offered with the sedan and hardtop body styles as the Fairlane 500 whilst the Sunliner and Skyliner convertibles were moved across from the Fairlane 500 range. Styling varied from the Fairlane 500 with the addition of a Ford Thunderbird-style C pillar on all, although a separate series from the Fairlane 500,1959 Galaxie models carried both Fairlane 500 and Galaxie badging. In keeping with the era, the 1959 Galaxie was a chrome and it was the very image of the ostentatious late-1950s American automobiles, though somewhat tamer than its Chevrolet and Plymouth competitors. Ford advertised safety anchorage for the front seats, the parking brake was now a pedal. Seat belts, a dashboard, and child-proof rear door locks were optional, while a deep-dished steering wheel. Among the models was the Skyliner, moved upward from the Fairlane 500 model and this feature, complicated and expensive, left very little trunk room when folded down. Not until 2006, when the Pontiac G6 convertible, Peugeot 206 CC and Volkswagen Eos appeared, a fixture also was the previous years 352 V8, still developing 300 horsepower. 1960 The 1960 Galaxie introduced all-new design with less ornamentation, a new body style was the Starliner, featuring a huge, curving rear observation window on a pillarless, hardtop bodyshell. The formal roofed 2-door hardtop was not available this year, but the roofline was used for the Galaxie 2-door pillared sedan and it had been the most popular body style in the line for 1959, and sales dropped off sharply. Contrary to Fords tradition of pie-plate round taillghts, the 1960 featured half-moon lenses turned downward, the A pillar now swept forward instead of backward, making entering and exiting the car more convenient. 1961 For 1961, the bodywork was again, although the underpinnings were the same as for 1960. This time, the tailfins were almost gone, the small blade-like fins capped smaller versions of 1959s pie-plate round taillamps once again, the latter was rated at 401 hp
Ford Galaxie
–
1963 Ford Galaxie 500 4-Door Sedan
Ford Galaxie
–
1959 Ford Galaxie Club Victoria
Ford Galaxie
–
1959 Ford Galaxie Town Sedan
Ford Galaxie
27.
Ford Custom 500
–
The Ford Custom is an automobile which was produced by Ford in the United States, Canada, Europe and Australia in certain years from 1949 to 1981. For the 1949 model year, the Custom nameplate was used for the top level in Fords range automobile. It was part of the new redesign of Ford cars after the war. In 1950, it had a 114-inch wheelbase and 196. 8-inch overall length, for 1950 the name was changed to Custom Deluxe and then to Customline for 1952 when it moved to the midrange position between the new Mainline and Crestline models. The Custom name returned for the 1957 model year along with a new Custom 300 series, the base Custom was the bottom-rung model, whose primary customers were fleet buyers. The Custom 300 was a step up and intended for value-conscious customers, the Custom and Custom 300 generally replaced the fleet-oriented Mainline and mid-range Customline, respectively, from 1956. The Custom 300 became the model for 1958, but was dropped from the range for 1960. From 1960-1963, the Custom and number-affixated variant nameplates were absent from the lineup, base 1963 Fords were badged as the Ford 300. The Custom nameplate reappeared in 1964, once again on the line of models. As in 1957-1958, the Custom range consisted of two series, a base Custom range and a slightly-better trimmed Custom 500 series. The six-cylinder engine/manual transmission power team was shelved for 1973, all full-sized Fords from 1973 onward, including the Custom 500, had a V8 engine, the Ford Custom was dropped after the 1972 model year, although the Custom 500 continued for several more years. Starting in 1975, all big Fords were restyled and grew in size, from that time until 1978, the car was only available as fleet vehicle and wasnt even featured in sales catalogues. The Custom 500 line continued from 1979 until 1981 in Canada, in the United States, the Custom 500 was renamed LTD S. The companion station wagon series sold with Custom and Custom 500 trim was the Ranch Wagon, like the coupe and sedan models, these cars were intended for fleet buyers. The 1979-1981 Custom 500s for the Canadian market were restyled using the Panther platform and had the base-model 1979 Ford LTD grill, base powerteam in 1979 was the 302 cubic-inch V8 and SelectShift transmission. For 1980, to meet EPA CAFE standards, a 255 cubic-inch V8 was made standard, approximately 7,850,000 full-size Fords and Mercurys were sold over 1969-78. This makes it the tenth best selling automobile platform in history, marion Crane, played by Janet Leigh, traded a black 1956 Ford for a white 1957 Ford Custom in the Alfred Hitchcock film Psycho. Unusually, scenes of the movie depict the cars with either a manual or automatic transmissions, a blue 1973 Ford Galaxie 460 Interceptor was used in the movie THE DRIVER1978
Ford Custom 500
–
1951 Ford Custom Deluxe Tudor
Ford Custom 500
–
1950 Ford Custom Deluxe Club Coupe
Ford Custom 500
–
1957 Ford Custom
Ford Custom 500
–
1958 Ford Custom 300 Sedan
28.
Galaxie 500
–
Galaxie 500 was an American alternative rock band that formed in 1987 and split up in 1991 after releasing three albums. Wareham and Krukowski had formed a series of punk-influenced student bands, before Wareham returned to New York. When he returned in 1987 he and Krukowski formed a new band, with Yang joining the group on guitar, the new group deciding on the name Galaxie 500, after a friends car. In their early years, Krukowski didnt own a drum kit, so he borrowed one from his Harvard classmate Conan OBrien and this drum kit can be heard on many of Galaxie 500s early recordings. The band began playing gigs in Boston and New York City, and recorded a demo which they sent to Shimmy Disc label boss and producer Mark Kramer, Galaxie 500 recorded two sessions for John Peels BBC Radio 1 programme, these later released on the Peel Sessions album. Their cover of Jonathan Richmans Dont Let Our Youth Go To Waste was also voted into number 41 in 1989s Festive 50 by listeners to the show, the band split up in the spring of 1991 after the release of their third album, This Is Our Music. Wareham, who had moved back to New York, quit the band after a lengthy American tour. Galaxie 500s records were released in the US and UK on the independent Rough Trade label. When Rough Trade went bankrupt in 1991, Krukowski and Yang purchased the masters at auction, Galaxie 500 used fairly simple instrumental techniques enhanced with an atmospheric production style. The Velvet Underground and Jonathan Richman have been identified as key influences, in interviews on the Galaxie 500 DVD Dont Let Our Youth Go to Waste, Wareham cites Spacemen 3 as another key inspiration. After leaving Galaxie 500, Wareham tried his hand at production and he released a solo single, Anesthesia, in February 1992, and formed a new band, Luna. Krukowski and Yang continued to record under the moniker Pierre Etoile, and then Damon and Naomi and they also began the avant-garde press Exact Change. Galaxie 500s music had an influence on many later indie music groups and it has been covered and referenced by several well known artists. In Liz Phairs song Stratford-on-Guy, she sings, And I was pretending that I was in a Galaxie 500 video, in Xiu Xius song Dr. Troll, Jamie Stewart sings, Listen to On Fire and pretend someone could love you. The Brian Jonestown Massacres And This Is Our Music was titled in reference to the groups album This Is Our Music, sonic Youth frontman Thurston Moore has cited Galaxie 500s album Today as the guitar record of 1988. Welsh lo-fi band Joanna Gruesome, and Portastatic, in 2010 the bands Cloudland Canyon and Citay, appeared on a 7 EP together wherein they both covered Galaxie 500, the former taking on Temperatures Rising and the latter doing a version of Tugboat. English artist World Of Fox covered Flowers in his 2011 release on Where Its At Is Where You Are Records, in 2012 the song Tugboat was featured in the film The Perks of Being a Wallflower, directed by Stephen Chbosky and based on his book of the same name. Black Postcards, A Rock & Roll Romance
Galaxie 500
–
Galaxie 500.
29.
Galaxie (band)
–
Galaxie is a francophone indie garage rock band formed in 2002 in Montreal, Quebec, Canada. Formerly known as Galaxie 500, they should not be confused with the American alternative rock band Galaxie 500, under their original name, the band released two albums, Galaxie 500 and Le Temps au point mort, on the C4 Records label. Following the release of Le Temps au Point Mort, Galaxie 500 was nominated for the Group of the Year award in the 10th annual MIMI awards, the lineup that recorded Galaxie 500 consisted of Olivier Langevin, Pierre Girard, Fred Fortin, Simon Gauthier, and Michel Dufour. Several changes in personnel occurred between the recording of the two albums, for Le Temps au point mort, Langevin was joined by returning members Girard and Fortin, and by Vincent Peake of Groovy Aardvark and Frank Lafontaine of Karkwa. Under its current name, the band released its album, Tigre et diesel. The album was named a shortlisted nominee for the 2011 Polaris Music Prize
Galaxie (band)
–
Galaxie live in June 2011
30.
500 (card game)
–
500 or Five Hundred is a trick-taking game that is an extension of Euchre with some ideas from Bridge. For two to six players it is most commonly played by four players in partnerships but is recommended as a good three player game. It arose in America before 1900 and was promoted by the United States Playing Card Company,500 is a social card game and was highly popular in the United States until around 1920 when first Auction bridge and then Contract Bridge drove it from favour. It continues to enjoy popularity in Australia, New Zealand, Quebec, of the many variants to 500, the standard deck contains 43 playing cards, a Joker is included, and the 2s, 3s, and two 4s are removed. Cards are dealt to each of the four players and three are dealt face down on the table to form the kitty Alternatively, a 45 card deck can be used, each player still receives a hand of 10 cards, but the kitty is increased to five cards. Players play in pairs, usually opposite each other, as in Euchre, in non-trump suits, the order of cards from highest to lowest is Ace, King, Queen,10,9,8,7,6,5. Bower is an Anglicization of the German Bauer, a word meaning farmer, peasant and this name is often used to refer to the Jack of German games. After the deal, players call in turn, electing either to bid or to pass. A bid indicates the number of tricks the bidder believes he and his partner will take. In American play, a bid of six is called cheating, a player who bids inkle spades is indicating to their partner that they have some spades but not enough to bid seven. Only the first two players may inkle, a player may elect not to bid, or to pass. Bidding proceeds clockwise around the table, with each player passing or making a higher-scoring bid, a player who passes cannot subsequently make a bid in that hand. A player who has bid may only bid again in that if there has been an intervening bid by another player. However, in some variations a player who has bid and not passed may always bid again in that hand, the order of seniority of suits in bidding is hearts, diamonds, clubs, spades. Therefore, for example, a player who bids seven clubs may be outbid by a subsequent bidding player on seven diamonds or seven hearts, a no trumps bid beats any suited bid of the same number. Inkles are typically also similarly ranked, If the first player bids six hearts and their only options are to inkle no trump, bid seven or more, or pass. Eventually, all but one player passes and the bid is decided, in American play, there is only one round of bidding, with each player getting one chance, in turn, to either bid or pass. The player making the bid then collects the kitty
500 (card game)
–
11 of Hearts
31.
500 Rum
–
500 rum, also called pinochle rummy, Michigan rummy, rummy 500 or 500 rummy, is a popular variant of rummy. The game of canasta and several games are believed to have developed from this popular form of rummy. The distinctive feature of 500 Rum is that player scores the value of the sets he melds. It may be played by 2 to 8 players, but it is best for 3 to 5, the term Michigan Rummy may also refer to an unrelated game involving a playing board, chips, and accumulated pots that are awarded to players who play certain cards. 500 rum is played using a standard French deck and can use 52 cards, when playing with 5 or more players, a double pack should be substituted for 104-108 cards. The players draw for deal, low dealing first, Ace is the lowest card in the draw. The dealer shuffles, and the player to the right cuts, the dealer completes the cut and deals cards to each player and an extra one to the player to the left who discards. The player that wins the previous hand then becomes the dealer in the next game, the number of cards dealt depends on the number of players. The object of the game is to score points by laying down and laying off cards as in regular rummy, Aces are high or low, they may be played after the king or before the two card. The remaining portion of the cards, placed face down, forms the stock, the discard pile should be slightly spread, so that players can readily see all the cards in it. Each player in turn, beginning with the player to the left of the dealer, there are three conditions when drawing a card from the discard pile, The player must take all the cards on top of the selected card. The card so drawn must immediately be used, either by laying it down in a set or by laying it off on a set already on the table. Once a card is picked up, either of the stock or the pile, it is final, the remaining cards taken with the discard may be melded in the same turn or simply added to the players hand. Each player in turn, after drawing but before discarding, may lay down any matched set or may lay off any card that matches a set already on the table, cards that are laid off are kept on the table in front of the player. The player ends his turn by discarding a card from his hand. Sequences may not go round the corner, thus, Q K A or A23 may be melded, but not K A2. If jokers are used in the game, they are treated as wild cards, the game is over when one player has no cards in his or her hand and either by melding or laying off all cards or when there are no cards left in the stock pile. Players receive no bonus for finishing first, when picking up from the discard pile you cannot pick up just to share a card
500 Rum
–
500 Rum
32.
(500) Days of Summer
–
500 Days of Summer is a 2009 American romantic comedy-drama film directed by Marc Webb from a screenplay written by Scott Neustadter and Michael H. Weber, and produced by Mark Waters. The film stars Joseph Gordon-Levitt and Zooey Deschanel, and employs a narrative structure, with the story based upon its male protagonist. As an independent production, the film was picked up for distribution by Fox Searchlight Pictures and it garnered critical acclaim and became a successful sleeper hit, earning over $60 million in worldwide returns, far exceeding its $7.5 million budget. Many critics lauded the film as one of the best from 2009 and drew comparisons to other acclaimed films such as Annie Hall, the film is presented in a nonlinear narrative, jumping between various days within the 500 days of Tom and Summers relationship. This is a summary of the plot. On January 8, Tom Hansen meets Summer Finn, his bosss new assistant, Tom is trained as an architect but works as a writer at a greeting card company in Los Angeles. After discovering they have a taste in music, they have a conversation about love, Tom believes in it. Following a karaoke night, Toms friend and co-worker McKenzie drunkenly reveals that Tom likes Summer, a few days later, Summer kisses Tom in the copy room at work. During the next few months Summer and Tom grow closer, Tom shows Summer his favorite spot in the city, which overlooks a number of buildings he likes, though the view is somewhat spoiled by parking lots. One night, Tom gets into a fight with a man who tries to pick up Summer in a bar, which causes their first argument. They make up and Summer concedes Tom deserves some certainty, on day 290, Summer breaks up with Tom in a diner after an awkward conversation at the record store, where Summer appears to have lost interest in Tom. Summer wants them to friends, but Tom is devastated. Summer quits her job at the card company. Toms boss moves him to the department, as his depression is not suitable for happier events. Tom goes on a date with a woman named Alison. The date does not go well as he spends it complaining about Summer until an exasperated Alison ends up taking Summers side, months later, Tom attends co-worker Millies wedding and tries to avoid Summer on the train, but she spots him and invites him for coffee. They have a time at the wedding, dance together. She invites Tom to a party at her apartment and falls asleep on Toms shoulder on the ride back
(500) Days of Summer
–
Theatrical release poster
(500) Days of Summer
–
The
Bradbury Building in Los Angeles was a filming location.
(500) Days of Summer
–
Joseph Gordon-Levitt and Zooey Deschanel at the film's premiere in March 2009.
(500) Days of Summer
–
500 Days of Summer
33.
Marc Webb
–
Marc Preston Webb is an American music video, short film, and film director. Webb was born in Bloomington, Indiana, the son of Margaret Ruth and Norman Lott Webb, when he was eighteen months old, Webbs family moved to Madison, Wisconsin, where he was raised. He graduated from Madison West High School in 1992, and subsequently attended Colorado College, and his feature length debut, Days of Summer, starring Joseph Gordon-Levitt and Zooey Deschanel, was released in July 2009 to a positive critical reception. In January 2010, Columbia Pictures hired Webb to direct The Amazing Spider-Man and he returned to direct the sequel, The Amazing Spider-Man 2, which was released on May 2,2014. In 2015, Marc Webb directed promotional ads for a partnership between Samsung and Avengers, Age of Ultron, Webb is signed to DNA in Hollywood, California and Academy Productions Ltd in the United Kingdom. Webbs signature is a lamb, which has appeared in a few of his videos. In Brand News Sic Transit Gloria, glory Fades video, the lamb appears on the door before Jesse Lacey enters the bar. It also appears on the shirt of a girl in the bar, in Yellowcards Ocean Avenue and Rough Landing, Holly videos, the lamb appears on the briefcase Ryan Key carries around. Crazy Ex-Girlfriend Where Is Joshs Friend. O. D. – Sleeping Awake AFI – The Leaving Song Pt. II Santana & Alex Band – Why Dont You & I3 Doors Down – Here Without You Memento – Savior Wakefield – Say You Will MxPx – Everything Sucks P. O. D. – Will You Brand New – Sic Transit Gloria, glory Fades Santana featuring Musiq – Nothing at All 2004 Cold – With My Mind P. O. D. Green Day – 21st Century Breakdown Weezer – I Want You To 2010 Green Day – Last of the American Girls MxPx – Everything Sucks Brand New – Sic Transit Gloria. Glory Fades Marc Webb at the Internet Movie Database Marc Webb on Twitter Marc Webb at MVDbase. com Die Musik Video Datenbank
Marc Webb
–
Webb in July 2013
34.
HTTP 500
–
This is a list of Hypertext Transfer Protocol response status codes. It includes codes from IETF Request for Comments, other specifications, the first digit of the status code specifies one of five standard classes of responses. The message phrases shown are typical, but any human-readable alternative may be provided, unless otherwise stated, the status code is part of the HTTP/1.1 standard. The Internet Assigned Numbers Authority maintains the registry of HTTP status codes. An informational response indicates that the request was received and understood and it is issued on a provisional basis while request processing continues. It alerts the client to wait for a final response, the message consists only of the status line and optional header fields, and is terminated by an empty line. As the HTTP/1.0 standard did not define any 1xx status codes,100 Continue The server has received the request headers and the client should proceed to send the request body. Sending a large request body to a server after a request has been rejected for inappropriate headers would be inefficient. To have a check the requests headers, a client must send Expect, 100-continue as a header in its initial request. The response 417 Expectation Failed indicates the request should not be continued,101 Switching Protocols The requester has asked the server to switch protocols and the server has agreed to do so. 102 Processing A WebDAV request may contain many sub-requests involving file operations and this code indicates that the server has received and is processing the request, but no response is available yet. This prevents the client from timing out and assuming the request was lost and this class of status codes indicates the action requested by the client was received, understood, accepted, and processed successfully. 200 OK Standard response for successful HTTP requests, the actual response will depend on the request method used. In a GET request, the response will contain an entity corresponding to the requested resource, in a POST request, the response will contain an entity describing or containing the result of the action. 201 Created The request has been fulfilled, resulting in the creation of a new resource,202 Accepted The request has been accepted for processing, but the processing has not been completed. The request might or might not be acted upon. 203 Non-Authoritative Information The server is a proxy that received a 200 OK from its origin. 204 No Content The server successfully processed the request and is not returning any content,205 Reset Content The server successfully processed the request, but is not returning any content
HTTP 500
–
404 error on German Wikipedia
35.
Simple Mail Transfer Protocol
–
Simple Mail Transfer Protocol is an Internet standard for electronic mail transmission. First defined by RFC821 in 1982, it was last updated in 2008 with Extended SMTP additions by RFC5321, for retrieving messages, client applications usually use either IMAP or POP3. SMTP communication between mail servers uses TCP port 25, Mail clients on the other hand, often submit the outgoing emails to a mail server on port 587. Despite being deprecated, mail providers sometimes still permit the use of nonstandard port 465 for this purpose, SMTP connections secured by SSL, known as SMTPS, can be made using STARTTLS. Various forms of electronic messaging were used in the 1960s. People communicated with one another using systems developed for specific mainframe computers, as more computers were interconnected, especially in the US Governments ARPANET, standards were developed to allow users of different systems to email one another. SMTP grew out of these standards developed during the 1970s, fewer than 50 hosts were connected to the ARPANET at this time. Further implementations include FTP Mail and Mail Protocol, both from 1973, development work continued throughout the 1970s, until the ARPANET transitioned into the modern Internet around 1980. Jon Postel then proposed a Mail Transfer Protocol in 1980 that began to remove the reliance on FTP. SMTP was published as RFC788 in November 1981, also by Postel, the SMTP standard was developed around the same time as Usenet, a one-to-many communication network with some similarities. SMTP became widely used in the early 1980s, at the time, it was a complement to Unix to Unix Copy Program mail, which was better suited for handling email transfers between machines that were intermittently connected. SMTP, on the hand, works best when both the sending and receiving machines are connected to the network all the time. Both use a store and forward mechanism and are examples of push technology, though Usenets newsgroups are still propagated with UUCP between servers, UUCP as a mail transport has virtually disappeared along with the bang paths it used as message routing headers. Sendmail, released with 4. 1cBSD, right after RFC788, was one of the first mail transfer agents to implement SMTP, over time, as BSD Unix became the most popular operating system on the Internet, sendmail became the most common MTA. Some other popular SMTP server programs include Postfix, qmail, Novell GroupWise, Exim, Novell NetMail, Microsoft Exchange Server, Message submission and SMTP-AUTH were introduced in 1998 and 1999, both describing new trends in email delivery. Originally, SMTP servers were typically internal to an organization, receiving mail for the organization from the outside and this behavior is helpful when the message being fixed is an initial submission, but dangerous and harmful when the message originated elsewhere and is being relayed. Cleanly separating mail into submission and relay was seen as a way to permit, as spam became more prevalent, it was also seen as a way to provide authorization for mail being sent out from an organization, as well as traceability. This separation of relay and submission quickly became a foundation for modern email security practices, as this protocol started out purely ASCII text-based, it did not deal well with binary files, or characters in many non-English languages
Simple Mail Transfer Protocol
–
An
Opte Project visualization of
routing paths through a portion of the Internet
36.
500 BC
–
The year 500 BC was a year of the pre-Julian Roman calendar. In the Roman Empire it was known as the Year of the Consulship of Camerinus and Longus, the denomination 500 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Vulca makes Apollo of Veii, from Portonaccio Temple and it is now kept at Museo Nazionale di Villa Giulia, Rome. The Nordic Bronze Age civilization ends and the Pre-Roman Iron Age begins in Scandinavia, darius I of Persia proclaims that Aramaic be the official language of the western half of his empire. Bantu-speaking people migrate into south-west Uganda from Northeastern Africa, the Hutu tribe begins around this time, in Middle and Southern Africa. Approximate date Hanno the Navigators naval exploration of the western coast of Africa could have reached as far south as Gabon, the first republic in Vaishali, Bihar, India is founded. Yayoi period starts in Ancient Japan, the oldest known Zapotec writing appears. The Olmecs establish Monte Albán, the city, and continue building pyramids. World population reaches 100,000, 000—the population is 85,000,000 in Eastern hemisphere and 15,000,000 in Western Hemisphere, she-Wolf, with late 15th century or early 16th century additions, is made. It is now kept at the Museo Capitolino in Rome
500 BC
–
The world's cultural distribution at 500 BC
37.
Permille
–
A per mille, also spelled per mil, per mill, permil, permill, or permille is a sign indicating parts per thousand. Per mil should not be confused with parts per million, the sign is written ‰, which looks like a percent sign with an extra zero in the divisor. It is included in the General Punctuation block of Unicode characters and it is accessible in Windows using ALT+0137. The term is common in other European languages where it is used in contexts, such as blood alcohol content. Examples of common use include, Legal limits of blood-alcohol content for driving a vehicle in some countries. Seawater salinity, for example, the salinity is 35‰
Permille
–
A railroad distance and gradient sign in the
Czech Republic. The 20‰
grade is equivalent to 2%.
38.
Folk song
–
Folk music includes both traditional music and the genre that evolved from it during the 20th century folk revival. The term originated in the 19th century, but is applied to music older than that. Some types of music are also called world music. Traditional folk music has been defined in several ways, as music transmitted orally, music with unknown composers and it has been contrasted with commercial and classical styles. Starting in the century, a new form of popular folk music evolved from traditional folk music. This process and period is called the revival and reached a zenith in the 1960s. This form of music is called contemporary folk music or folk revival music to distinguish it from earlier folk forms. Smaller, similar revivals have occurred elsewhere in the world at other times and this type of folk music also includes fusion genres such as folk rock, folk metal, electric folk, and others. Even individual songs may be a blend of the two, a consistent definition of traditional folk music is elusive. The terms folk music, folk song, and folk dance are comparatively recent expressions and they are extensions of the term folklore, which was coined in 1846 by the English antiquarian William Thoms to describe the traditions, customs, and superstitions of the uncultured classes. Traditional folk music also includes most indigenous music, however, despite the assembly of an enormous body of work over some two centuries, there is still no certain definition of what folk music is. Some do not even agree that the term Folk Music should be used, Folk music may tend to have certain characteristics but it cannot clearly be differentiated in purely musical terms. One meaning often given is that of old songs, with no known composers, the fashioning and re-fashioning of the music by the community that give it its folk character. Such definitions depend upon processes rather than abstract musical types, one widely used definition is simply Folk music is what the people sing. For Scholes, as well as for Cecil Sharp and Béla Bartók, Folk music was already. seen as the authentic expression of a way of life now past or about to disappear, particularly in a community uninfluenced by art music and by commercial and printed song. In these terms folk music may be seen as part of a schema comprising four types, primitive or tribal, elite or art, folk. Music in this genre is often called traditional music. Although the term is only descriptive, in some cases people use it as the name of a genre
Folk song
–
Béla Bartók recording Slovak peasant singers in 1908
Folk song
–
Indians always distinguished between classical and folk music, though in the past even classical Indian music used to rely on the unwritten transmission of repertoire.
Folk song
–
Armenian traditional musicians
Folk song
–
Assyrians playing
zurna and
Davul, the typically used instruments for their folk music.
39.
I would walk 500 miles
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Im Gonna Be is a song written and performed by Scottish duo The Proclaimers, and first released as the lead single from their 1988 album Sunshine on Leith. Im Gonna Be has become a staple at the Proclaimers concerts. The duo played it at Edinburgh 50,000 – The Final Push at Murrayfield Stadium on 6 July 2005, the song was mainly written by Craig Reid in mid-1987 while waiting to travel to a Proclaimers concert in Aberdeen. Reid recalled, I can remember sitting at the piano and the chords just came to me, I reckon I wrote the whole thing in 45 minutes. I knew that it was a song, maybe even a single. Reid has said that the earnings from the song are about five times the rest of their catalogue combined. All tracks written and composed by Charlie and Craig Reid, except where noted, there is a slight change in the title of the song, with the parentheses placed around Im Gonna Be rather than 500 Miles. The lyrics also include a change, with the words roll 500 miles replacing walk 500 miles, because the characters Brian Potter and Andy Pipkin are both in wheelchairs. 500 Miles was released as a charity single for Comic Relief immediately following its performance on the Comic Relief 2007 and it reached number 3 on the official UK Singles Chart on download sales alone, and one week later reached number 1, where it remained for three weeks. It sold 126,000 copies in its first week, making it the biggest selling number one of the year up to that point. Its sales were double that of the official Comic Relief single by Girls Aloud vs. Sugababes, the song ended 2007 as the years 8th biggest-selling single in the UK. The song was popular in Ireland as well, and peaked at #7 in Irish Singles Chart, osama bin Laden, Lord Lucan and Shergar are also falsely credited as appearing in the video. CD single 500 Miles –3,41500 Miles –3,39 The enhanced CD and DVD also featured the video for the song. The song is played in the warm up before the Scotland football team matches when playing at home at Hampden Park in Glasgow. The song is often played at Easter Road before Scottish Premiership side Hibernians home matches. Scottish darts player Robert Thornton uses the song as his walk-on song, in 2007, Alvin and the Chipmunks covered the song, with minor lyric changes, for their video game Alvin and the Chipmunks. The song was very popular in Spain in the late 1990s thanks to TV advertisements. It was a song for the ads of Retevisión, one of the first private telecommunications companies in Spain
I would walk 500 miles
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"I'm Gonna Be (500 Miles)"
40.
The Proclaimers
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The Proclaimers are a Scottish band composed of twin brothers Charlie and Craig Reid. They are best known for the songs Im Gonna Be, Sunshine on Leith, Im On My Way and Letter from America, the band tours extensively throughout the world. They have released ten studio albums since 1987 as well as three albums and a DVD. Craig Reid and Charlie Reid were born in Leith on 5 March 1962, when they lived in Auchtermuchty they attended Bell Baxter High School. After several punk bands at school they formed the Proclaimers in 1983. The follow-up album Sunshine on Leith featured the singles Im Gonna Be, which went to one in Australia and New Zealand. They had a hit with their EP King of the Road, Im Gonna Be belatedly peaked at number three in the US in 1993, after appearing in the movie Benny & Joon. After seven low-profile years, they released their comeback album Persevere in 2001, in March 2007 they recorded a new version of Im Gonna Be with television comedy characters Andy Pipkin and Brian Potter for the Comic Relief charity. A long list of celebrities were featured in the video for this new version, including David Bellamy, Rod, Jane and Freddy, Paul OGrady, David Tennant, Frank Sidebottom. This new version of the reached number one in the UK Singles Chart. A stage musical featuring their songs, Sunshine on Leith, was created in 2007 for Dundee Rep, the band was one of the B-52s touring partners on their Funplex tour in Australia and New Zealand in November 2009, alongside Mental as Anything. They featured in VH1s 100 greatest one hit wonders, Im Gonna Be having been their only US hit single. On 16 May 2006 the twins announced their participation in a campaign to free a fellow Scot, Kenny Richey, from his death row sentence in Ohio, US, including an appearance at a charity concert. Also, in March 2010 they participated with Billy Bragg in a show at the Electric Palace, Bridport, supporting Reprieve, a charity that seeks to end the use of the death penalty
The Proclaimers
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The Proclaimers on stage in June 2008
The Proclaimers
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The Proclaimers
41.
Sunshine on Leith (album)
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Sunshine on Leith is The Proclaimers second studio album, released in August 1988. The album title is about their birthplace Leith, the title track Sunshine on Leith is played by Hibernian F. C. at the beginning of matches. A remastered edition of the album was released in 2011, all Songs Written By Craig & Charlie Reid, except where noted
Sunshine on Leith (album)
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Sunshine on Leith
42.
Benny and Joon
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Benny & Joon is a 1993 romantic comedy film released by Metro-Goldwyn-Mayer about how two eccentric individuals, Sam and Juniper Joon, find each other and fall in love. Aidan Quinn also stars, and it was directed by Jeremiah S. Chechik, the film is perhaps best known for Depps humorous physical comedy routines and for popularizing, in the United States, the song Im Gonna Be by The Proclaimers. Benny & Joon was shot primarily on location in Spokane, Washington, while the scenes at the beginning were shot near Metaline Falls. As adults, Benjamin Benny Pearl and his ill sister Juniper Joon Pearl. Bennys friend Mike has his cinephile cousin Sam staying with him, Joon joins a poker game at Mikes that Benny is unaware of, and loses a bet that commits Sam to live with the Pearls. Joon aids an illiterate Sam when he is struggling with writing to his mother, and she takes them on an errand, and then takes them home. After Ruthie stays for dinner, her car wont start, and Benny drives her home, meanwhile, left alone, Joon and Sam kiss. Benny and Ruthie have a fun date, but it ends abruptly because Benny wants to get home to Joon, Sam goes to a video store to try and apply for a job there. Benny, Joon and Sam go to a park where Sam starts doing Keatonesque tricks with his hat, Benny stays at the park to reflect and sends Joon home with Sam, where they make love. Sam then tells Joon he loves her which Joon reciprocates, Benny tries to persuade Sam that he could do more with his life than be Joons housekeeper and persuades a buddy to let Sam audition. When Benny makes suggestions to Sam about his comedy routines, Joon becomes agitated and makes Sam explain that he and Joon are romantically involved. An angry Benny throws Sam out of the house, yells at Joon, Joon starts hitting Benny and screaming I hate you. Feeling bad, Benny leaves to get her some tapioca, while Benny is away, Sam arrives. They pack suitcases and get on a bus, but Joon soon begins to hear voices in her head and argues with them, Sam tries to soothe her, but she continues to become more agitated. The bus is stopped, and two men with the ambulance service restrain Joon, when Benny arrives at the hospital, Dr. Garvey tells him Joon doesnt want to see him. He finds Sam in the room, and they argue. Sam who told Benny that he became a different person, goes to stay with Ruthie, at that point, Benny begins to feel guilty about his treatment towards Joon. Benny discovers Sam, now working at the store and asks for his help
Benny and Joon
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Theatrical release poster
43.
How I Met Your Mother
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How I Met Your Mother is an American sitcom that originally aired on CBS from September 19,2005 to March 31,2014. The series follows the character, Ted Mosby, and his group of friends in Manhattan. As a framing device, Ted, in the year 2030, recounts to his son, the series was created by Craig Thomas and Carter Bays, who also served as the shows executive producers and were frequent writers. The series was inspired by their friendship when they both lived in New York City. Among the 208 episodes, there were four directors, Pamela Fryman, Rob Greenberg, Michael Shea. Known for its structure and eccentric humor, How I Met Your Mother has gained a cult following over the years. The show initially received positive reviews, while the later seasons received more mixed reviews, the show was nominated for 28 Emmy Awards, winning nine. In 2010, Alyson Hannigan won the Peoples Choice Award for Favorite TV Comedy Actress, in 2012, seven years after its premiere, the series won the Peoples Choice Award for Favorite Network TV Comedy, and Neil Patrick Harris won the award for Favorite TV Comedy Actor. The series concerns the adventures of Ted Mosby narrating the story of how he met the mother of his children, the lives of all characters are entwined in each others. The shows frame story depicts Ted verbally retelling the story to his son Luke, the show instead focuses on Teds prior relationships and his dissatisfaction with those women, thus setting the stage for his eventual happiness with Tracy. The two drew from their friendship in creating the characters, Ted is based loosely on Bays, and Marshall and Lily are based loosely on Thomas and his wife. Thomas wife Rebecca was initially reluctant to have a character based on her, Hannigan was looking to do more comedy work, and was available. The role of Barney was initially envisioned as a John Belushi-type character before Neil Patrick Harris won the role after being invited to an audition by the casting director Megan Branman. Pamela Fryman invited Bob Saget to be the narrator, Future Ted, explaining to him that the show would be like The Wonder Years. Saget either went to the studio and recorded the narration while watching the episode, or did so separately. He normally did not attend table readings, but did so for the last episode, in various interviews Bays and Thomas have stated that a pretty famous actress turned down the role of Robin, whom they revealed in February 2014 to have been Jennifer Love Hewitt. They then cast Cobie Smulders for the role who, at the time, was fairly unknown, Bays and Thomas later said, Thank God we did for a million reasons. When Teds seeing her for the first time, Americas seeing her for the first time — the intriguingness of that propelled the show going forward, according to an Entertainment Weekly article, the writers adopted facets of each main actors personality and incorporated them into their characters
How I Met Your Mother
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How I Met Your Mother
How I Met Your Mother
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Main cast
How I Met Your Mother
How I Met Your Mother
44.
On-Line Encyclopedia of Integer Sequences
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The On-Line Encyclopedia of Integer Sequences, also cited simply as Sloanes, is an online database of integer sequences. It was created and maintained by Neil Sloane while a researcher at AT&T Labs, Sloane continues to be involved in the OEIS in his role as President of the OEIS Foundation. OEIS records information on integer sequences of interest to professional mathematicians and amateurs, and is widely cited. As of 30 December 2016 it contains nearly 280,000 sequences, the database is searchable by keyword and by subsequence. Neil Sloane started collecting integer sequences as a student in 1965 to support his work in combinatorics. The database was at first stored on punched cards and he published selections from the database in book form twice, A Handbook of Integer Sequences, containing 2,372 sequences in lexicographic order and assigned numbers from 1 to 2372. The Encyclopedia of Integer Sequences with Simon Plouffe, containing 5,488 sequences and these books were well received and, especially after the second publication, mathematicians supplied Sloane with a steady flow of new sequences. The collection became unmanageable in book form, and when the database had reached 16,000 entries Sloane decided to go online—first as an e-mail service, as a spin-off from the database work, Sloane founded the Journal of Integer Sequences in 1998. The database continues to grow at a rate of some 10,000 entries a year, Sloane has personally managed his sequences for almost 40 years, but starting in 2002, a board of associate editors and volunteers has helped maintain the database. In 2004, Sloane celebrated the addition of the 100, 000th sequence to the database, A100000, in 2006, the user interface was overhauled and more advanced search capabilities were added. In 2010 an OEIS wiki at OEIS. org was created to simplify the collaboration of the OEIS editors and contributors, besides integer sequences, the OEIS also catalogs sequences of fractions, the digits of transcendental numbers, complex numbers and so on by transforming them into integer sequences. Sequences of rationals are represented by two sequences, the sequence of numerators and the sequence of denominators, important irrational numbers such as π =3.1415926535897. are catalogued under representative integer sequences such as decimal expansions, binary expansions, or continued fraction expansions. The OEIS was limited to plain ASCII text until 2011, yet it still uses a form of conventional mathematical notation. Greek letters are represented by their full names, e. g. mu for μ. Every sequence is identified by the letter A followed by six digits, sometimes referred to without the leading zeros, individual terms of sequences are separated by commas. Digit groups are not separated by commas, periods, or spaces, a represents the nth term of the sequence. Zero is often used to represent non-existent sequence elements, for example, A104157 enumerates the smallest prime of n² consecutive primes to form an n×n magic square of least magic constant, or 0 if no such magic square exists. The value of a is 2, a is 1480028129, but there is no such 2×2 magic square, so a is 0
On-Line Encyclopedia of Integer Sequences
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On-Line Encyclopedia of Integer Sequences
45.
HTTP status code
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This is a list of Hypertext Transfer Protocol response status codes. It includes codes from IETF Request for Comments, other specifications, the first digit of the status code specifies one of five standard classes of responses. The message phrases shown are typical, but any human-readable alternative may be provided, unless otherwise stated, the status code is part of the HTTP/1.1 standard. The Internet Assigned Numbers Authority maintains the registry of HTTP status codes. An informational response indicates that the request was received and understood and it is issued on a provisional basis while request processing continues. It alerts the client to wait for a final response, the message consists only of the status line and optional header fields, and is terminated by an empty line. As the HTTP/1.0 standard did not define any 1xx status codes,100 Continue The server has received the request headers and the client should proceed to send the request body. Sending a large request body to a server after a request has been rejected for inappropriate headers would be inefficient. To have a check the requests headers, a client must send Expect, 100-continue as a header in its initial request. The response 417 Expectation Failed indicates the request should not be continued,101 Switching Protocols The requester has asked the server to switch protocols and the server has agreed to do so. 102 Processing A WebDAV request may contain many sub-requests involving file operations and this code indicates that the server has received and is processing the request, but no response is available yet. This prevents the client from timing out and assuming the request was lost and this class of status codes indicates the action requested by the client was received, understood, accepted, and processed successfully. 200 OK Standard response for successful HTTP requests, the actual response will depend on the request method used. In a GET request, the response will contain an entity corresponding to the requested resource, in a POST request, the response will contain an entity describing or containing the result of the action. 201 Created The request has been fulfilled, resulting in the creation of a new resource,202 Accepted The request has been accepted for processing, but the processing has not been completed. The request might or might not be acted upon. 203 Non-Authoritative Information The server is a proxy that received a 200 OK from its origin. 204 No Content The server successfully processed the request and is not returning any content,205 Reset Content The server successfully processed the request, but is not returning any content
HTTP status code
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404 error on German Wikipedia
46.
Prime number
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A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a number is called a composite number. For example,5 is prime because 1 and 5 are its only positive integer factors, the property of being prime is called primality. A simple but slow method of verifying the primality of a number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and n, algorithms much more efficient than trial division have been devised to test the primality of large numbers. Particularly fast methods are available for numbers of forms, such as Mersenne numbers. As of January 2016, the largest known prime number has 22,338,618 decimal digits, there are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no simple formula that separates prime numbers from composite numbers. However, the distribution of primes, that is to say, many questions regarding prime numbers remain open, such as Goldbachs conjecture, and the twin prime conjecture. Such questions spurred the development of branches of number theory. Prime numbers give rise to various generalizations in other domains, mainly algebra, such as prime elements. A natural number is called a number if it has exactly two positive divisors,1 and the number itself. Natural numbers greater than 1 that are not prime are called composite, among the numbers 1 to 6, the numbers 2,3, and 5 are the prime numbers, while 1,4, and 6 are not prime. 1 is excluded as a number, for reasons explained below. 2 is a number, since the only natural numbers dividing it are 1 and 2. Next,3 is prime, too,1 and 3 do divide 3 without remainder, however,4 is composite, since 2 is another number dividing 4 without remainder,4 =2 ·2. 5 is again prime, none of the numbers 2,3, next,6 is divisible by 2 or 3, since 6 =2 ·3. The image at the right illustrates that 12 is not prime,12 =3 ·4, no even number greater than 2 is prime because by definition, any such number n has at least three distinct divisors, namely 1,2, and n
Prime number
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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.
47.
Eisenstein prime
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In mathematics, an Eisenstein prime is an Eisenstein integer z = a + b ω that is irreducible in the ring-theoretic sense, its only Eisenstein divisors are the units, a + bω itself and its associates. The associates and the conjugate of any Eisenstein prime are also prime. It follows that the absolute value squared of every Eisenstein prime is a prime or the square of a natural prime. The first few Eisenstein primes that equal a natural prime 3n −1 are,2,5,11,17,23,29,41,47,53,59,71,83,89,101. Natural primes that are congruent to 0 or 1 modulo 3 are not Eisenstein primes, some non-real Eisenstein primes are 2 + ω,3 + ω,4 + ω,5 + 2ω,6 + ω,7 + ω,7 + 3ω. Up to conjugacy and unit multiples, the primes listed above, as of March 2017, the largest known Eisenstein prime is the seventh largest known prime 10223 ×231172165 +1, discovered by Péter Szabolcs and PrimeGrid. All larger known primes are Mersenne primes, discovered by GIMPS, real Eisenstein primes are congruent to 2 mod 3, and Mersenne primes are congruent to 1 mod 3, thus no Mersenne prime is an Eisenstein prime
Eisenstein prime
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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.
48.
Semi-meandric number
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In mathematics, a meander or closed meander is a self-avoiding closed curve which intersects a line a number of times. Intuitively, a meander can be viewed as a road crossing a river through a number of bridges, the line and curve together form a meandric system. Two meanders are said to be equivalent if there is a homeomorphism of the plane that takes L to itself. The meander of order 1 intersects the line twice, The meanders of order 2 intersect the line four times, the first fifteen meandric numbers are given below. The curve is oriented upward at the intersection labelled 1, the cyclic permutation with no fixed points is obtained by following the oriented curve through the labelled intersection points. In the diagram on the right, the order 4 meandric permutation is given by and this is a permutation written in cyclic notation and not to be confused with one-line notation. If π is a permutation, then π2 consists of two cycles, one containing of all the even symbols and the other all the odd symbols. Permutations with this property are called alternate permutations, since the symbols in the original permutation alternate between odd and even integers, however, not all alternate permutations are meandric because it may not be possible to draw them without introducing a self-intersection in the curve. For example, the order 3 alternate permutation, is not meandric, two open meanders are said to be equivalent if they are homeomorphic in the plane. The open meander of order 1 intersects the line once, The open meander of order 2 intersects the line twice, the first fifteen open meandric numbers are given below. Two semi-meanders are said to be equivalent if they are homeomorphic in the plane, the semi-meander of order 1 intersects the ray once, The semi-meander of order 2 intersects the ray twice, The number of distinct semi-meanders of order n is the semi-meandric number Mn. The first fifteen semi-meandric numbers are given below
Semi-meandric number
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Contents
49.
Jeans
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Jeans are pants, a type of garment, typically made from denim or dungaree cloth. Prior to the Levi Strauss patented trousers, the blue jeans had been long in use for various garments. Originally designed for cowboys and miners, jeans became popular in the 1950s among teenagers, Jeans were a common fashion item in the 1960s Hippie subculture and they continued to be popular in the 1970s and 1980s youth subcultures of punk rock and heavy metal. Historic brands include Levis, Lee, and Wrangler, distressed jeans trousers have become increasingly fashionable, making pre-sale factory distressing a common feature in commercially sold jeans. In the 2010s, jeans are a popular article of casual dress around the world. They come in many styles and colors, however, blue jeans are particularly identified with American culture, especially the Old West. Research on the trade of jean fabric shows that it emerged in the cities of Genoa, Italy, gênes, the French word for Genoa, may be the origin of the word jeans. In Nimes, weavers tried to reproduce jean but instead developed a similar fabric that became known as denim, from de Nimes. Genoa’s jean was a fustian textile of medium quality and of reasonable cost, very similar to cotton corduroy for which Genoa was famous, nimes’s denim was coarser, considered higher quality and was used for over garments such as smocks or overalls. Nearly all Indigo, needed for dyeing, came from indigo bush plantations in India till the late 19th century and it was replaced by indigo synthesis methods developed in Germany. By the 17th century, jean was a crucial textile for working-class people in Northern Italy and this is seen in a series of genre paintings from around the 17th century attributed to an artist now named The Master of the Blue Jeans. The ten paintings depict impoverished scenes with lower-class figures wearing a fabric that looks like denim, the fabric would have been Genoese jean, which was cheaper. Genre painting came to prominence in late 16th century, and the subject matter in all ten paintings places them among others that portray similar scenes. Denim is not the only sturdy cotton fabric used for everything from working clothes to fashion items and this cloth was dungri in Hindi. Dungri was exported to England and used for manufacturing of cheap and it was rumored that men would carry dead dung beetles in their pocket for luck. In English, the word dungri became pronounced as dungaree, the importance of jean is also shown by the history of textile trade. Genoese sailors used jean to cover and protect their goods on the docks from the weather, during the Republic of Genoa, sailors exported jeans throughout Europe. Jean became popular in the United States when Levi Strauss & Co. s introduced blue jean overalls in 1873
Jeans
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A pair of factory-distressed, loose fit men's jeans
Jeans
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A traditional female Genoese dress in "blue jeans" (1890s)
Jeans
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Copper
rivets for reinforcing pockets are a characteristic feature of blue jeans.
Jeans
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Levi Strauss