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

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

3.
Factorization
–
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

4.
Greek numerals
–
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

5.
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

6.
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

7.
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

8.
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

9.
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

10.
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

11.
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

12.
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

13.
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

14.
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

15.
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

16.
Forbidden City
–
The Forbidden City was the Chinese imperial palace from the Ming dynasty to the end of the Qing dynasty—the years 1420 to 1912. It is located in the center of Beijing, China, and it served as the home of emperors and their households as well as the ceremonial and political center of Chinese government for almost 500 years. Constructed from 1406 to 1420, the complex consists of 980 buildings, the palace complex exemplifies traditional Chinese palatial architecture, and has influenced cultural and architectural developments in East Asia and elsewhere. The Forbidden City was declared a World Heritage Site in 1987, part of the museums former collection is now located in the National Palace Museum in Taipei. Both museums descend from the institution, but were split after the Chinese Civil War. With over 14.6 million annual visitors, the Palace Museum is the most visited art museum in the world, the common English name, the Forbidden City, is a translation of the Chinese name Zijin Cheng. The name Zijin Cheng first formally appeared in 1576, another English name of similar origin is Forbidden Palace. The name Zijin Cheng is a name with significance on many levels, zi, or Purple, refers to the North Star, which in ancient China was called the Ziwei Star, and in traditional Chinese astrology was the heavenly abode of the Celestial Emperor. The surrounding celestial region, the Ziwei Enclosure, was the realm of the Celestial Emperor, the Forbidden City, as the residence of the terrestrial emperor, was its earthly counterpart. Jin, or Forbidden, referred to the fact no one could enter or leave the palace without the emperors permission. Today, the site is most commonly known in Chinese as Gùgōng, the museum which is based in these buildings is known as the Palace Museum. When Hongwu Emperors son Zhu Di became the Yongle Emperor, he moved the capital from Nanjing to Beijing, construction lasted 14 years and required more than a million workers. Material used include whole logs of precious Phoebe zhennan wood found in the jungles of south-western China, the floors of major halls were paved with golden bricks, specially baked paving bricks from Suzhou. From 1420 to 1644, the Forbidden City was the seat of the Ming dynasty, in April 1644, it was captured by rebel forces led by Li Zicheng, who proclaimed himself emperor of the Shun dynasty. He soon fled before the armies of former Ming general Wu Sangui and Manchu forces. By October, the Manchus had achieved supremacy in northern China, the Qing rulers changed the names on some of the principal buildings, to emphasise Harmony rather than Supremacy, made the name plates bilingual, and introduced Shamanist elements to the palace. In 1860, during the Second Opium War, Anglo-French forces took control of the Forbidden City, in 1900 Empress Dowager Cixi fled from the Forbidden City during the Boxer Rebellion, leaving it to be occupied by forces of the treaty powers until the following year. Under an agreement with the new Republic of China government, Puyi remained in the Inner Court, while the Outer Court was given over to public use, the Palace Museum was then established in the Forbidden City in 1925

17.
Joss paper
–
Joss paper, as well as other papier-mâché items, are also burned or buried in various Asian funerals, to ensure that the spirit of the deceased has lots of good things in the afterlife. In Taiwan alone, the revenue of temples from burning ghost money was US$400 million as of 2014. Joss paper is made from coarse bamboo paper, which feels handmade with many variances and imperfections. Traditional joss is cut into squares or rectangles. Depending on the region, Joss paper may be decorated with seals, stamps, pieces of contrasting paper, different types of spirit money are given to distinct categories of spirits. The three main types of money are cash, silver and gold. Cash monies are given to newly deceased spirits and spirits of the unknown, gold spirit money is given to both the deceased and higher gods such as the Jade Emperor. Silver spirit money is given exclusively to ancestral spirits as well as spirits of local deities and these distinctions between the three categories of spirit money must be followed precisely to prevent confusion or insult of the spirits. More contemporary or westernized varieties of Joss paper include paper currency, credit cards, cheques, as well as clothes, houses, cars, toiletries, electronics. The designs on paper items vary from the simple to very elaborate. The most well known joss paper item among Westerners is the Hell Bank Note, the word hell may have been derived from, What was preached by Christian missionaries, which told the Chinese that non-Christians go to hell when they die. Hell Bank Notes are also known for their enormous denominations ranging from $10,000 to $5,000,000,000, the bills almost always feature an image of the Jade Emperor on the front and the headquarters of the Hell Bank on the back. Another common feature is the signatures of both the Jade Emperor and the lord of the Underworld, both who apparently also serve as the banks governor and deputy governor. Spirit money is most often used for venerating those departed but has also known to be used for other purposes such as a gift from a grooms family to the brides ancestors. Spirit money has been said to have given for the purpose of enabling their deceased family members to have all they will need or want in the afterlife. It has also noted that these offerings have been given as a bribe to Yanluo to hold their ancestors for a shorter period of time. Venerating the ancestors is based on the belief that the spirits of the continue to dwell in the natural world and have the power to influence the fortune. The goal of worship is to ensure the ancestors continued well-being and positive disposition towards the living

18.
Emergency telephone number
–
In many countries the public switched telephone network has a single emergency telephone number that allows a caller to contact local emergency services for assistance. The emergency number differs from country to country, it is typically a number so that it can be easily remembered and dialed quickly. Some countries have a different emergency number for each of the different emergency services, see List of emergency telephone numbers. The emergency telephone number is a case in the countrys telephone number plan. In the past, calls to the telephone number were often routed over special dedicated circuits. Though with the advent of electronic exchanges these calls are now mixed with ordinary telephone traffic. Often the system is set up so that once a call is made to a telephone number. Should the caller abandon the call, the line may still be held until the emergency service answers, an emergency telephone number call may be answered by either a telephone operator or an emergency service dispatcher. The nature of the emergency is then determined, if the call has been answered by a telephone operator, they then connect the call to the appropriate emergency service, who then dispatches the appropriate help. In the case of services being needed on a call. Emergency dispatchers are trained to control the call in order to help in an appropriate manner. The emergency dispatcher may find it necessary to give urgent advice in life-threatening situations, some dispatchers have special training in telling people how to perform first aid or CPR. In many parts of the world, a service can identify the telephone number that a call has been placed from. This is normally done using the system that the company uses to bill calls. For an individual fixed landline telephone, the number can often be associated with the callers address. However, with phones and business telephones, the address may be a mailing address rather than the callers location. The latest enhanced systems, such as Enhanced 911, are able to provide the location of mobile telephones. This is often specifically mandated in a countrys legislation, when an emergency happened in the pre-dial telephone era, the user simply picked up the telephone receiver and waited for the operator to answer number, please

19.
Oman
–
Oman, officially the Sultanate of Oman, is an Arab country on the southeastern coast of the Arabian Peninsula. The coast is formed by the Arabian Sea on the southeast, the Madha and Musandam exclaves are surrounded by the UAE on their land borders, with the Strait of Hormuz and Gulf of Oman forming Musandams coastal boundaries. From the late 17th century, the Omani Sultanate was an empire, vying with Portugal and Britain for influence in the Persian Gulf. At its peak in the 19th century, Omani influence or control extended across the Strait of Hormuz to modern-day Iran and Pakistan, as its power declined in the 20th century, the sultanate came under the influence of the United Kingdom. Historically, Muscat was the trading port of the Persian Gulf region. Muscat was also among the most important trading ports of the Indian Ocean, the Sultan Qaboos bin Said al Said has been the hereditary leader of the country since 1970. Sultan Qaboos is the current ruler in the Middle East. Oman has modest oil reserves, ranking 25th globally, nevertheless, in 2010 the UNDP ranked Oman as the most improved nation in the world in terms of development during the preceding 40 years. A significant portion of its economy is tourism and trade of fish, dates and this sets it apart from its neighbors solely oil-dependent economies. Oman is categorized as an economy and ranks as the 74th most peaceful country in the world according to the Global Peace Index. Two optically stimulated luminescence age estimates place the Arabian Nubian Complex at 106,000 years old and this supports the proposition that early human populations moved from Africa into Arabia during the Late Pleistocene. Dereaze, located in the city of Ibri, is the oldest known settlement in the area. Archaeological remains have been discovered here from the Stone Age and the Bronze Age, findings have included stone implements, animal bones, shells and fire hearths, with the latter dating back to 7615 BC as the oldest signs of human settlement in the area. Other discoveries include hand-molded pottery bearing distinguishing pre-Bronze Age marks, heavy flint implements, pointed tools, sumerian tablets refer to a country called Magan or Makan, a name believed to refer to Omans ancient copper mines. Mazoon, another used for the region, is derived from the word muzn. The present-day name of the country, Oman, is believed to originate from the Arab tribes who migrated to its territory from the Uman region of Yemen. Many such tribes settled in Oman, making a living by fishing, herding or stock breeding, from the 6th century BC to the arrival of Islam in the 7th century AD, Oman was controlled and/or influenced by three Persian dynasties, the Achaemenids, Parthians and Sassanids. A few scholars believe that in the 6th century BC, the Achaemenids exerted a strong degree of control over the Omani peninsula, Central Oman has its own indigenous so-called Late Iron Age cultural assemblage, the Samad al-Shan

20.
Programming languages
–
A programming language is a formal computer language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to programs to control the behavior of a machine or to express algorithms. From the early 1800s, programs were used to direct the behavior of such as Jacquard looms. Thousands of different programming languages have created, mainly in the computer field. Many programming languages require computation to be specified in an imperative form while other languages use forms of program specification such as the declarative form. The description of a language is usually split into the two components of syntax and semantics. Some languages are defined by a document while other languages have a dominant implementation that is treated as a reference. Some languages have both, with the language defined by a standard and extensions taken from the dominant implementation being common. A programming language is a notation for writing programs, which are specifications of a computation or algorithm, some, but not all, authors restrict the term programming language to those languages that can express all possible algorithms. For example, PostScript programs are created by another program to control a computer printer or display. More generally, a language may describe computation on some, possibly abstract. It is generally accepted that a specification for a programming language includes a description, possibly idealized. In most practical contexts, a programming language involves a computer, consequently, abstractions Programming languages usually contain abstractions for defining and manipulating data structures or controlling the flow of execution. Expressive power The theory of computation classifies languages by the computations they are capable of expressing, all Turing complete languages can implement the same set of algorithms. ANSI/ISO SQL-92 and Charity are examples of languages that are not Turing complete, markup languages like XML, HTML, or troff, which define structured data, are not usually considered programming languages. Programming languages may, however, share the syntax with markup languages if a computational semantics is defined, XSLT, for example, is a Turing complete XML dialect. Moreover, LaTeX, which is used for structuring documents. The term computer language is used interchangeably with programming language

21.
BASIC
–
BASIC is a family of general-purpose, high-level programming languages whose design philosophy emphasizes ease of use. In 1964, John G. Kemeny and Thomas E. Kurtz designed the original BASIC language at Dartmouth College in the U. S. state of New Hampshire and they wanted to enable students in fields other than science and mathematics to use computers. At the time, nearly all use of computers required writing custom software, versions of BASIC became widespread on microcomputers in the mid-1970s and 1980s. Microcomputers usually shipped with BASIC, often in the machines firmware, having an easy-to-learn language on these early personal computers allowed small business owners, professionals, hobbyists, and consultants to develop custom software on computers they could afford. In the 2010s, BASIC remains popular in many computing dialects and in new languages influenced by BASIC, before the mid-1960s, the only computers were huge mainframe computers. Users submitted jobs on punched cards or similar media to specialist computer operators, the computer stored these, then used a batch processing system to run this queue of jobs one after another, allowing very high levels of utilization of these expensive machines. As the performance of computing hardware rose through the 1960s, multi-processing was developed and this allowed a mix of batch jobs to be run together, but the real revolution was the development of time-sharing. The original BASIC language was released on May 1,1964 by John G. Kemeny and Thomas E. Kurtz, the acronym BASIC comes from the name of an unpublished paper by Thomas Kurtz. BASIC was designed to allow students to write computer programs for the Dartmouth Time-Sharing System. It was intended specifically for technical users who did not have or want the mathematical background previously expected. Being able to use a computer to support teaching and research was quite novel at the time, the language was based on FORTRAN II, with some influences from ALGOL60 and with additions to make it suitable for timesharing. Wanting use of the language to become widespread, its designers made the available free of charge. They also made it available to schools in the Hanover area. In the following years, as dialects of BASIC appeared, Kemeny. A version was a part of the Pick operating system from 1973 onward. During this period a number of computer games were written in BASIC. A number of these were collected by DEC employee David H. Ahl and he later collected a number of these into book form,101 BASIC Computer Games, published in 1973. During the same period, Ahl was involved in the creation of a computer for education use

22.
The King of Fighters
–
The King of Fighters, officially abbreviated KOF, is a series of fighting games by SNK that began with The King of Fighters 94 in 1994. Only two King of Fighters games were made on the Atomiswave platform before SNK decided to discontinue using the platform for the series, the last arcade hardware for the series is the Taito Type X2, with its first usage coming with the release of The King of Fighters XII. Ports of the games and original The King of Fighters games have been released for several video games consoles. The latest entry in the series, The King of Fighters XIV, was released only for the PlayStation 4, the first game in the series, The King of Fighters 94, was released by SNK on August 25,1994. The game featured characters from SNKs previous fighting game series Fatal Fury and Art of Fighting, the success of the game led SNK to release yearly installments of the series and numbered the games for the year they were released. The King of Fighters 95, in addition to adding new characters and it was also the first game in the series that allowed the players to create their own team of three members, out of any character in the game. The King of Fighters 96 established the part of The Orochi Saga. Depending on the characters in a team, an exclusive ending will be played. The King of Fighters 97 concluded The Orochi Saga story arc, the King of Fighters 98, and unlike the previous games of the series, did not feature a story. Instead, the game was promoted as a Dream Match game that allowed players to choose most of the characters available from the previous titles, SNK refitted the Dreamcast version and renamed it The King of Fighters, Dream Match 1999 with an extended cel animated introduction and 3D backgrounds. The King of Fighters 99 introduced a new story arc known as The NESTS Chronicles along with new characters into the series. In a new tactic, a person from a team would be an assistant called a Striker. The Dreamcast version was titled The King of Fighters, Evolution, with improvements in the game such as new Strikers. The King of Fighters 2000 is the part of The NESTS Saga as well as the last KOF game to be made by SNK before the bankruptcy. It adds a few new characters and a couple of Strikers. The King of Fighters 2001 ends the story arc. Due to economic problems that SNK had at the time, the Korean company Eolith helped in the development of the game after SNK was bankrupted, the King of Fighters 2002 was created to reunite old characters from previous KOF games and featured no story, similar to KOF98. It was also developed by Eolith, a new KOF story arc called the Tales of Ash started in The King of Fighters 2003, the last KOF game to be released for the Neo Geo system

23.
Yale University Press
–
Yale University Press is a university press associated with Yale University. It was founded in 1908 by George Parmly Day, and became a department of Yale University in 1961. As of 2009, Yale University Press published approximately 300 new hardcover and 150 new paperback books annually and has more than 6,000 books in print and its books have won five National Book Awards, two National Book Critics Circle Awards and eight Pulitzer Prizes. Since its inception in 1919, the Yale Series of Younger Poets Competition has published the first collection of poetry by new poets, the first winner was Howard Buck, the 2011 winner was Katherine Larson. Yale University Press and Yale Repertory Theatre jointly sponsor the Yale Drama Series, the winner of the annual competition is awarded the David C. Horn Prize of $10,000, publication of his/her manuscript by Yale University Press, the Yale Drama Series and David C. Horn Prize are funded by the David Charles Horn Foundation, in 2007, Yale University Press acquired the Anchor Bible Series, a collection of more than 115 volumes of biblical scholarship, from the Doubleday Publishing Group. New and backlist titles are now published under the Anchor Yale Bible Series name, the Dwight H. Terry Lectureship was established in 1905 to encourage the consideration of religion in the context of modern science, psychology, and philosophy. Many of the lectures, which are hosted by Yale University, have been edited into book form by the Yale University Press, the Yale Publishing Course was founded in 2010 by former Publishing Director of the Yale University Press, Tina C. It filled the gap created by the closing of the legendary Stanford Publishing Course and it operates under the aegis of the Office of International Affairs of Yale University. The Course trains mid to senior-level publishing professionals to tackle the most compelling issues facing the publishing industry, the curriculum focuses on in-depth analyses of global trends, innovative business models, management strategies, and new advances in technology. Its immersive week-long programs, one devoted to publishing and the other to magazine and digital publishing, combine lectures, discussion groups. The faculty is made up of leading experts and members of the Yale School of Management, the Yale Library. Participants come from all over the world and represent all areas of publishing within organizations of all sizes and types of publications, in 1963, the Press published a revised edition of Ludwig von Misess Human Action. Official website, including a mission statement Yale University Press, London Yale Publishing Course, New Haven, Connecticut

24.
1995
–
America Online and Prodigy offered access to the World Wide Web system for the first time this year, releasing browsers that made it easily accessible to the general public. January 1 The World Trade Organization is established to replace the General Agreement on Tariffs, austria, Finland and Sweden join the European Union. The Draupner wave in the North Sea in Norway is detected, january 6–7 – A chemical fire occurs in an apartment complex in Manila, Philippines. Policemen led by watch commander Aida Fariscal and investigators find a factory and a laptop computer and disks that contain plans for Project Bojinka. The mastermind, Ramzi Yousef, is arrested one month later, january 9 – Valeri Polyakov completes 366 days in space while aboard the Mir space station, breaking a duration record. January 16 An avalanche hits the village Súðavík in Iceland, killing 14 people, the fourth Star Trek TV series, Voyager, premieres on UPN in the United States. January 17 The 6.9 Mw Great Hanshin earthquake shakes the southern Hyōgo Prefecture with a maximum Shindo of VII, leaving 5, 502–6,434 people dead, Prodigy begins offering access to the World Wide Web. January 24 – Opening statements in the O. J. Simpson murder case trial in Los Angeles, january 25 – Norwegian rocket incident, A rocket launched from the space exploration centre at Andøya, Norway is briefly interpreted by the Russians as an incoming attack. January 30 – John Howard becomes leader of the Liberal Party of Australia to challenge Paul Keating for the 1996 Federal Election, january 31 – U. S. President Bill Clinton invokes emergency powers, to extend a $20 billion loan to help Mexico avert financial collapse. His car is found two weeks later at Severn View services in Aust, february 9 – STS-63, Dr. Bernard A. Harris, Jr. and Michael Foale became the second African American and Briton, respectively, to walk in space. February 13 – A United Nations tribunal on human rights violations in the Balkans charges 21 Bosnian Serb commanders with genocide, february 15 – Hacker Kevin Mitnick is arrested by the FBI and charged with penetrating some of the United States most secure computer systems. February 17 Colin Ferguson is convicted of six counts of murder for the December 1993 Long Island Rail Road shooting, february 21 Serkadji prison mutiny in Algeria, Four guards and 96 prisoners are killed in a day and a half. Ibrahim Ali, a 17-year-old Comorian living in France, is murdered by 3 far-right National Front activists, Steve Fossett lands in Leader, Saskatchewan, Canada, becoming the first person to make a solo flight across the Pacific Ocean in a balloon. February 23 – The Dow Jones Industrial Average gains 30.28 to close at 4,003.33 – the Dows first ever close above 4,000, february 25 – Amazon Cooperation Treaty Organization. February 26 – The United Kingdoms oldest investment banking firm, Barings Bank, february 28 – Members of the group Patriots Council are convicted in Minnesota of manufacturing ricin. March 1 Julio María Sanguinetti is sworn in as President of Uruguay for his second term, polish Prime Minister Waldemar Pawlak resigns from Parliament and is replaced by ex-communist Józef Oleksy. In Moscow, Russian anti-corruption journalist Vladislav Listyev is killed by a gunman, March 2 – Nick Leeson is arrested in Singapore for his role in the collapse of Barings Bank. March 3 – In Somalia, the United Nations peacekeeping mission ends, March 6 – On an episode of The Jenny Jones Show in the United States, Scott Amedure reveals a crush on his heterosexual friend Jonathan Schmitz

25.
Wired (magazine)
–
Wired is a monthly American magazine, published in print and online editions, that focuses on how emerging technologies affect culture, the economy, and politics. Owned by Condé Nast, it is headquartered in San Francisco, California, several spin-offs have been launched including, Wired UK, Wired Italia, Wired Japan and Wired Germany. In its earliest colophons, Wired credited Canadian media theorist Marshall McLuhan as its patron saint, from its beginning, the strongest influence on the magazines editorial outlook came from techno-utopian co-founder Stewart Brand and his associate Kevin Kelly. From 1998 to 2006, Wired magazine and Wired News had separate owners, however, Wired News remained responsible for republishing Wired magazines content online due to an agreement when Condé Nast purchased the magazine. In 2006, Condé Nast bought Wired News for $25 million, the founding designers were John Plunkett and Barbara Kuhr, beginning with a 1991 prototype and continuing through the first five years of publication, 1993–98. Wired, which touted itself as the Rolling Stone of technology, a great success at its launch, it was lauded for its vision, originality, innovation and cultural impact. In its first four years, the magazine won two National Magazine Awards for General Excellence and one for Design. The founding executive editor of Wired, Kevin Kelly, was an editor of the Whole Earth Catalog and the Whole Earth Review, six authors of the first Wired issue had written for Whole Earth Review, most notably Bruce Sterling and Stewart Brand. However, the first issue did contain a few references to the Internet, including online-dating and Internet sex, the last page, a column written by Nicholas Negroponte, was written in the style of an e-mail message, but contained obviously fake, non-standard email addresses. Wired was among the first magazines to list the email address of its authors and contributors, associate publisher Kathleen Lyman was brought on board to launch Wired with an advertising base of major technology and consumer advertisers. The magazine was followed by a companion website HotWired, a book publishing division, HardWired, a Japanese edition. Wired UK was relaunched in April 2009, in 1994, John Battelle, co-founding editor, commissioned Jules Marshall to write a piece on the Zippies. The cover story broke records for being one of the most publicized stories of the year and was used to promote Wireds HotWired news service, HotWired spawned websites Webmonkey, the search engine HotBot, and a weblog, Suck. com. In June 1998, the magazine launched an index, The Wired Index. The fortune of the magazine and allied enterprises corresponded closely to that of the dot-com bubble, in 1996, Rossetto and the other participants in Wired Ventures attempted to take the company public with an IPO. The initial attempt had to be withdrawn in the face of a downturn in the stock market, the second try was also unsuccessful. Rossetto and Metcalfe lost control of Wired Ventures to financial investors Providence Equity Partners in May 1998, Wired was purchased by Advance Publications, who assigned it to Advances subsidiary, New York-based publisher Condé Nast Publications. Wired survived the bubble and found new direction under editor-in-chief Chris Anderson in 2001

26.
Number
–
Numbers that answer the question How many. Are 0,1,2,3 and so on, when used to indicate position in a sequence they are ordinal numbers. To the Pythagoreans and Greek mathematician Euclid, the numbers were 2,3,4,5, Euclid did not consider 1 to be a number. Numbers like 3 +17 =227, expressible as fractions in which the numerator and denominator are whole numbers, are rational numbers and these make it possible to measure such quantities as two and a quarter gallons and six and a half miles. What we today would consider a proof that a number is irrational Euclid called a proof that two lengths arising in geometry have no common measure, or are incommensurable, Euclid included proofs of incommensurability of lengths arising in geometry in his Elements. In the Rhind Mathematical Papyrus, a pair of walking forward marked addition. They were the first known civilization to use negative numbers, negative numbers came into widespread use as a result of their utility in accounting. They were used by late medieval Italian bankers, by 1740 BC, the Egyptians had a symbol for zero in accounting texts. In Maya civilization zero was a numeral with a shape as a symbol. The ancient Egyptians represented all fractions in terms of sums of fractions with numerator 1, for example, 2/5 = 1/3 + 1/15. Such representations are known as Egyptian Fractions or Unit Fractions. The earliest written approximations of π are found in Egypt and Babylon, in Babylon, a clay tablet dated 1900–1600 BC has a geometrical statement that, by implication, treats π as 25/8 =3.1250. In Egypt, the Rhind Papyrus, dated around 1650 BC, astronomical calculations in the Shatapatha Brahmana use a fractional approximation of 339/108 ≈3.139. Other Indian sources by about 150 BC treat π as √10 ≈3.1622 The first references to the constant e were published in 1618 in the table of an appendix of a work on logarithms by John Napier. However, this did not contain the constant itself, but simply a list of logarithms calculated from the constant and it is assumed that the table was written by William Oughtred. The discovery of the constant itself is credited to Jacob Bernoulli, the first known use of the constant, represented by the letter b, was in correspondence from Gottfried Leibniz to Christiaan Huygens in 1690 and 1691. Leonhard Euler introduced the letter e as the base for natural logarithms, Euler started to use the letter e for the constant in 1727 or 1728, in an unpublished paper on explosive forces in cannons, and the first appearance of e in a publication was Eulers Mechanica. While in the subsequent years some researchers used the letter c, e was more common, the first numeral system known is Babylonian numeric system, that has a 60 base, it was introduced in 3100 B. C. and is the first Positional numeral system known