1.
Integer
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An integer is a number that can be written without a fractional component. For example,21,4,0, and −2048 are integers, while 9.75, 5 1⁄2, the set of integers consists of zero, the positive natural numbers, also called whole numbers or counting numbers, and their additive inverses. This is often denoted by a boldface Z or blackboard bold Z standing for the German word Zahlen, ℤ is a subset of the sets of rational and real numbers and, like the natural numbers, is countably infinite. The integers form the smallest group and the smallest ring containing the natural numbers, in algebraic number theory, the integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, the integers are the integers that are also rational numbers. Like the natural numbers, Z is closed under the operations of addition and multiplication, that is, however, with the inclusion of the negative natural numbers, and, importantly,0, Z is also closed under subtraction. The integers form a ring which is the most basic one, in the following sense, for any unital ring. This universal property, namely to be an object in the category of rings. Z is not closed under division, since the quotient of two integers, need not be an integer, although the natural numbers are closed under exponentiation, the integers are not. The following lists some of the properties of addition and multiplication for any integers a, b and c. In the language of algebra, the first five properties listed above for addition say that Z under addition is an abelian group. As a group under addition, Z is a cyclic group, in fact, Z under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to Z. The first four properties listed above for multiplication say that Z under multiplication is a commutative monoid. However, not every integer has an inverse, e. g. there is no integer x such that 2x =1, because the left hand side is even. This means that Z under multiplication is not a group, all the rules from the above property table, except for the last, taken together say that Z together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of algebraic structure. Only those equalities of expressions are true in Z for all values of variables, note that certain non-zero integers map to zero in certain rings. The lack of zero-divisors in the means that the commutative ring Z is an integral domain
2.
Negative number
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In mathematics, a negative number is a real number that is less than zero. If positive represents movement to the right, negative represents movement to the left, if positive represents above sea level, then negative represents below level. If positive represents a deposit, negative represents a withdrawal and they are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, if a quantity may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. In the medical context of fighting a tumor, an expansion could be thought of as a negative shrinkage, negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common idea of an opposite is reflected in arithmetic. For example, − −3 =3 because the opposite of an opposite is the original thing, negative numbers are usually written with a minus sign in front. For example, −3 represents a quantity with a magnitude of three, and is pronounced minus three or negative three. To help tell the difference between a subtraction operation and a number, occasionally the negative sign is placed slightly higher than the minus sign. Conversely, a number that is greater than zero is called positive, the positivity of a number may be emphasized by placing a plus sign before it, e. g. +3. In general, the negativity or positivity of a number is referred to as its sign, every real number other than zero is either positive or negative. The positive whole numbers are referred to as natural numbers, while the positive and negative numbers are referred to as integers. In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, Liu Hui established rules for adding and subtracting negative numbers. By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers, islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients. Western mathematicians accepted the idea of numbers by the 17th century. Prior to the concept of numbers, mathematicians such as Diophantus considered negative solutions to problems false. Negative numbers can be thought of as resulting from the subtraction of a number from a smaller. For example, negative three is the result of subtracting three from zero,0 −3 = −3, in general, the subtraction of a larger number from a smaller yields a negative result, with the magnitude of the result being the difference between the two numbers
3.
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
4.
Divisor
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In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some other integer to produce n. In this case one says also that n is a multiple of m, an integer n is divisible by another integer m if m is a divisor of n, this implies dividing n by m leaves no remainder. Under this definition, the statement m ∣0 holds for every m, as before, but with the additional constraint k ≠0. Under this definition, the statement m ∣0 does not hold for m ≠0, in the remainder of this article, which definition is applied is indicated where this is significant. Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4, they are 1,2,4, −1, −2, and −4,1 and −1 divide every integer. Every integer is a divisor of itself, every integer is a divisor of 0. Integers divisible by 2 are called even, and numbers not divisible by 2 are called odd,1, −1, n and −n are known as the trivial divisors of n. A divisor of n that is not a divisor is known as a non-trivial divisor. A non-zero integer with at least one divisor is known as a composite number, while the units −1 and 1. There are divisibility rules which allow one to recognize certain divisors of a number from the numbers digits, the generalization can be said to be the concept of divisibility in any integral domain. 7 is a divisor of 42 because 7 ×6 =42 and it can also be said that 42 is divisible by 7,42 is a multiple of 7,7 divides 42, or 7 is a factor of 42. The non-trivial divisors of 6 are 2, −2,3, the positive divisors of 42 are 1,2,3,6,7,14,21,42. 5 ∣0, because 5 ×0 =0, if a ∣ b and b ∣ a, then a = b or a = − b. If a ∣ b and a ∣ c, then a ∣ holds, however, if a ∣ b and c ∣ b, then ∣ b does not always hold. If a ∣ b c, and gcd =1, then a ∣ c, if p is a prime number and p ∣ a b then p ∣ a or p ∣ b. A positive divisor of n which is different from n is called a proper divisor or a part of n. A number that does not evenly divide n but leaves a remainder is called an aliquant part of n, an integer n >1 whose only proper divisor is 1 is called a prime number
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
6.
Roman numerals
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The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet, Roman numerals, as used today, are based on seven symbols, The use of Roman numerals continued long after the decline of the Roman Empire. The numbers 1 to 10 are usually expressed in Roman numerals as follows, I, II, III, IV, V, VI, VII, VIII, IX, Numbers are formed by combining symbols and adding the values, so II is two and XIII is thirteen. Symbols are placed left to right in order of value. Named after the year of its release,2014 as MMXIV, the year of the games of the XXII Olympic Winter Games The standard forms described above reflect typical modern usage rather than a universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval, Roman inscriptions, especially in official contexts, seem to show a preference for additive forms such as IIII and VIIII instead of subtractive forms such as IV and IX. Both methods appear in documents from the Roman era, even within the same document, double subtractives also occur, such as XIIX or even IIXX instead of XVIII. Sometimes V and L are not used, with such as IIIIII. Such variation and inconsistency continued through the period and into modern times. Clock faces that use Roman numerals normally show IIII for four o’clock but IX for nine o’clock, however, this is far from universal, for example, the clock on the Palace of Westminster in London uses IV. Similarly, at the beginning of the 20th century, different representations of 900 appeared in several inscribed dates. For instance,1910 is shown on Admiralty Arch, London, as MDCCCCX rather than MCMX, although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used
7.
Binary number
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The base-2 system is a positional notation with a radix of 2. Because of its implementation in digital electronic circuitry using logic gates. Each digit is referred to as a bit, the modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de lArithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions, the method used for ancient Egyptian multiplication is also closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, the I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique and it is based on taoistic duality of yin and yang. Eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, the Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, Pingalas Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingalas system increases towards the right, the residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Africa, sets of binary combinations similar to the I Ching have also been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been applied in sub-Saharan Africa. Leibnizs system uses 0 and 1, like the modern binary numeral system, Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own beliefs as a Christian. Binary numerals were central to Leibnizs theology and he believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. Is not easy to impart to the pagans, is the ex nihilo through Gods almighty power. In 1854, British mathematician George Boole published a paper detailing an algebraic system of logic that would become known as Boolean algebra
8.
Ternary numeral system
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The ternary numeral system has three as its base. Analogous to a bit, a digit is a trit. One trit is equivalent to bits of information. Representations of integer numbers in ternary do not get uncomfortably lengthy as quickly as in binary, for example, decimal 365 corresponds to binary 101101101 and to ternary 111112. However, they are far less compact than the corresponding representations in bases such as decimal – see below for a compact way to codify ternary using nonary. The value of a number with n bits that are all 1 is 2n −1. Then N = M, N = /, and N = bd −1, for a three-digit ternary number, N =33 −1 =26 =2 ×32 +2 ×31 +2 ×30 =18 +6 +2. Nonary or septemvigesimal can be used for representation of ternary. A base-three system is used in Islam to keep track of counting Tasbih to 99 or to 100 on a hand for counting prayers. In certain analog logic, the state of the circuit is often expressed ternary and this is most commonly seen in Transistor–transistor logic using 7406 open collector logic. The output is said to either be low, high, or open, in this configuration the output of the circuit is actually not connected to any voltage reference at all. Where the signal is usually grounded to a reference, or at a certain voltage level. Thus, the voltage level is sometimes unpredictable. A rare ternary point is used to denote fractional parts of an inning in baseball, since each inning consists of three outs, each out is considered one third of an inning and is denoted as.1. For example, if a player pitched all of the 4th, 5th and 6th innings, plus 2 outs of the 7th inning, his Innings pitched column for that game would be listed as 3.2, meaning 3⅔. In this usage, only the part of the number is written in ternary form. Ternary numbers can be used to convey self-similar structures like the Sierpinski triangle or the Cantor set conveniently, additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed. The Cantor set consists of the points from 0 to 1 that have an expression that does not contain any instance of the digit 1
9.
Quaternary numeral system
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Quaternary is the base-4 numeral system. It uses the digits 0,1,2 and 3 to represent any real number. Four is the largest number within the range and one of two numbers that is both a square and a highly composite number, making quaternary a convenient choice for a base at this scale. Despite being twice as large, its economy is equal to that of binary. However, it no better in the localization of prime numbers. See decimal and binary for a discussion of these properties, as with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system. Each radix 4,8 and 16 is a power of 2, so the conversion to and from binary is implemented by matching each digit with 2,3 or 4 binary digits, for example, in base 4,302104 =11001001002. Although octal and hexadecimal are widely used in computing and computer programming in the discussion and analysis of binary arithmetic and logic, by analogy with byte and nybble, a quaternary digit is sometimes called a crumb. There is a surviving list of Ventureño language number words up to 32 written down by a Spanish priest ca, the Kharosthi numerals have a partial base 4 counting system from 1 to decimal 10. Quaternary numbers are used in the representation of 2D Hilbert curves, here a real number between 0 and 1 is converted into the quaternary system. Every single digit now indicates in which of the respective 4 sub-quadrants the number will be projected, parallels can be drawn between quaternary numerals and the way genetic code is represented by DNA. The four DNA nucleotides in order, abbreviated A, C, G and T, can be taken to represent the quaternary digits in numerical order 0,1,2. With this encoding, the complementary digit pairs 0↔3, and 1↔2 match the complementation of the pairs, A↔T and C↔G. For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010, quaternary line codes have been used for transmission, from the invention of the telegraph to the 2B1Q code used in modern ISDN circuits
10.
Quinary
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Quinary is a numeral system with five as the base. A possible origination of a system is that there are five fingers on either hand. The base five is stated from 0–4, in the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100, today, the main usage of base 5 is as a biquinary system, which is decimal using five as a sub-base. Another example of a system, is sexagesimal, base 60. Each quinary digit has log25 bits of information, many languages use quinary number systems, including Gumatj, Nunggubuyu, Kuurn Kopan Noot, Luiseño and Saraveca. Gumatj is a true 5–25 language, in which 25 is the group of 5. The Gumatj numerals are shown below, In the video game Riven and subsequent games of the Myst franchise, a decimal system with 2 and 5 as a sub-bases is called biquinary, and is found in Wolof and Khmer. Roman numerals are a biquinary system, the numbers 1,5,10, and 50 are written as I, V, X, and L respectively. Eight is VIII and seventy is LXX, most versions of the abacus use a biquinary system to simulate a decimal system for ease of calculation. Urnfield culture numerals and some tally mark systems are also biquinary, units of currencies are commonly partially or wholly biquinary. A vigesimal system with 4 and 5 as a sub-bases is found in Nahuatl, pentimal system Quibinary Yan Tan Tethera References, Quinary Base Conversion, includes fractional part, from Math Is Fun Media related to Quinary numeral system at Wikimedia Commons
11.
Senary
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
12.
Octal
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The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping binary digits into groups of three. For example, the representation for decimal 74 is 1001010. Two zeroes can be added at the left,1001010, corresponding the octal digits 112, in the decimal system each decimal place is a power of ten. For example,7410 =7 ×101 +4 ×100 In the octal system each place is a power of eight. The Yuki language in California and the Pamean languages in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves and it has been suggested that the reconstructed Proto-Indo-European word for nine might be related to the PIE word for new. Based on this, some have speculated that proto-Indo-Europeans used a number system. In 1716 King Charles XII of Sweden asked Emanuel Swedenborg to elaborate a number based on 64 instead of 10. Swedenborg however argued that for people with less intelligence than the king such a big base would be too difficult, in 1718 Swedenborg wrote a manuscript, En ny rekenkonst som om vexlas wid Thalet 8 i stelle then wanliga wid Thalet 10. The numbers 1-7 are there denoted by the l, s, n, m, t, f, u. Thus 8 = lo,16 = so,24 = no,64 = loo,512 = looo etc, numbers with consecutive consonants are pronounced with vowel sounds between in accordance with a special rule. Writing under the pseudonym Hirossa Ap-Iccim in The Gentlemans Magazine, July 1745, Hugh Jones proposed a system for British coins, weights. In 1801, James Anderson criticized the French for basing the Metric system on decimal arithmetic and he suggested base 8 for which he coined the term octal. In the mid 19th century, Alfred B. Taylor concluded that Our octonary radix is, therefore, so, for example, the number 65 would be spoken in octonary as under-un. Taylor also republished some of Swedenborgs work on octonary as an appendix to the above-cited publications, in the 2009 film Avatar, the language of the extraterrestrial Navi race employs an octal numeral system, probably due to the fact that they have four fingers on each hand. In the TV series Stargate SG-1, the Ancients, a race of beings responsible for the invention of the Stargates, in the tabletop game series Warhammer 40,000, the Tau race use an octal number system. Octal became widely used in computing systems such as the PDP-8, ICL1900. Octal was an abbreviation of binary for these machines because their word size is divisible by three
13.
Duodecimal
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The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written by a rotated 2 and this notation was introduced by Sir Isaac Pitman. These digit forms are available as Unicode characters on computerized systems since June 2015 as ↊ and ↋, other notations use A, T, or X for ten and B or E for eleven. The number twelve is written as 10 in duodecimal, whereas the digit string 12 means 1 dozen and 2 units. Similarly, in duodecimal 100 means 1 gross,1000 means 1 great gross, the number twelve, a superior highly composite number, is the smallest number with four non-trivial factors, and the smallest to include as factors all four numbers within the subitizing range. As a result, duodecimal has been described as the number system. Of its factors,2 and 3 are prime, which means the reciprocals of all 3-smooth numbers have a representation in duodecimal. In particular, the five most elementary fractions all have a terminating representation in duodecimal. This all makes it a convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary. Although the trigesimal and sexagesimal systems do even better in respect, this is at the cost of unwieldy multiplication tables. In this section, numerals are based on decimal places, for example,10 means ten,12 means twelve. Languages using duodecimal number systems are uncommon, germanic languages have special words for 11 and 12, such as eleven and twelve in English. However, they are considered to come from Proto-Germanic *ainlif and *twalif, historically, units of time in many civilizations are duodecimal. There are twelve signs of the zodiac, twelve months in a year, traditional Chinese calendars, clocks, and compasses are based on the twelve Earthly Branches. There are 12 inches in a foot,12 troy ounces in a troy pound,12 old British pence in a shilling,24 hours in a day. The Romans used a system based on 12, including the uncia which became both the English words ounce and inch. The importance of 12 has been attributed to the number of cycles in a year. It is possible to count to 12 with the acting as a pointer
14.
Hexadecimal
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In mathematics and computing, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, Hexadecimal numerals are widely used by computer system designers and programmers. As each hexadecimal digit represents four binary digits, it allows a more human-friendly representation of binary-coded values, one hexadecimal digit represents a nibble, which is half of an octet or byte. For example, a byte can have values ranging from 00000000 to 11111111 in binary form. In a non-programming context, a subscript is typically used to give the radix, several notations are used to support hexadecimal representation of constants in programming languages, usually involving a prefix or suffix. The prefix 0x is used in C and related languages, where this value might be denoted as 0x2AF3, in contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers expressed in other bases. There are several conventions for expressing values unambiguously, a numerical subscript can give the base explicitly,15910 is decimal 159,15916 is hexadecimal 159, which is equal to 34510. Some authors prefer a text subscript, such as 159decimal and 159hex, or 159d and 159h. example. com/name%20with%20spaces where %20 is the space character, thus ’, represents the right single quotation mark, Unicode code point number 2019 in hex,8217. In the Unicode standard, a value is represented with U+ followed by the hex value. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #, white, CSS allows 3-hexdigit abbreviations with one hexdigit per component, #FA3 abbreviates #FFAA33. *nix shells, AT&T assembly language and likewise the C programming language, to output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h, some assembly languages use the notation HABCD. Ada and VHDL enclose hexadecimal numerals in based numeric quotes, 16#5A3#, for bit vector constants VHDL uses the notation x5A3. Verilog represents hexadecimal constants in the form 8hFF, where 8 is the number of bits in the value, the Smalltalk language uses the prefix 16r, 16r5A3 PostScript and the Bourne shell and its derivatives denote hex with prefix 16#, 16#5A3. For PostScript, binary data can be expressed as unprefixed consecutive hexadecimal pairs, in early systems when a Macintosh crashed, one or two lines of hexadecimal code would be displayed under the Sad Mac to tell the user what went wrong. Common Lisp uses the prefixes #x and #16r, setting the variables *read-base* and *print-base* to 16 can also used to switch the reader and printer of a Common Lisp system to Hexadecimal number representation for reading and printing numbers. Thus Hexadecimal numbers can be represented without the #x or #16r prefix code, MSX BASIC, QuickBASIC, FreeBASIC and Visual Basic prefix hexadecimal numbers with &H, &H5A3 BBC BASIC and Locomotive BASIC use & for hex. TI-89 and 92 series uses a 0h prefix, 0h5A3 ALGOL68 uses the prefix 16r to denote hexadecimal numbers, binary, quaternary and octal numbers can be specified similarly
15.
Vigesimal
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The vigesimal or base 20 numeral system is based on twenty. In a vigesimal system, twenty individual numerals are used. One modern method of finding the extra needed symbols is to write ten as the letter A20, to write nineteen as J20, and this is similar to the common computer-science practice of writing hexadecimal numerals over 9 with the letters A–F. Another method skips over the letter I, in order to avoid confusion between I20 as eighteen and one, so that the number eighteen is written as J20, the number twenty is written as 1020. According to this notation,2020 means forty in decimal = + D020 means two hundred and sixty in decimal = +10020 means four hundred in decimal = + +, in the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example,10 means ten,20 means twenty, in decimal, dividing by three twice only gives one digit periods because 9 is the number below ten. 21, however, the adjacent to 20 that is divisible by 3, is not divisible by 9. Ninths in vigesimal have six-digit periods, the prime factorization of twenty is 22 ×5, so it is not a perfect power. However, its part,5, is congruent to 1. Thus, according to Artins conjecture on primitive roots, vigesimal has infinitely many cyclic primes, but the fraction of primes that are cyclic is not necessarily ~37. 395%. An UnrealScript program that computes the lengths of recurring periods of various fractions in a set of bases found that, of the first 15,456 primes. In many European languages,20 is used as a base, vigesimal systems are common in Africa, for example in Yoruba. Ogún,20, is the basic numeric block, ogójì,40, =20 multiplied by 2. Ogota,60, =20 multiplied by 3, ogorin,80, =20 multiplied by 4. Ogorun,100, =20 multiplied by 5, twenty was a base in the Maya and Aztec number systems. The Maya used the names for the powers of twenty, kal, bak, pic, calab, kinchil. See also Maya numerals and Maya calendar, Mayan languages, Yucatec, the Aztec called them, cempoalli, centzontli, cenxiquipilli, cempoalxiquipilli, centzonxiquipilli and cempoaltzonxiquipilli. Note that the ce prefix at the beginning means one and is replaced with the number to get the names of other multiples of the power
16.
Base 36
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
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
18.
Sphenic number
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In number theory, a sphenic number is a positive integer that is the product of three distinct prime numbers. A sphenic number is a product pqr where p, q and this definition is more stringent than simply requiring the integer to have exactly three prime factors. For instance,60 =22 ×3 ×5 has exactly 3 prime factors, the smallest sphenic number is 30 =2 ×3 ×5, the product of the smallest three primes. The first few numbers are 30,42,66,70,78,102,105,110,114,130,138,154,165. As of January 2016 the largest known number is × ×. It is the product of the three largest known primes, all sphenic numbers have exactly eight divisors. If we express the number as n = p ⋅ q ⋅ r, where p, q. For example,24 is not a number, but it has exactly eight divisors. All sphenic numbers are by definition squarefree, because the factors must be distinct. The Möbius function of any number is −1. The cyclotomic polynomials Φ n, taken over all sphenic numbers n, the first case of two consecutive sphenic integers is 230 = 2×5×23 and 231 = 3×7×11. The first case of three is 1309 = 7×11×17,1310 = 2×5×131, and 1311 = 3×19×23, there is no case of more than three, because every fourth consecutive positive integer is divisible by 4 = 2×2 and therefore not squarefree. The numbers 2013,2014, and 2015 are all sphenic, the next three consecutive sphenic years will be 2665,2666 and 2667. Semiprimes, products of two prime numbers
19.
The Book of One Thousand and One Nights
–
One Thousand and One Nights is a collection of Middle Eastern and South Asian stories and folk tales compiled in Arabic during the Islamic Golden Age. It is often known in English as the Arabian Nights, from the first English-language edition, the work was collected over many centuries by various authors, translators, and scholars across West, Central, and South Asia and North Africa. The tales themselves trace their roots back to ancient and medieval Arabic, Persian, Mesopotamian, Indian, Jewish, the stories proceed from this original tale, some are framed within other tales, while others begin and end of their own accord. Some editions contain only a few hundred nights, while others include 1,001 or more, the bulk of the text is in prose, although verse is occasionally used for songs and riddles and to express heightened emotion. Most of the poems are single couplets or quatrains, although some are longer, the main frame story concerns Shahryār, whom the narrator calls a Sasanian king ruling in India and China. Shahryār begins to marry a succession of only to execute each one the next morning. Eventually the vizier, whose duty it is to provide them, Scheherazade, the viziers daughter, offers herself as the next bride and her father reluctantly agrees. On the night of their marriage, Scheherazade begins to tell the king a tale, the king, curious about how the story ends, is thus forced to postpone her execution in order to hear the conclusion. The next night, as soon as she finishes the tale, she begins a new one, so it goes on for 1,001 nights. The tales vary widely, they include historical tales, love stories, tragedies, comedies, poems, burlesques, numerous stories depict jinns, ghouls, apes, sorcerers, magicians, and legendary places, which are often intermingled with real people and geography, not always rationally. The different versions have different individually detailed endings but they all end with the giving his wife a pardon. The narrators standards for what constitutes a cliffhanger seem broader than in modern literature, the history of the Nights is extremely complex and modern scholars have made many attempts to untangle the story of how the collection as it currently exists came about. Most scholars agreed that the Nights was a work and that the earliest tales in it came from India and Persia. At some time, probably in the early 8th century, these tales were translated into Arabic under the title Alf Layla and this collection then formed the basis of The Thousand and One Nights. The original core of stories was quite small, then, in Iraq in the 9th or 10th century, this original core had Arab stories added to it – among them some tales about the Caliph Harun al-Rashid. Devices found in Sanskrit literature such as stories and animal fables are seen by some scholars as lying at the root of the conception of the Nights. Indian folklore is represented in the Nights by certain animal stories, the influence of the Panchatantra and Baital Pachisi is particularly notable. The Jataka Tales are a collection of 547 Buddhist stories, which are for the most part moral stories with an ethical purpose
20.
Arab
–
Arabs are an ethnic group inhabiting the Arab world. They primarily live in the Arab states in Western Asia, North Africa, the Horn of Africa, the Arabs are first mentioned in the mid-ninth century BCE as a tribal people dwelling in the central Arabian Peninsula. The Arabs appear to have been under the vassalage of the Neo-Assyrian Empire, tradition holds that Arabs descend from Ishmael, the son of Abraham. The Arabian Desert is the birthplace of Arab, there are other Arab groups as well that spread in the land and existed for millennia. Before the expansion of the Caliphate, Arab referred to any of the largely nomadic Semitic people from the northern to the central Arabian Peninsula and Syrian Desert. Presently, Arab refers to a number of people whose native regions form the Arab world due to spread of Arabs throughout the region during the early Arab conquests of the 7th and 8th centuries. The Arabs forged the Rashidun, Umayyad and the Abbasid caliphates, whose borders reached southern France in the west, China in the east, Anatolia in the north, and this was one of the largest land empires in history. The Great Arab Revolt has had as big an impact on the modern Middle East as the World War I, the war signaled the end of the Ottoman Empire. They are modern states and became significant as distinct political entities after the fall and defeat, following adoption of the Alexandria Protocol in 1944, the Arab League was founded on 22 March 1945. The Charter of the Arab League endorsed the principle of an Arab homeland whilst respecting the sovereignty of its member states. Beyond the boundaries of the League of Arab States, Arabs can also be found in the global diaspora, the ties that bind Arabs are ethnic, linguistic, cultural, historical, identical, nationalist, geographical and political. The Arabs have their own customs, language, architecture, art, literature, music, dance, media, cuisine, dress, society, sports, the total number of Arabs are an estimated 450 million. This makes them the second largest ethnic group after the Han Chinese. Arabs are a group in terms of religious affiliations and practices. In the pre-Islamic era, most Arabs followed polytheistic religions, some tribes had adopted Christianity or Judaism, and a few individuals, the hanifs, apparently observed monotheism. Today, Arabs are mainly adherents of Islam, with sizable Christian minorities, Arab Muslims primarily belong to the Sunni, Shiite, Ibadi, Alawite, Druze and Ismaili denominations. Arab Christians generally follow one of the Eastern Christian Churches, such as the Maronite, Coptic Orthodox, Greek Orthodox, Greek Catholic, or Chaldean churches. Listed among the booty captured by the army of king Shalmaneser III of Assyria in the Battle of Qarqar are 1000 camels of Gi-in-di-buu the ar-ba-a-a or Gindibu belonging to the Arab
21.
Arabic language
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Arabic is a Central Semitic language that was first spoken in Iron Age northwestern Arabia and is now the lingua franca of the Arab world. Arabic is also the language of 1.7 billion Muslims. It is one of six languages of the United Nations. The modern written language is derived from the language of the Quran and it is widely taught in schools and universities, and is used to varying degrees in workplaces, government, and the media. The two formal varieties are grouped together as Literary Arabic, which is the language of 26 states. Modern Standard Arabic largely follows the standards of Quranic Arabic. Much of the new vocabulary is used to denote concepts that have arisen in the post-Quranic era, Arabic has influenced many languages around the globe throughout its history. During the Middle Ages, Literary Arabic was a vehicle of culture in Europe, especially in science, mathematics. As a result, many European languages have borrowed many words from it. Many words of Arabic origin are found in ancient languages like Latin. Balkan languages, including Greek, have acquired a significant number of Arabic words through contact with Ottoman Turkish. Arabic has also borrowed words from languages including Greek and Persian in medieval times. Arabic is a Central Semitic language, closely related to the Northwest Semitic languages, the Ancient South Arabian languages, the Semitic languages changed a great deal between Proto-Semitic and the establishment of the Central Semitic languages, particularly in grammar. Innovations of the Central Semitic languages—all maintained in Arabic—include, The conversion of the suffix-conjugated stative formation into a past tense, the conversion of the prefix-conjugated preterite-tense formation into a present tense. The elimination of other prefix-conjugated mood/aspect forms in favor of new moods formed by endings attached to the prefix-conjugation forms, the development of an internal passive. These features are evidence of descent from a hypothetical ancestor. In the southwest, various Central Semitic languages both belonging to and outside of the Ancient South Arabian family were spoken and it is also believed that the ancestors of the Modern South Arabian languages were also spoken in southern Arabia at this time. To the north, in the oases of northern Hijaz, Dadanitic and Taymanitic held some prestige as inscriptional languages, in Najd and parts of western Arabia, a language known to scholars as Thamudic C is attested
22.
Detergent
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A detergent is a surfactant or a mixture of surfactants with cleaning properties in dilute solutions. In most household contexts, the term detergent by itself refers specifically to laundry detergent or dish detergent, detergents are commonly available as powders or concentrated solutions. Detergents, like soaps, work because they are amphiphilic, partly hydrophilic and their dual nature facilitates the mixture of hydrophobic compounds with water. Because air is not hydrophilic, detergents are also foaming agents to varying degrees, detergents are classified into three broad groupings, depending on the electrical charge of the surfactants. The alkylbenzene portion of these anions is lipophilic and the sulfonate is hydrophilic, two different varieties have been popularized, those with branched alkyl groups and those with linear alkyl groups. The former were phased out in economically advanced societies because they are poorly biodegradable. An estimated 6 billion kilograms of detergents are produced annually for domestic markets. Bile acids, such as acid, are anionic detergents produced by the liver to aid in digestion and absorption of fats. The ammonium center is positively charged, non-ionic detergents are characterized by their uncharged, hydrophilic headgroups. Typical non-ionic detergents are based on polyoxyethylene or a glycoside, common examples of the former include Tween, Triton, and the Brij series. These materials are known as ethoxylates or PEGlyates and their metabolites. Glycosides have a sugar as their uncharged hydrophilic headgroup, examples include octyl thioglucoside and maltosides. HEGA and MEGA series detergents are similar, possessing an alcohol as headgroup. Zwitterionic detergents possess a net zero charge arising from the presence of numbers of +1. In World War I, there was a shortage of oils, synthetic detergents were first made in Germany. One of the largest applications of detergents is for household cleaning including dish washing and washing laundry, the formulations are complex, reflecting the diverse demands of the application and the highly competitive consumer market. Both carburetors and fuel injector components of Otto engines benefit from detergents in the fuels to prevent fouling, typical detergents are long-chain amines and amides such as polyisobuteneamine and polyisobuteneamide/succinimide. Reagent grade detergents are employed for the isolation and purification of integral membrane proteins found in biological cells, solubilization of cell membrane bilayers requires a detergent that can enter the inner membrane monolayer
23.
Mawlawiyyah
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The Mawlawīyya / Mevlevi Order is a Sufi order in Konya founded by the followers of Jalal al-Din Muhammad Balkhi-Rumi, a 13th-century Persian poet, Islamic theologian and Sufi mystic. The Mevlevi are also known as the Whirling Dervishes due to their famous practice of whirling as a form of dhikr. Dervish is a term for an initiate of the Sufi path, the whirling is part of the formal Sama ceremony. In 2008, UNESCO confirmed the The Mevlevi Sema Ceremony of Turkey as amongst the Masterpieces of the Oral and he was an accomplished Sufi mystic with great organizing talents. His personal efforts were continued by his successor Ulu Arif Çelebi, the Mevlevi believe in performing their dhikr in the form of a dance and musical ceremony known as the Sama, which involves the whirling, from which the order acquired its nickname. The Sama represents a journey of mans spiritual ascent through mind. Turning towards the truth, the follower grows through love, deserts his ego, finds the truth and he then returns from this spiritual journey as a man who has reached maturity and a greater perfection, able to love and to be of service to the whole of creation. Rumi has said in reference to Sama, For them it is the Sama of this world, even more for the circle of dancers within the Sama Who turn and have, in their midst, their own Kaaba. The origin of Sama is credited to Rumi, Sufi master, the story of the creation of this unique form of dhikr tells that Rumi was walking through the town marketplace one day, when he heard the rhythmic hammering of the goldbeaters. With that, the practice of Sama and the dervishes of the Mevlevi Order were born, the Sama was practised in the samahane according to a precisely prescribed symbolic ritual with the dervishes whirling in a circle around their sheikh, who is the only one whirling around his axis. The Sama is performed by spinning on the Left foot, the dervishes wear a white gown, a wide black cloak and a tall brown hat, symbol of the tombstone. Sama ceremonies are broken up into four parts all have their own meanings. Naat and Taksim – Naat is the beginning of the ceremony where a solo singer offers praise for the Islamic prophet Muhammad, the first part is finished with taksim of the ney reed flute which symbolizes our separation from God. Devr-i Veled – During the following Devr-i Veled, the bow to each other. The bow is said to represent the acknowledgement of the Divine breath which has been breathed into all of us, after all the dervishes have done this they kneel and remove their black cloaks. The Four Salams – The Four Salams are the part of Sama. The samazens or whirling dervishes are representative of the moon and they spin on the outside of the Sheikh who is representative of the sun. They, as mentioned, spin on their left foot and additionally, they have their right palm facing upwards towards Heaven
24.
Sufi
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Sufism or Taṣawwuf, which is often defined as Islamic mysticism, the inward dimension of Islam, or the phenomenon of mysticism within Islam, is a mystical trend in Islam characterized. These orders meet for sessions in meeting places known as zawiyas, khanqahs. They strive for ihsan as detailed in a hadith, Ihsan is to worship Allah as if you see Him, if you cant see Him, Rumi stated, The Sufi is hanging on to Muhammad, like Abu Bakr. Sufis regard Muhammad as al-Insān al-Kāmil, the perfect man who exemplifies the morality of God. The orders largely follow one of the four madhhabs of Sunni Islam, classical Sufis were characterized by their asceticism, especially by their attachment to dhikr, the practice of repeating the names of God, often performed after prayers. According to William Chittick, In a broad sense, Sufism can be described as the interiorization, historically, Muslims have used the Arabic word taṣawwuf to identify the practice of Sufis. In this view, it is necessary to be a Muslim to be a true Sufi. However, Islamic scholars themselves are not by any means in agreement about the meaning of the word sufi, Sufis themselves claim that Tasawwuf is an aspect of Islam similar to Sharia, inseparable from Islam and an integral part of Islamic belief and practice. Classical Sufi scholars have defined Tasawwuf as a science whose objective is the reparation of the heart and turning it away from all else, two origins of the word sufi have been suggested. Commonly, the root of the word is traced to ṣafā. Another origin is ṣūf, wool in Arabic, referring to the simple cloaks the early Muslim ascetics wore, the two were combined by the Sufi al-Rudhabari, who said, The Sufi is the one who wears wool on top of purity. Scholars generally agree that ṣūf or wool is probably the word of Sufi. This term was given to them because they wore woollen garments, the term labisal-suf meant he clad himself in wool and applied to a person who renounced the world and became an ascetic. Others have suggested that the word comes from the term ahl aṣ-ṣuffah and these men and women who sat at al-Masjid an-Nabawi are considered by some to be the first Sufis. Al-Qushayri and Ibn Khaldun both rejected all other than ṣūf on linguistic grounds. Sufi orders are based on the bayah that was given to the Prophet Muhammad by his Sahaba, by pledging allegiance to the Prophet Muhammad, the Sahaba had committed themselves to the service of God. According to Islamic belief, by pledging allegiance to Prophet Muhammad and it is through the Prophet Muhammad that Sufis aim to learn about, understand and connect with God. Such a concept may be understood by the hadith, which Sufis regard to be authentic, in which Prophet Muhammad said, I am the city of knowledge, eminent Sufis such as Ali Hujwiri refer to Ali as having a very high ranking in Tasawwuf
25.
Islam
–
Islam is an Abrahamic monotheistic religion which professes that there is only one and incomparable God and that Muhammad is the last messenger of God. It is the worlds second-largest religion and the major religion in the world, with over 1.7 billion followers or 23% of the global population. Islam teaches that God is merciful, all-powerful, and unique, and He has guided mankind through revealed scriptures, natural signs, and a line of prophets sealed by Muhammad. The primary scriptures of Islam are the Quran, viewed by Muslims as the word of God. Muslims believe that Islam is the original, complete and universal version of a faith that was revealed many times before through prophets including Adam, Noah, Abraham, Moses. As for the Quran, Muslims consider it to be the unaltered, certain religious rites and customs are observed by the Muslims in their family and social life, while social responsibilities to parents, relatives, and neighbors have also been defined. Besides, the Quran and the sunnah of Muhammad prescribe a comprehensive body of moral guidelines for Muslims to be followed in their personal, social, political, Islam began in the early 7th century. Originating in Mecca, it spread in the Arabian Peninsula. The expansion of the Muslim world involved various caliphates and empires, traders, most Muslims are of one of two denominations, Sunni or Shia. Islam is the dominant religion in the Middle East, North Africa, sizable Muslim communities are also found in Horn of Africa, Europe, China, Russia, Mainland Southeast Asia, Philippines, Northern Borneo, Caucasus and the Americas. Converts and immigrant communities are found in almost every part of the world, Islam is a verbal noun originating from the triliteral root s-l-m which forms a large class of words mostly relating to concepts of wholeness, submission, safeness and peace. In a religious context it means voluntary submission to God, Islām is the verbal noun of Form IV of the root, and means submission or surrender. Muslim, the word for an adherent of Islam, is the active participle of the verb form. The word sometimes has connotations in its various occurrences in the Quran. In some verses, there is stress on the quality of Islam as a state, Whomsoever God desires to guide. Other verses connect Islām and dīn, Today, I have perfected your religion for you, I have completed My blessing upon you, still others describe Islam as an action of returning to God—more than just a verbal affirmation of faith. In the Hadith of Gabriel, islām is presented as one part of a triad that also includes imān, Islam was historically called Muhammadanism in Anglophone societies. This term has fallen out of use and is said to be offensive because it suggests that a human being rather than God is central to Muslims religion
26.
Thousand and One Nights
–
One Thousand and One Nights is a collection of Middle Eastern and South Asian stories and folk tales compiled in Arabic during the Islamic Golden Age. It is often known in English as the Arabian Nights, from the first English-language edition, the work was collected over many centuries by various authors, translators, and scholars across West, Central, and South Asia and North Africa. The tales themselves trace their roots back to ancient and medieval Arabic, Persian, Mesopotamian, Indian, Jewish, the stories proceed from this original tale, some are framed within other tales, while others begin and end of their own accord. Some editions contain only a few hundred nights, while others include 1,001 or more, the bulk of the text is in prose, although verse is occasionally used for songs and riddles and to express heightened emotion. Most of the poems are single couplets or quatrains, although some are longer, the main frame story concerns Shahryār, whom the narrator calls a Sasanian king ruling in India and China. Shahryār begins to marry a succession of only to execute each one the next morning. Eventually the vizier, whose duty it is to provide them, Scheherazade, the viziers daughter, offers herself as the next bride and her father reluctantly agrees. On the night of their marriage, Scheherazade begins to tell the king a tale, the king, curious about how the story ends, is thus forced to postpone her execution in order to hear the conclusion. The next night, as soon as she finishes the tale, she begins a new one, so it goes on for 1,001 nights. The tales vary widely, they include historical tales, love stories, tragedies, comedies, poems, burlesques, numerous stories depict jinns, ghouls, apes, sorcerers, magicians, and legendary places, which are often intermingled with real people and geography, not always rationally. The different versions have different individually detailed endings but they all end with the giving his wife a pardon. The narrators standards for what constitutes a cliffhanger seem broader than in modern literature, the history of the Nights is extremely complex and modern scholars have made many attempts to untangle the story of how the collection as it currently exists came about. Most scholars agreed that the Nights was a work and that the earliest tales in it came from India and Persia. At some time, probably in the early 8th century, these tales were translated into Arabic under the title Alf Layla and this collection then formed the basis of The Thousand and One Nights. The original core of stories was quite small, then, in Iraq in the 9th or 10th century, this original core had Arab stories added to it – among them some tales about the Caliph Harun al-Rashid. Devices found in Sanskrit literature such as stories and animal fables are seen by some scholars as lying at the root of the conception of the Nights. Indian folklore is represented in the Nights by certain animal stories, the influence of the Panchatantra and Baital Pachisi is particularly notable. The Jataka Tales are a collection of 547 Buddhist stories, which are for the most part moral stories with an ethical purpose
27.
Islamic world
–
The terms Muslim world and Islamic world commonly refer to the Islamic community, comprising all those who adhere to the religion of Islam, or to societies where Islam is practiced. In a modern sense, these terms refer to countries where Islam is widespread. In the modern era, most of the Muslim world came under influence or colonial domination of European powers. The nation states emerged in the post-colonial era have adopted a variety of political and economic models. As of 2015, over 1.7 billion or about 23% of the population are Muslims including the 4% who live as minorities. Muslim history involves the history of the Islamic faith as a religion, the history of Islam began in Arabia with the Islamic prophet Muhammads first recitations of the Quran in the 7th century in the month of Ramadan. However, Islam under the Rashidun Caliphate grew rapidly, a century after the death of last Islamic prophet Muhammad, the Islamic empire extended from Spain in the west to Indus in the east. The Islamic Golden Age coincided with the Middle Ages in the Muslim world, starting with the rise of Islam and establishment of the first Islamic state in 622. The end of the age is given as 1258 with the Mongolian Sack of Baghdad, or 1492 with the completion of the Christian Reconquista of the Emirate of Granada in Al-Andalus. The Abbasids were influenced by the Quranic injunctions and hadiths, such as the ink of a scholar is more holy than the blood of a martyr, that stressed the value of knowledge. The major Islamic capital cities of Baghdad, Cairo, and Córdoba became the intellectual centers for science, philosophy, medicine. Between the 8th and 18th centuries, the use of glaze was prevalent in Islamic art. Tin-opacified glazing was one of the earliest new technologies developed by the Islamic potters, the first Islamic opaque glazes can be found as blue-painted ware in Basra, dating to around the 8th century. Another contribution was the development of fritware, originating from 9th century Iraq, other centers for innovative ceramic pottery in the Old world included Fustat, Damascus and Tabriz. The original concept is derived from a pre-Islamic Persian prototype Hezār Afsān that relied on particular Indian elements and it reached its final form by the 14th century, the number and type of tales have varied from one manuscript to another. All Arabian fantasy tales tend to be called Arabian Nights stories when translated into English, regardless of whether they appear in The Book of One Thousand and this work has been very influential in the West since it was translated in the 18th century, first by Antoine Galland. Imitations were written, especially in France, various characters from this epic have themselves become cultural icons in Western culture, such as Aladdin, Sinbad the Sailor and Ali Baba. A famous example of Arabic poetry and Persian poetry on romance is Layla and Majnun and it is a tragic story of undying love much like the later Romeo and Juliet, which was itself said to have been inspired by a Latin version of Layla and Majnun to an extent
28.
1001 Books You Must Read Before You Die
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Each title is accompanied by a brief synopsis and critique briefly explaining why the book was chosen. This book is part of a series from Quintessence Editions Ltd, the list contains 1001 titles and is made up of novels, short stories, and short story collections. There is also one pamphlet, one book of collected text, the most featured authors on the list are J. M. Coetzee and Charles Dickens with ten titles each. The 2010 revised and updated edition of the book is less Anglocentric and lists only four titles from Dickens and five from Coetzee and it also includes a collection of essays by Albert Camus, The Rebel. There was a revision of 280 odd titles in 2008. Minor changes of fewer than 20 books were made in 2010 and 2012,1001 Books You Must Read Before You Die, edited by Dr. Peter Boxall, Universe Publishing United Kingdom 2006 9781844-34178
29.
1001 Movies You Must See Before You Die
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1001 Movies You Must See Before You Die is a film reference book edited by Steven Jay Schneider with original essays on each film contributed by over 70 film critics. It is a part of a designed and produced by Quintessence Editions, a London-based company, and published in English-language versions by Cassell Illustrated, ABC Books. The first edition was published in 2003, the most recent edition was published in 2014, contributors include Adrian Martin, Jonathan Rosenbaum, Richard Peña, David Stratton, and Margaret Pomeranz. Each title is accompanied by a brief synopsis and critique, some with photographs, the localized editions include a few of the countrys own films. Schneider, Steven Jay, ed.1001 Movies You Must See Before You Die, hauppauge, New York, Barrons Educational Series. Schneider, Steven Jay, ed.1001 Movies You Must See Before You Die, hauppauge, New York, Barrons Educational Series. Schneider, Steven Jay, ed.1001 Movies You Must See Before You Die, hauppauge, New York, Barrons Educational Series. Schneider, Steven Jay, ed.1001 Movies You Must See Before You Die, hauppauge, New York, Barrons Educational Series. Schneider, Steven Jay, ed.1001 Movies You Must See Before You Die, hauppauge, New York, Barrons Educational Series. Schneider, Steven Jay, ed.1001 Movies You Must See Before You Die, hauppauge, New York, Barrons Educational Series. Schneider, Steven Jay, ed.1001 Movies You Must See Before You Die, hauppauge, New York, Barrons Educational Series. Schneider, Steven Jay, ed.1001 Movies You Must See Before You Die, hauppauge, New York, Barrons Educational Series. Schneider, Steven Jay, ed.1001 Movies You Must See Before You Die, hauppauge, New York, Barrons Educational Series. Schneider, Steven Jay, ed.1001 Movies You Must See Before You Die, hauppauge, New York, Barrons Educational Series. Schneider, Steven Jay, ed.1001 Movies You Must See Before You Die, hauppauge, New York, Barrons Educational Series. Schneider, Steven Jay, ed.1001 Movies You Must See Before You Die, sydney, ABC Books for Australian Broadcasting Corp. p.960. Source, WorldCat 1001 Albums You Must Hear Before You Die 1001 Books You Must Read Before You Die 1001 Video Games You Must Play Before You Die 1,000 Recordings to Hear Before You Die Bernard Trink, Read the book then see the movies. 1001 ways to give cinema new scope, the must-see movies of all time
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1001 Albums You Must Hear Before You Die
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1001 Albums You Must Hear Before You Die is a musical reference book first published in 2005 by Universe Publishing. It compiles writings and information on albums chosen by a panel of critics to be the most important, influential. The book was edited by Robert Dimery, a writer and editor who had worked for magazines such as Time Out. Each entry in the books list of albums is accompanied by an essay written by a music critic, along with pictures, quotes. Only albums consisting fully of original material by a particular artist were included, the most recent edition consists of a list of albums released between 1955 and 2016, part of a series from Quintessence Editions Ltd. The book is arranged chronologically, starting with Frank Sinatras In the Wee Small Hours, in February 2006, Publishers Weekly called the book a. bookshelf-busting testament to music geeks mania for lists and said it. is about as comprehensive a best-of as any sane person could want. They continued, For music lovers, it doesnt get much better, the 2006 version had an average rating of 3.92 stars out of 5 on Amazon. coms social cataloging website Goodreads, with 860 ratings as of April 30,2015. The same 2006 version had a rating of 3.5 stars out of 5 on Amazon. com. Most of the recommendations are rock and pop albums from the Western world. 1001 Albums also features selections from world music, rhythm and blues, blues, folk, hip hop, country, electronic music, and jazz. The rock and pop albums include such subgenres as punk rock, grindcore, heavy metal, alternative rock, progressive rock, easy listening, thrash metal, grunge and 1950s-style rock, classical and modern art music are excluded. These artists have the most albums in the 2016 edition,7 albums, The Beatles, Elvis Costello, Bob Dylan. 6 albums, Morrissey, The Rolling Stones,5 albums, The Byrds, Brian Eno, Led Zeppelin, Iggy Pop, Sonic Youth, Bruce Springsteen, Tom Waits, The Who. 4 albums, Nick Cave and The Bad Seeds, Leonard Cohen, Miles Davis, P. J. Harvey, The Kinks, Metallica, Joni Mitchell, Pink Floyd, Radiohead, steely Dan, The Talking Heads, U2, Stevie Wonder. Originally published in 2005, the book was revised in 2008,2011,2013, the 2011 edition includes 25 albums released from 2005 to 2009, with the same number of albums removed from the first edition to keep the total at 1001