1.
120 (number)
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120, read as one hundred twenty, is the natural number following 119 and preceding 121. In English and other Germanic languages, it was formerly known as one hundred. This hundred of six score is now obsolete, but is described as the hundred or great hundred in historical contexts. 120 is the factorial of 5, and the sum of a twin prime pair,120 is the sum of four consecutive prime numbers, four consecutive powers of 2, and four consecutive powers of 3. It is also a sparsely totient number,120 is the smallest number to appear six times in Pascals triangle. 120 is also the smallest multiple of 6 with no adjacent prime number and it is the eighth hexagonal number and the fifteenth triangular number, as well as the sum of the first eight triangular numbers, making it also a tetrahedral number. 120 is divisible by the first 5 triangular numbers and the first 4 tetrahedral numbers,120 is the first multiply perfect number of order three. The sum of its factors sum to 360, exactly three times 120, note that perfect numbers are order two by the same definition. 120 is divisible by the number of primes below it,30 in this case, however, there is no integer which has 120 as the sum of its proper divisors, making 120 an untouchable number. The sum of Eulers totient function φ over the first nineteen integers is 120,120 figures in Pierre de Fermats modified Diophantine problem as the largest known integer of the sequence 1,3,8,120. Fermat wanted to another positive integer that multiplied with any of the other numbers in the sequence yields a number that is one less than a square. Leonhard Euler also searched for this number, but failed to find it, the internal angles of a regular hexagon are all 120 degrees. 120 is a Harshad number in base 10,120 is the atomic number of Unbinilium, an element yet to be discovered. The cubits of the height of the Temple building The age at which Moses died, in astrology, when two planets in a persons chart are 120 degrees apart from each other, this is called a trine. This is supposed to bring luck in the persons life. The height in inches of a hoop in the National Basketball Association. 120 is also, The medical telephone number in China In Austria, in the US Army, a common diameter for a mortar in mm. TT scale, a scale for model trains, is 1,120. 120 film is a medium format film developed by Kodak,120, a 2008 Turkish film The Israeli national legislature, the Knesset, has 120 seats
2.
121 (number)
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121 is the natural number following 120 and preceding 122. One hundred twenty-one is a square and is the sum of three consecutive primes, there are no squares besides 121 known to be of the form 1 + p + p 2 + p 3 + p 4, where p is prime. Other such squares must have at least 35 digits, there are only two other squares known to be of the form n. Another example of 121 being of the few examples supporting a conjecture is that Fermat conjectured that 4 and 121 are the perfect squares of the form x3 -4. It is also a number and a centered octagonal number. In base 10, it is a Smith number since its digits add up to the value as its factorization. But it can not be expressed as the sum of any other number plus that numbers digits, making 121 a self number
3.
125 (number)
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125 is the natural number following 124 and preceding 126. It can be expressed as a sum of two squares in two different ways,125 = 10² + 5² = 11² + 2²,125 and 126 form a Ruth-Aaron pair under the second definition in which repeated prime factors are counted as often as they occur. Like many other powers of 5, it is a Friedman number in base 10 since 125 =51 +2
4.
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
5.
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
6.
100 (number)
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100 or one hundred is the natural number following 99 and preceding 101. In medieval contexts, it may be described as the hundred or five score in order to differentiate the English. The standard SI prefix for a hundred is hecto-,100 is the basis of percentages, with 100% being a full amount. 100 is the sum of the first nine prime numbers, as well as the sum of pairs of prime numbers e. g.3 +97,11 +89,17 +83,29 +71,41 +59. 100 is the sum of the cubes of the first four integers and this is related by Nicomachuss theorem to the fact that 100 also equals the square of the sum of the first four integers,100 =102 =2. 26 +62 =100, thus 100 is a Leyland number and it is divisible by the number of primes below it,25 in this case. It can not be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient and it can be expressed as a sum of some of its divisors, making it a semiperfect number. 100 is a Harshad number in base 10, and also in base 4, there are exactly 100 prime numbers whose digits are in strictly ascending order. 100 is the smallest number whose common logarithm is a prime number,100 senators are in the U. S One hundred is the atomic number of fermium, an actinide. On the Celsius scale,100 degrees is the temperature of pure water at sea level. The Kármán line lies at an altitude of 100 kilometres above the Earths sea level and is used to define the boundary between Earths atmosphere and outer space. There are 100 blasts of the Shofar heard in the service of Rosh Hashana, a religious Jew is expected to utter at least 100 blessings daily. In Hindu Religion - Mythology Book Mahabharata - Dhritarashtra had 100 sons known as kauravas, the United States Senate has 100 Senators. Most of the currencies are divided into 100 subunits, for example, one euro is one hundred cents. The 100 Euro banknotes feature a picture of a Rococo gateway on the obverse, the U. S. hundred-dollar bill has Benjamin Franklins portrait, the Benjamin is the largest U. S. bill in print. American savings bonds of $100 have Thomas Jeffersons portrait, while American $100 treasury bonds have Andrew Jacksons portrait, One hundred is also, The number of years in a century. The number of pounds in an American short hundredweight, in Greece, India, Israel and Nepal,100 is the police telephone number. In Belgium,100 is the ambulance and firefighter telephone number, in United Kingdom,100 is the operator telephone number
7.
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
8.
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
9.
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
10.
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
11.
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
12.
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
13.
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
14.
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
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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
16.
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
17.
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
18.
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
19.
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
20.
6 (number)
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6 is the natural number following 5 and preceding 7. The SI prefix for 10006 is exa-, and for its reciprocal atto-,6 is the smallest positive integer which is neither a square number nor a prime number. Six is the second smallest composite number, its proper divisors are 1,2 and 3, since six equals the sum of its proper divisors, six is the smallest perfect number, Granville number, and S -perfect number. As a perfect number,6 is related to the Mersenne prime 3,6 is the only even perfect number that is not the sum of successive odd cubes. As a perfect number,6 is the root of the 6-aliquot tree, and is itself the sum of only one number. Six is the number that is both the sum and the product of three consecutive positive numbers. Unrelated to 6 being a number, a Golomb ruler of length 6 is a perfect ruler. Six is the first discrete biprime and the first member of the discrete biprime family, Six is the smallest natural number that can be written as the sum of two positive rational cubes which are not integers,6 =3 +3. Six is a perfect number, a harmonic divisor number and a superior highly composite number. The next superior highly composite number is 12,5 and 6 form a Ruth-Aaron pair under either definition. There are no Graeco-Latin squares with order 6, if n is a natural number that is not 2 or 6, then there is a Graeco-Latin square with order n. The smallest non-abelian group is the symmetric group S3 which has 3, s6, with 720 elements, is the only finite symmetric group which has an outer automorphism. This automorphism allows us to construct a number of mathematical objects such as the S Steiner system, the projective plane of order 4. This can also be expressed category theoretically, consider the category whose objects are the n element sets and this category has a non-trivial functor to itself only for n =6. 6 similar coins can be arranged around a central coin of the radius so that each coin makes contact with the central one. This makes 6 the answer to the kissing number problem. The densest sphere packing of the plane is obtained by extending this pattern to the lattice in which each circle touches just six others. 6 is the largest of the four all-Harshad numbers, a six-sided polygon is a hexagon, one of the three regular polygons capable of tiling the plane
21.
Book of Numbers
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The Book of Numbers is the fourth book of the Hebrew Bible, and the fourth of five books of the Jewish Torah. The book has a long and complex history, but its form is probably due to a Priestly redaction of a Yahwistic source made some time in the early Persian period. The name of the book comes from the two taken of the Israelites. Numbers begins at Mount Sinai, where the Israelites have received their laws, the task before them is to take possession of the Promised Land. The people are numbered and preparations are made for resuming their march, the Israelites begin the journey, but they murmur at the hardships along the way, and about the authority of Moses and Aaron. For these acts, God destroys approximately 15,000 of them through various means and they arrive at the borders of Canaan and send spies into the land. Upon hearing the spies fearful report concerning the conditions in Canaan, God condemns them to death in the wilderness until a new generation can grow up and carry out the task. The book ends with the new generation of Israelites in the Plain of Moab ready for the crossing of the Jordan River, Numbers is the culmination of the story of Israels exodus from oppression in Egypt and their journey to take possession of the land God promised their fathers. Numbers also demonstrates the importance of holiness, faithfulness and trust, despite Gods presence and his priests, Israel lacks faith and the possession of the land is left to a new generation. God orders Moses, in the wilderness of Sinai, to number those able to bear all the men from twenty years old and upward. A total of 603,550 Israelites are found to be fit for military service, the tribe of Levi is exempted from military service and therefore not included in the census. Moses consecrates the Levites for the service of the Tabernacle in the place of the first-born sons, the Levites are divided into three families, the Gershonites, the Kohathites, and the Merarites, each under a chief. The Kohathites were headed by Eleazar, son of Aaron, while the Gershonites and Merarites were headed by Aarons other son, preparations are then made for resuming the march to the Promised Land. Various ordinances and laws are decreed, the Israelites set out from Sinai. The people murmur against God and are punished by fire, Moses complains of their stubbornness and is ordered to choose seventy elders to assist him in the government of the people, twelve spies are sent out into Canaan and come back to report to Moses. Yahweh decrees that the Israelites will be punished for their loss of faith by having to wander in the wilderness for 40 years, Moses is ordered by God to make plates to cover the altar. The children of Israel murmur against Moses and Aaron on account of the destruction of Korahs men and are stricken with the plague, Aaron and his family are declared by God to be responsible for any iniquity committed in connection with the sanctuary. The Levites are again appointed to help in the keeping of the Tabernacle, the Levites are ordered to surrender to the priests a part of the tithes taken to them
22.
Aaron
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In the Hebrew Bible, Aaron was the elder brother of Moses and a Prophet of God. Islamic literature, which also considers Aaron a Prophet of God, knowledge of Aaron, along with his brother Moses, comes exclusively from religious texts, such as the Bible and Qur’an. The Hebrew Bible relates that, unlike Moses, who grew up in the Egyptian royal court, Aaron, when Moses first confronted the Egyptian king about the Israelites, Aaron served as his brothers spokesman to Pharaoh. Part of the Law that Moses received from God at Sinai granted Aaron the priesthood for himself and his male descendants, Aaron died before the Israelites crossed the North Jordan river and he was buried on Mount Hor. Aaron is also mentioned in the New Testament of the Bible, according to the Book of Exodus, Aaron first functioned as Moses assistant. Because Moses complained that he could not speak well, God appointed Aaron as Moses prophet, at the command of Moses, he let his rod turn into a snake. Then he stretched out his rod in order to bring on the first three plagues, after that, Moses tended to act and speak for himself. During the journey in the wilderness, Aaron was not always prominent or active, at the battle with Amalek, he was chosen with Hur to support the hand of Moses that held the rod of God. When the revelation was given to Moses at Mount Sinai, he headed the elders of Israel who accompanied Moses on the way to the summit, while Joshua went with Moses to the top, however, Aaron and Hur remained below to look after the people. From here on in Exodus, Leviticus and Numbers, Joshua appears in the role of Moses assistant while Aaron functions instead as the first high priest. The books of Exodus, Leviticus and Numbers maintain that Aaron received from God a monopoly over the priesthood for himself, the family of Aaron had the exclusive right and responsibility to make offerings on the altar to the God of Israel. The rest of his tribe, the Levites, were given subordinate responsibilities within the sanctuary, Moses anointed and consecrated Aaron and his sons to the priesthood, and arrayed them in the robes of office. He also related to them Gods detailed instructions for performing their duties while the rest of the Israelites listened, Aaron and his successors as high priest were given control over the Urim and Thummim by which the will of God could be determined. God commissioned the Aaronide priests to distinguish the holy from the common and the clean from the unclean, the priests were also commissioned to bless the people. In this way, the institution of the Aaronide priesthood was established, in later books of the Old Testament, Aaron and his kin are not mentioned very often except in literature dating to the Babylonian Exile and later. The books of Judges, Samuel and Kings mention priests and Levites, the book of Ezekiel, which devotes much attention to priestly matters, calls the priestly upper class the Zadokites after one of King Davids priests. It does reflect a two-tier priesthood with the Levites in subordinate position, a two-tier hierarchy of Aaronides and Levites appears in Ezra, Nehemiah and Chronicles. As a result, many think that Aaronide families did not control the priesthood in pre-exilic Israel
23.
Emergency telephone number
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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
24.
Colombia
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Colombia, officially the Republic of Colombia, is a transcontinental country largely situated in the northwest of South America, with territories in Central America. Colombia shares a border to the northwest with Panama, to the east with Venezuela and Brazil and to the south with Ecuador and it shares its maritime limits with Costa Rica, Nicaragua, Honduras, Jamaica, Haiti and the Dominican Republic. It is a unitary, constitutional republic comprising thirty-two departments, the territory of what is now Colombia was originally inhabited by indigenous peoples including the Muisca, the Quimbaya and the Tairona. The Spanish arrived in 1499 and initiated a period of conquest and colonization ultimately creating the Viceroyalty of New Granada, independence from Spain was won in 1819, but by 1830 the Gran Colombia Federation was dissolved. What is now Colombia and Panama emerged as the Republic of New Granada, the new nation experimented with federalism as the Granadine Confederation, and then the United States of Colombia, before the Republic of Colombia was finally declared in 1886. Since the 1960s the country has suffered from an asymmetric low-intensity armed conflict, Colombia is one of the most ethnically and linguistically diverse countries in the world, and thereby possesses a rich cultural heritage. Cultural diversity has also influenced by Colombias varied geography. The urban centres are located in the highlands of the Andes mountains. Colombian territory also encompasses Amazon rainforest, tropical grassland and both Caribbean and Pacific coastlines, ecologically, it is one of the worlds 17 megadiverse countries, and the most densely biodiverse of these per square kilometer. Colombia is a power and a regional actor with the fourth-largest economy in Latin America, is part of the CIVETS group of six leading emerging markets and is an accessing member to the OECD. Colombia has an economy with macroeconomic stability and favorable growth prospects in the long run. The name Colombia is derived from the last name of Christopher Columbus and it was conceived by the Venezuelan revolutionary Francisco de Miranda as a reference to all the New World, but especially to those portions under Spanish and Portuguese rule. The name was adopted by the Republic of Colombia of 1819. When Venezuela, Ecuador and Cundinamarca came to exist as independent states, New Granada officially changed its name in 1858 to the Granadine Confederation. In 1863 the name was changed, this time to United States of Colombia. To refer to country, the Colombian government uses the terms Colombia. Owing to its location, the present territory of Colombia was a corridor of early human migration from Mesoamerica, the oldest archaeological finds are from the Pubenza and El Totumo sites in the Magdalena Valley 100 km southwest of Bogotá. These sites date from the Paleoindian period, at Puerto Hormiga and other sites, traces from the Archaic Period have been found
25.
Telephone number
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A telephone number serves as an address for switching telephone calls using a system of destination code routing. Telephone numbers are entered or dialed by a party on the originating telephone set. The exchange completes the call either to another locally connected subscriber or via the PSTN to the called party, telephone numbers were first used in 1879 in Lowell, Massachusetts when they replaced the request for subscriber names by callers connecting to the switchboard operator. Telephone numbers are dialed in conjunction with other signaling code sequences, such as vertical service codes. When telephone numbers were first used they were short, from one to three digits, and were communicated orally to a switchboard operator when initiating a call. As telephone systems have grown and interconnected to encompass worldwide communication, in addition to telephones, they have been used to access other devices, such as computer modems, pagers, and fax machines. The number contains the necessary to identify uniquely the intended endpoint for the telephone call. Each such endpoint must have a number within the public switched telephone network. Most countries use fixed length numbers and therefore the number of endpoints determines the length of the telephone number. It is also possible for each subscriber to have a set of numbers for the endpoints most often used. These shorthand or speed calling numbers are translated to unique telephone numbers before the call can be connected. Some special services have their own short numbers The dialing plan in some areas permits dialing numbers in the local calling area without using area code or city code prefixes. For example, a number in North America consists of a three-digit area code, a three-digit central office code. If the area has no area code overlays, seven-digit dialing may be permissible for calls within the area, for each large metro area, all of these lines will share the same prefix, the last digits typically corresponding to the stations frequency, callsign, or moniker. In the international network, the format of telephone numbers is standardized by ITU-T recommendation E.164. This code specifies that the number should be 15 digits or shorter. For most countries, this is followed by a code or city code and the subscriber number. ITU-T recommendation E.123 describes how to represent an international telephone number in writing or print, starting with a plus sign and the country code
26.
Speaking clock
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A speaking clock or talking clock is a live or recorded human voice service, usually accessed by telephone, that gives the correct time. The first telephone speaking clock service was introduced in France, in association with the Paris Observatory, the format of the service is similar to that of radio time signal services. At set intervals a voice announces At the third stroke, the time will be twelve forty-six, some countries have sponsored time announcements and include the sponsors name in the message. In 1995, the ASEAN has set up nine speaking clocks and this service replaced services in Malaysia, Philippines, Singapore and Thailand, which already had speaking clock services. In Argentina, users can reach the time service dialing 113 from almost every fixed line operator. In Australia, the number 1194 gives the clock in all areas. It is always the current time from where the call originates, a male voice, often known by Australians as the time man, says At the third stroke, it will be and seconds/precisely. At the third stroke, it will be three thirty three and forty seconds and these are done in 10 second increments and the beep is 1 kHz. Prior to automatic systems, the subscriber rang an operator who would quote the time from a clock in the exchange with a phrase such as The time by the exchange clock is. This was not precise and the operator could not always answer when the subscriber wanted, in 1954, British-made systems were installed in Melbourne and Sydney. The mechanical speaking clock used rotating glass discs where different parts of the time were recorded on the disc, a synchronous motor drove the disc with the driving source derived from a 5 MHz Quartz Oscillator via a multi stage valve divider. This was amplified to give sufficient impetus to drive the motor, because of the low torque available, a hand wheel was used to spin the motor on start up. The voice was provided by Gordon Gow, the units were designed for continuous operation. Both units in Melbourne and Sydney were run in tandem, as well as the speaking clocks, there was ancillary equipment to provide timing signals,1 pulse per second,8 pulses per minute and 8 pulses per hour. The Time and Frequency Standards Section in the PMG Research Laboratories at 59 Little Collins Street and this mechanical system was replaced with a digital system in 1990. The voice was provided by Richard Peach, a former ABC broadcaster, the various components were sent for commercial production after a working prototype was built in the Telstra Research Laboratory. Assmann Australia used a German announcing unit and built a unit to TRL specifications. Design 2000 incorporated TRL oscillators in the phase locked oscillator units designed at TRL, ged Company built civil time receivers
27.
Time
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Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future. Time is often referred to as the dimension, along with the three spatial dimensions. Time has long been an important subject of study in religion, philosophy, and science, nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems. Two contrasting viewpoints on time divide prominent philosophers, one view is that time is part of the fundamental structure of the universe—a dimension independent of events, in which events occur in sequence. Isaac Newton subscribed to this realist view, and hence it is referred to as Newtonian time. This second view, in the tradition of Gottfried Leibniz and Immanuel Kant, holds that time is neither an event nor a thing, Time in physics is unambiguously operationally defined as what a clock reads. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities, Time is used to define other quantities—such as velocity—so defining time in terms of such quantities would result in circularity of definition. The operational definition leaves aside the question there is something called time, apart from the counting activity just mentioned, that flows. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy. Furthermore, it may be there is a subjective component to time. Temporal measurement has occupied scientists and technologists, and was a motivation in navigation. Periodic events and periodic motion have long served as standards for units of time, examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and the beat of a heart. Currently, the unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms. Time is also of significant social importance, having economic value as well as value, due to an awareness of the limited time in each day. In day-to-day life, the clock is consulted for periods less than a day whereas the calendar is consulted for periods longer than a day, increasingly, personal electronic devices display both calendars and clocks simultaneously. The number that marks the occurrence of an event as to hour or date is obtained by counting from a fiducial epoch—a central reference point. Artifacts from the Paleolithic suggest that the moon was used to time as early as 6,000 years ago. Lunar calendars were among the first to appear, either 12 or 13 lunar months, without intercalation to add days or months to some years, seasons quickly drift in a calendar based solely on twelve lunar months
28.
United Kingdom
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The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom or Britain, is a sovereign country in western Europe. Lying off the north-western coast of the European mainland, the United Kingdom includes the island of Great Britain, Northern Ireland is the only part of the United Kingdom that shares a land border with another sovereign state—the Republic of Ireland. The Irish Sea lies between Great Britain and Ireland, with an area of 242,500 square kilometres, the United Kingdom is the 78th-largest sovereign state in the world and the 11th-largest in Europe. It is also the 21st-most populous country, with an estimated 65.1 million inhabitants, together, this makes it the fourth-most densely populated country in the European Union. The United Kingdom is a monarchy with a parliamentary system of governance. The monarch is Queen Elizabeth II, who has reigned since 6 February 1952, other major urban areas in the United Kingdom include the regions of Birmingham, Leeds, Glasgow, Liverpool and Manchester. The United Kingdom consists of four countries—England, Scotland, Wales, the last three have devolved administrations, each with varying powers, based in their capitals, Edinburgh, Cardiff and Belfast, respectively. The relationships among the countries of the UK have changed over time, Wales was annexed by the Kingdom of England under the Laws in Wales Acts 1535 and 1542. A treaty between England and Scotland resulted in 1707 in a unified Kingdom of Great Britain, which merged in 1801 with the Kingdom of Ireland to form the United Kingdom of Great Britain and Ireland. Five-sixths of Ireland seceded from the UK in 1922, leaving the present formulation of the United Kingdom of Great Britain, there are fourteen British Overseas Territories. These are the remnants of the British Empire which, at its height in the 1920s, British influence can be observed in the language, culture and legal systems of many of its former colonies. The United Kingdom is a country and has the worlds fifth-largest economy by nominal GDP. The UK is considered to have an economy and is categorised as very high in the Human Development Index. It was the worlds first industrialised country and the worlds foremost power during the 19th, the UK remains a great power with considerable economic, cultural, military, scientific and political influence internationally. It is a nuclear weapons state and its military expenditure ranks fourth or fifth in the world. The UK has been a permanent member of the United Nations Security Council since its first session in 1946 and it has been a leading member state of the EU and its predecessor, the European Economic Community, since 1973. However, on 23 June 2016, a referendum on the UKs membership of the EU resulted in a decision to leave. The Acts of Union 1800 united the Kingdom of Great Britain, Scotland, Wales and Northern Ireland have devolved self-government