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.
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
4.
Factorization
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In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 ×5, in all cases, a product of simpler objects is obtained. The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viètes formulas relate the coefficients of a polynomial to its roots, the opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms. Integer factorization for large integers appears to be a difficult problem, there is no known method to carry it out quickly. Its complexity is the basis of the security of some public key cryptography algorithms. A matrix can also be factorized into a product of matrices of special types, One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types, QR decomposition, LQ, QL, RQ and this situation is generalized by factorization systems. By the fundamental theorem of arithmetic, every integer greater than 1 has a unique prime factorization. Given an algorithm for integer factorization, one can factor any integer down to its constituent primes by repeated application of this algorithm, for very large numbers, no efficient classical algorithm is known. Modern techniques for factoring polynomials are fast and efficient, but use sophisticated mathematical ideas and these techniques are used in the construction of computer routines for carrying out polynomial factorization in Computer algebra systems. This article is concerned with classical techniques. While the general notion of factoring just means writing an expression as a product of simpler expressions, when factoring polynomials this means that the factors are to be polynomials of smaller degree. Thus, while x 2 − y = is a factorization of the expression, another issue concerns the coefficients of the factors. It is not always possible to do this, and a polynomial that can not be factored in this way is said to be irreducible over this type of coefficient, thus, x2 -2 is irreducible over the integers and x2 +4 is irreducible over the reals. In the first example, the integers 1 and -2 can also be thought of as real numbers, and if they are, then x 2 −2 = shows that this polynomial factors over the reals. Similarly, since the integers 1 and 4 can be thought of as real and hence complex numbers, x2 +4 splits over the complex numbers, i. e. x 2 +4 =. The fundamental theorem of algebra can be stated as, Every polynomial of n with complex number coefficients splits completely into n linear factors
5.
Prime number
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A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a number is called a composite number. For example,5 is prime because 1 and 5 are its only positive integer factors, the property of being prime is called primality. A simple but slow method of verifying the primality of a number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and n, algorithms much more efficient than trial division have been devised to test the primality of large numbers. Particularly fast methods are available for numbers of forms, such as Mersenne numbers. As of January 2016, the largest known prime number has 22,338,618 decimal digits, there are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no simple formula that separates prime numbers from composite numbers. However, the distribution of primes, that is to say, many questions regarding prime numbers remain open, such as Goldbachs conjecture, and the twin prime conjecture. Such questions spurred the development of branches of number theory. Prime numbers give rise to various generalizations in other domains, mainly algebra, such as prime elements. A natural number is called a number if it has exactly two positive divisors,1 and the number itself. Natural numbers greater than 1 that are not prime are called composite, among the numbers 1 to 6, the numbers 2,3, and 5 are the prime numbers, while 1,4, and 6 are not prime. 1 is excluded as a number, for reasons explained below. 2 is a number, since the only natural numbers dividing it are 1 and 2. Next,3 is prime, too,1 and 3 do divide 3 without remainder, however,4 is composite, since 2 is another number dividing 4 without remainder,4 =2 ·2. 5 is again prime, none of the numbers 2,3, next,6 is divisible by 2 or 3, since 6 =2 ·3. The image at the right illustrates that 12 is not prime,12 =3 ·4, no even number greater than 2 is prime because by definition, any such number n has at least three distinct divisors, namely 1,2, and n
6.
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
7.
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
8.
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
9.
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
10.
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
11.
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
12.
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
13.
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
14.
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
15.
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
16.
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
17.
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
18.
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
19.
Natural number
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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
20.
Eisenstein prime
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In mathematics, an Eisenstein prime is an Eisenstein integer z = a + b ω that is irreducible in the ring-theoretic sense, its only Eisenstein divisors are the units, a + bω itself and its associates. The associates and the conjugate of any Eisenstein prime are also prime. It follows that the absolute value squared of every Eisenstein prime is a prime or the square of a natural prime. The first few Eisenstein primes that equal a natural prime 3n −1 are,2,5,11,17,23,29,41,47,53,59,71,83,89,101. Natural primes that are congruent to 0 or 1 modulo 3 are not Eisenstein primes, some non-real Eisenstein primes are 2 + ω,3 + ω,4 + ω,5 + 2ω,6 + ω,7 + ω,7 + 3ω. Up to conjugacy and unit multiples, the primes listed above, as of March 2017, the largest known Eisenstein prime is the seventh largest known prime 10223 ×231172165 +1, discovered by Péter Szabolcs and PrimeGrid. All larger known primes are Mersenne primes, discovered by GIMPS, real Eisenstein primes are congruent to 2 mod 3, and Mersenne primes are congruent to 1 mod 3, thus no Mersenne prime is an Eisenstein prime
21.
Pythagorean prime
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A Pythagorean prime is a prime number of the form 4n +1. Pythagorean primes are exactly the odd numbers that are the sum of two squares. For instance, the number 5 is a Pythagorean prime, √5 is the hypotenuse of a triangle with legs 1 and 2. The first few Pythagorean primes are 5,13,17,29,37,41,53,61,73,89,97,101,109,113, by Dirichlets theorem on arithmetic progressions, this sequence is infinite. More strongly, for n, the numbers of Pythagorean and non-Pythagorean primes up to n are approximately equal. However, the number of Pythagorean primes up to n is frequently smaller than the number of non-Pythagorean primes. For example, the values of n up to 600000 for which there are more Pythagorean than non-Pythagorean odd primes are 26861 and 26862. Sum of one odd square and one square is congruent to 1 mod 4. Fermats theorem on sums of two states that the prime numbers that can be represented as sums of two squares are exactly 2 and the odd primes congruent to 1 mod 4. The representation of such number is unique, up to the ordering of the two squares. Another way to understand this representation as a sum of two squares involves Gaussian integers, the numbers whose real part and imaginary part are both integers. The norm of a Gaussian integer x + yi is the number x2 + y2, thus, the Pythagorean primes occur as norms of Gaussian integers, while other primes do not. Within the Gaussian integers, the Pythagorean primes are not considered to be prime numbers, similarly, their squares can be factored in a different way than their integer factorization, as p2 =22 =. The real and imaginary parts of the factors in these factorizations are the leg lengths of the right triangles having the given hypotenuses, in the finite field Z/p with p a Pythagorean prime, the polynomial equation x2 = −1 has two solutions. This may be expressed by saying that −1 is a quadratic residue mod p, in contrast, this equation has no solution in the finite fields Z/p where p is an odd prime but is not Pythagorean. Pythagorean Primes, including 5,13 and 137, sloanes A007350, Where prime race 4n-1 vs. 4n+1 changes leader. The On-Line Encyclopedia of Integer Sequences
22.
Arithmetic mean
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In mathematics and statistics, the arithmetic mean, or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection. The collection is often a set of results of an experiment, the term arithmetic mean is preferred in some contexts in mathematics and statistics because it helps distinguish it from other means, such as the geometric mean and the harmonic mean. In addition to mathematics and statistics, the mean is used frequently in fields such as economics, sociology, and history. For example, per capita income is the average income of a nations population. While the arithmetic mean is used to report central tendencies, it is not a robust statistic. In a more obscure usage, any sequence of values that form a sequence between two numbers x and y can be called arithmetic means between x and y. The arithmetic mean is the most commonly used and readily understood measure of central tendency, in statistics, the term average refers to any of the measures of central tendency. The arithmetic mean is defined as being equal to the sum of the values of each. For example, let us consider the monthly salary of 10 employees of a firm,2500,2700,2400,2300,2550,2650,2750,2450,2600,2400. The arithmetic mean is 2500 +2700 +2400 +2300 +2550 +2650 +2750 +2450 +2600 +240010 =2530, If the data set is a statistical population, then the mean of that population is called the population mean. If the data set is a sample, we call the statistic resulting from this calculation a sample mean. The arithmetic mean of a variable is denoted by a bar, for example as in x ¯. The arithmetic mean has several properties that make it useful, especially as a measure of central tendency and these include, If numbers x 1, …, x n have mean x ¯, then + ⋯ + =0. The mean is the single number for which the residuals sum to zero. If the arithmetic mean of a population of numbers is desired, the arithmetic mean may be contrasted with the median. The median is defined such that half the values are larger than, and half are smaller than, If elements in the sample data increase arithmetically, when placed in some order, then the median and arithmetic average are equal. For example, consider the data sample 1,2,3,4, the average is 2.5, as is the median. However, when we consider a sample that cannot be arranged so as to increase arithmetically, such as 1,2,4,8,16, in this case, the arithmetic average is 6.2 and the median is 4
23.
Golden ratio
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In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship, expressed algebraically, for quantities a and b with a > b >0, a + b a = a b = def φ, where the Greek letter phi represents the golden ratio. Its value is, φ =1 +52 =1.6180339887 …, A001622 The golden ratio is also called the golden mean or golden section. Other names include extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, the golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts. The golden ratio has also used to analyze the proportions of natural objects as well as man-made systems such as financial markets. Two quantities a and b are said to be in the golden ratio φ if a + b a = a b = φ, one method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ, a + b a =1 + b a =1 +1 φ, multiplying by φ gives φ +1 = φ2 which can be rearranged to φ2 − φ −1 =0. First, the line segment A B ¯ is about doubled and then the semicircle with the radius A S ¯ around the point S is drawn, now the semicircle is drawn with the radius A B ¯ around the point B. The arising intersection point E corresponds 2 φ, next up, the perpendicular on the line segment A E ¯ from the point D will be establish. The subsequent parallel F S ¯ to the line segment C M ¯, produces, as it were and it is well recognizable, this triangle and the triangle M S C are similar to each other. The hypotenuse F S ¯ has due to the cathetuses S D ¯ =1 and D F ¯ =2 according the Pythagorean theorem, finally, the circle arc is drawn with the radius 5 around the point F. The golden ratio has been claimed to have held a fascination for at least 2,400 years. But the fascination with the Golden Ratio is not confined just to mathematicians, biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry, the division of a line into extreme and mean ratio is important in the geometry of regular pentagrams and pentagons. Euclid explains a construction for cutting a line in extreme and mean ratio, throughout the Elements, several propositions and their proofs employ the golden ratio. The golden ratio is explored in Luca Paciolis book De divina proportione, since the 20th century, the golden ratio has been represented by the Greek letter φ or less commonly by τ. Timeline according to Priya Hemenway, Phidias made the Parthenon statues that seem to embody the golden ratio, plato, in his Timaeus, describes five possible regular solids, some of which are related to the golden ratio
24.
Golden angle
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It measures approximately 137.5077640500378546463487. ° A096627 or in radians 2.39996322972865332. The golden ratio is equal to φ = a/b given the conditions above, let ƒ be the fraction of the circumference subtended by the golden angle, or equivalently, the golden angle divided by the angular measurement of the circle. But since 1 + φ = φ2, it follows that f =1 φ2 This is equivalent to saying that φ2 golden angles can fit in a circle, the fraction of a circle occupied by the golden angle is therefore f ≈0.381966. The golden angle g can therefore be numerically approximated in degrees as, g ≈360 ×0.381966 ≈137.508 ∘, or in radians as, g ≈2 π ×0.381966 ≈2.39996. The golden angle plays a significant role in the theory of phyllotaxis, for example, the golden angle is the angle separating the florets on a sunflower
25.
Fine structure constant
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It is related to the elementary charge e, which characterizes the strength of the coupling of an elementary charged particle with the electromagnetic field, by the formula 4πε0ħcα = e2. Being a dimensionless quantity, it has the numerical value of about 1⁄137 in all systems of units. Arnold Sommerfeld introduced the fine-structure constant in 1916, the definition reflects the relationship between α and the elementary charge e, which equals √4παε0ħc. In electrostatic cgs units, the unit of charge, the statcoulomb, is defined so that the Coulomb constant, ke, or the permittivity factor, 4πε0, is 1. Then the expression of the constant, as commonly found in older physics literature. In natural units, commonly used in high energy physics, where ε0 = c = ħ =1, the value of the fine-structure constant is α = e 24 π. As such, the constant is just another, albeit dimensionless, quantity determining the elementary charge. The 2014 CODATA recommended value of α is α = e 2 ℏ c =0.0072973525664 and this has a relative standard uncertainty of 0.32 parts per billion. For reasons of convenience, historically the value of the reciprocal of the constant is often specified. The 2014 CODATA recommended value is given by α −1 =137.035999139, the theory of QED predicts a relationship between the dimensionless magnetic moment of the electron and the fine-structure constant α.035999173. This measurement of α has a precision of 0.25 parts per billion and this value and uncertainty are about the same as the latest experimental results. The fine-structure constant, α, has several physical interpretations, α is, The square of the ratio of the elementary charge to the Planck charge α =2. The ratio of the velocity of the electron in the first circular orbit of the Bohr model of the atom to the speed of light in vacuum and this is Sommerfelds original physical interpretation. Then the square of α is the ratio between the Hartree energy and the electron rest energy, the theory does not predict its value. Therefore, α must be determined experimentally, in fact, α is one of the about 20 empirical parameters in the Standard Model of particle physics, whose value is not determined within the Standard Model. In the electroweak theory unifying the weak interaction with electromagnetism, α is absorbed into two other coupling constants associated with the gauge fields. In this theory, the interaction is treated as a mixture of interactions associated with the electroweak fields. The strength of the electromagnetic interaction varies with the strength of the energy field, the absorption value for normal-incident light on graphene in vacuum would then be given by πα/2 or 2. 24%, and the transmission by 1/2 or 97. 75%
26.
Arthur Eddington
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Sir Arthur Stanley Eddington OM FRS was an English astronomer, physicist, and mathematician of the early 20th century who did his greatest work in astrophysics. He was also a philosopher of science and a populariser of science, the Eddington limit, the natural limit to the luminosity of stars, or the radiation generated by accretion onto a compact object, is named in his honour. He is famous for his work concerning the theory of relativity, Eddington wrote a number of articles that announced and explained Einsteins theory of general relativity to the English-speaking world. World War I severed many lines of communication and new developments in German science were not well known in England. Eddington was born 28 December 1882 in Kendal, Westmorland, England, the son of Quaker parents, Arthur Henry Eddington, headmaster of the Quaker School and his father taught at a Quaker training college in Lancashire before moving to Kendal to become headmaster of Stramongate School. He died in the epidemic which swept England in 1884. His mother was left to bring up her two children with little income. The family moved to Weston-super-Mare where at first Stanley was educated at home before spending three years at a preparatory school, the family lived at a house called Varzin,42 Walliscote Road, Weston-super-Mare. There is a plaque on the building explaining Sir Arthurs contribution to science. In 1893 Eddington entered Brynmelyn School and he proved to be a most capable scholar, particularly in mathematics and English literature. His performance earned him a scholarship to Owens College, Manchester in 1898 and he spent the first year in a general course, but turned to physics for the next three years. Eddington was greatly influenced by his physics and mathematics teachers, Arthur Schuster, at Manchester, Eddington lived at Dalton Hall, where he came under the lasting influence of the Quaker mathematician J. W. Graham. His progress was rapid, winning him several scholarships and he graduated with a B. Sc. in physics with First Class Honours in 1902, based on his performance at Owens College, he was awarded a scholarship to Trinity College at the University of Cambridge in 1902. His tutor at Cambridge was Robert Alfred Herman and in 1904 Eddington became the first ever student to be placed as Senior Wrangler. After receiving his M. A. in 1905, he began research on thermionic emission in the Cavendish Laboratory and this did not go well, and meanwhile he spent time teaching mathematics to first year engineering students. Through a recommendation by E. T, in January 1906, Eddington was nominated to the post of chief assistant to the Astronomer Royal at the Royal Greenwich Observatory. He left Cambridge for Greenwich the following month and he was put to work on a detailed analysis of the parallax of 433 Eros on photographic plates that had started in 1900. He developed a new statistical method based on the apparent drift of two stars, winning him the Smiths Prize in 1907
27.
Leon M. Lederman
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He is Director Emeritus of Fermi National Accelerator Laboratory in Batavia, Illinois, USA. He founded the Illinois Mathematics and Science Academy, in Aurora, Illinois in 1986, in 2012, he was awarded the Vannevar Bush Award for his extraordinary contributions to understanding the basic forces and particles of nature. Lederman was born in New York City, New York, the son of Minna and Morris Lederman, Lederman graduated from the James Monroe High School in the South Bronx. He received his bachelors degree from the City College of New York in 1943 and he then joined the Columbia faculty and eventually became Eugene Higgins Professor of Physics. In 1960, on leave from Columbia, he spent some time at CERN in Geneva as a Ford Foundation Fellow and he took an extended leave of absence from Columbia in 1979 to become director of Fermilab. In 1991, Lederman became President of the American Association for the Advancement of Science, Lederman is also one of the main proponents of the Physics First movement. Also known as Right-side Up Science and Biology Last, this movement seeks to rearrange the current high school curriculum so that physics precedes chemistry. A former president of the American Physical Society, Lederman also received the National Medal of Science, the Wolf Prize, Lederman served as President of the Board of Sponsors of The Bulletin of the Atomic Scientists. He also served on the board of trustees for Science Service, now known as Society for Science & the Public, from 1989 to 1992, among his achievements are the discovery of the muon neutrino in 1962 and the bottom quark in 1977. These helped establish his reputation as among the top particle physicists, in 1977, a group of physicists, the E288 experiment team, led by Leon Lederman announced that a particle with a mass of about 6.0 GeV was being produced by the Fermilab particle accelerator. The particles initial name was the greek letter Upsilon, after taking further data, the group discovered that this particle did not actually exist, and the discovery was named Oops-Leon as a pun on the original name and Ledermans first name. Lederman later wrote his 1993 popular science book The God Particle, If the Universe Is the Answer, – which sought to promote awareness of the significance of such a project – in the context of the projects last years and the changing political climate of the 1990s. The increasingly moribund project was finally shelved that same year after some $2 billion of expenditures, Lederman also received the National Medal of Science, the Elliott Cresson Medal for Physics, the Wolf Prize for Physics and the Enrico Fermi Award. In 1995, he received the Chicago History Museum Making History Award for Distinction in Science Medicine, Lederman was an early supporter of Science Debate 2008, an initiative to get the then-candidates for president, Barack Obama and John McCain, to debate the nations top science policy challenges. Lederman was also a member of the USA Science and Engineering Festivals Advisory Board, Lederman was born in New York to a family of Jewish immigrants from Russia. His father operated a hand laundry while encouraging Leon to pursue his education and he went to elementary school in New York City, continuing on to college and his doctorate in the city. In his book, The God Particle, If the Universe Is the Answer, Lederman wrote that, although he was a chemistry major, he became fascinated with physics, because of the clarity of the logic and the unambiguous results from experimentation. His best friend during his years, Martin Klein, convinced him of the splendors of physics during a long evening over many beers
28.
Fermilab
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Fermi National Accelerator Laboratory, located just outside Batavia, Illinois, near Chicago, is a United States Department of Energy national laboratory specializing in high-energy particle physics. Since 2007, Fermilab has been operated by the Fermi Research Alliance, a joint venture of the University of Chicago, Fermilab is a part of the Illinois Technology and Research Corridor. Fermilabs Tevatron was a particle accelerator, at 3.9 miles in circumference, it was the worlds fourth-largest particle accelerator. In 1995, the discovery of the top quark was announced by researchers who used the Tevatrons CDF, in addition to high-energy collider physics, Fermilab hosts fixed-target and neutrino experiments, such as MicroBooNE, NOνA and SeaQuest. Completed neutrino experiments include MINOS, MINOS+, MiniBooNE and SciBooNE, the MiniBooNE detector was a 40-foot diameter sphere containing 800 tons of mineral oil lined with 1,520 phototube detectors. An estimated 1 million neutrino events were recorded each year, SciBooNE sat in the same neutrino beam as MiniBooNE but had fine-grained tracking capabilities. In the public realm, Fermilab hosts many events, not only public science lectures and symposia. The site is open dawn to dusk to visitors who present valid photo identification. Asteroid 11998 Fermilab is named in honor of the laboratory, weston, Illinois, was a community next to Batavia voted out of existence by its village board in 1966 to provide a site for Fermilab. The laboratory was founded in 1967 as the National Accelerator Laboratory, the laboratorys first director was Robert Rathbun Wilson, under whom the laboratory opened ahead of time and under budget. Many of the sculptures on the site are of his creation and he is the namesake of the sites high-rise laboratory building, whose unique shape has become the symbol for Fermilab and which is the center of activity on the campus. After Wilson stepped down in 1978 to protest the lack of funding for the lab and it was under his guidance that the original accelerator was replaced with the Tevatron, an accelerator capable of colliding protons and antiprotons at a combined energy of 1.96 TeV. Lederman stepped down in 1989 and remains Director Emeritus, the science education center at the site was named in his honor. The later directors include, John Peoples,1989 to 1999 Michael S, as of 2014, the first stage in the acceleration process takes place in two ion sources which turn hydrogen gas into H− ions. A magnetron generates a plasma to form the ions near the metal surface, at the exit of RFQ, the beam is matched by medium energy beam transport into the entrance of the linear accelerator. The next stage of acceleration is linear particle accelerator and this stage consists of two segments. The first segment has 5 vacuum vessel for drift tubes, operating at 201 MHz, the second stage has 7 side-coupled cavities, operating at 805 MHz. At the end of linac, the particles are accelerated to 400 MeV, immediately before entering the next accelerator, the H− ions pass through a carbon foil, becoming H+ ions
29.
Richard Feynman
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For his contributions to the development of quantum electrodynamics, Feynman, jointly with Julian Schwinger and Sinichirō Tomonaga, received the Nobel Prize in Physics in 1965. Feynman developed a widely used pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, during his lifetime, Feynman became one of the best-known scientists in the world. In a 1999 poll of 130 leading physicists worldwide by the British journal Physics World he was ranked as one of the ten greatest physicists of all time. Along with his work in physics, Feynman has been credited with pioneering the field of quantum computing. Tolman professorship in physics at the California Institute of Technology. They were not religious, and by his youth, Feynman described himself as an avowed atheist, like Albert Einstein and Edward Teller, Feynman was a late talker, and by his third birthday had yet to utter a single word. He retained a Brooklyn accent as an adult and that accent was thick enough to be perceived as an affectation or exaggeration – so much so that his good friends Wolfgang Pauli and Hans Bethe once commented that Feynman spoke like a bum. The young Feynman was heavily influenced by his father, who encouraged him to ask questions to challenge orthodox thinking, from his mother, he gained the sense of humor that he had throughout his life. As a child, he had a talent for engineering, maintained a laboratory in his home. When he was in school, he created a home burglar alarm system while his parents were out for the day running errands. When Richard was five years old, his mother gave birth to a brother, Henry Philips. Four years later, Richards sister Joan was born, and the moved to Far Rockaway. Though separated by nine years, Joan and Richard were close and their mother thought that women did not have the cranial capacity to comprehend such things. Despite their mothers disapproval of Joans desire to study astronomy, Richard encouraged his sister to explore the universe, Joan eventually became an astrophysicist specializing in interactions between the Earth and the solar wind. Feynman attended Far Rockaway High School, a school in Far Rockaway, Queens, upon starting high school, Feynman was quickly promoted into a higher math class. A high-school-administered IQ test estimated his IQ at 125—high, but merely respectable according to biographer James Gleick and his sister Joan did better, allowing her to claim that she was smarter. Years later he declined to join Mensa International, saying that his IQ was too low, physicist Steve Hsu stated of the test, I suspect that this test emphasized verbal, as opposed to mathematical, ability. Feynman received the highest score in the United States by a margin on the notoriously difficult Putnam mathematics competition exam
30.
Bohr model
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After the cubic model, the plum-pudding model, the Saturnian model, and the Rutherford model came the Rutherford–Bohr model or just Bohr model for short. The improvement to the Rutherford model is mostly a physical interpretation of it. The models key success lay in explaining the Rydberg formula for the emission lines of atomic hydrogen. While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. Not only did the Bohr model explain the reason for the structure of the Rydberg formula, the Bohr model is a relatively primitive model of the hydrogen atom, compared to the valence shell atom. A related model was proposed by Arthur Erich Haas in 1910. The quantum theory of the period between Plancks discovery of the quantum and the advent of a quantum mechanics is often referred to as the old quantum theory. In the early 20th century, experiments by Ernest Rutherford established that atoms consisted of a cloud of negatively charged electrons surrounding a small, dense. The laws of mechanics, predict that the electron will release electromagnetic radiation while orbiting a nucleus. Because the electron would lose energy, it would rapidly spiral inwards and this atom model is disastrous, because it predicts that all atoms are unstable. Also, as the electron spirals inward, the emission would rapidly increase in frequency as the orbit got smaller and faster and this would produce a continuous smear, in frequency, of electromagnetic radiation. However, late 19th century experiments with electric discharges have shown that atoms will emit light at certain discrete frequencies. To overcome this difficulty, Niels Bohr proposed, in 1913 and he suggested that electrons could only have certain classical motions, Electrons in atoms orbit the nucleus. The electrons can only orbit stably, without radiating, in certain orbits at a discrete set of distances from the nucleus. These orbits are associated with definite energies and are called energy shells or energy levels. In these orbits, the electrons acceleration does not result in radiation, the Bohr model of an atom was based upon Plancks quantum theory of radiation. The frequency of the radiation emitted at an orbit of period T is as it would be in classical mechanics, it is the reciprocal of the orbit period. The significance of the Bohr model is that the laws of classical mechanics apply to the motion of the electron about the nucleus only when restricted by a quantum rule, is called the principal quantum number, and ħ = h/2π
31.
Wolfgang Pauli
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Wolfgang Ernst Pauli was an Austrian-born Swiss and American theoretical physicist and one of the pioneers of quantum physics. The discovery involved spin theory, which is the basis of a theory of the structure of matter, Pauli was born in Vienna to a chemist Wolfgang Joseph Pauli and his wife Bertha Camilla Schütz, his sister was Hertha Pauli, the writer and actress. Paulis middle name was given in honor of his godfather, physicist Ernst Mach, Paulis paternal grandparents were from prominent Jewish families of Prague, his great-grandfather was the Jewish publisher Wolf Pascheles. Paulis father converted from Judaism to Roman Catholicism shortly before his marriage in 1899, Paulis mother, Bertha Schütz, was raised in her own mothers Roman Catholic religion, her father was Jewish writer Friedrich Schütz. Pauli was raised as a Roman Catholic, although eventually he and he is considered to have been a deist and a mystic. Pauli attended the Döblinger-Gymnasium in Vienna, graduating with distinction in 1918, only two months after graduation, he published his first paper, on Albert Einsteins theory of general relativity. He attended the Ludwig-Maximilians University in Munich, working under Arnold Sommerfeld, Sommerfeld asked Pauli to review the theory of relativity for the Encyklopädie der mathematischen Wissenschaften. Two months after receiving his doctorate, Pauli completed the article and it was praised by Einstein, published as a monograph, it remains a standard reference on the subject to this day. From 1923 to 1928, he was a lecturer at the University of Hamburg, during this period, Pauli was instrumental in the development of the modern theory of quantum mechanics. In particular, he formulated the principle and the theory of nonrelativistic spin. In 1928, he was appointed Professor of Theoretical Physics at ETH Zurich in Switzerland where he made significant scientific progress and he held visiting professorships at the University of Michigan in 1931, and the Institute for Advanced Study in Princeton in 1935. He was awarded the Lorentz Medal in 1931, at the end of 1930, shortly after his postulation of the neutrino and immediately following his divorce and the suicide of his mother, Pauli experienced a personal crisis. He consulted psychiatrist and psychotherapist Carl Jung who, like Pauli, Jung immediately began interpreting Paulis deeply archetypal dreams, and Pauli became one of the depth psychologists best students. He soon began to criticize the epistemology of Jungs theory scientifically, a great many of these discussions are documented in the Pauli/Jung letters, today published as Atom and Archetype. Jungs elaborate analysis of more than 400 of Paulis dreams is documented in Psychology, the German annexation of Austria in 1938 made him a German citizen, which became a problem for him in 1939 after the outbreak of World War II. In 1940, he tried in vain to obtain Swiss citizenship, Pauli moved to the United States in 1940, where he was employed as a professor of theoretical physics at the Institute for Advanced Study. In 1946, after the war, he became a citizen of the United States and subsequently returned to Zurich. In 1949, he was granted Swiss citizenship, in 1958, Pauli was awarded the Max Planck medal
32.
Quantum physics
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Quantum mechanics, including quantum field theory, is a branch of physics which is the fundamental theory of nature at small scales and low energies of atoms and subatomic particles. Classical physics, the physics existing before quantum mechanics, derives from quantum mechanics as an approximation valid only at large scales, early quantum theory was profoundly reconceived in the mid-1920s. The reconceived theory is formulated in various specially developed mathematical formalisms, in one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle. In 1803, Thomas Young, an English polymath, performed the famous experiment that he later described in a paper titled On the nature of light. This experiment played a role in the general acceptance of the wave theory of light. In 1838, Michael Faraday discovered cathode rays, Plancks hypothesis that energy is radiated and absorbed in discrete quanta precisely matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, ludwig Boltzmann independently arrived at this result by considerations of Maxwells equations. However, it was only at high frequencies and underestimated the radiance at low frequencies. Later, Planck corrected this model using Boltzmanns statistical interpretation of thermodynamics and proposed what is now called Plancks law, following Max Plancks solution in 1900 to the black-body radiation problem, Albert Einstein offered a quantum-based theory to explain the photoelectric effect. Among the first to study quantum phenomena in nature were Arthur Compton, C. V. Raman, robert Andrews Millikan studied the photoelectric effect experimentally, and Albert Einstein developed a theory for it. In 1913, Peter Debye extended Niels Bohrs theory of structure, introducing elliptical orbits. This phase is known as old quantum theory, according to Planck, each energy element is proportional to its frequency, E = h ν, where h is Plancks constant. Planck cautiously insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the reality of the radiation itself. In fact, he considered his quantum hypothesis a mathematical trick to get the right rather than a sizable discovery. He won the 1921 Nobel Prize in Physics for this work, Einstein further developed this idea to show that an electromagnetic wave such as light could also be described as a particle, with a discrete quantum of energy that was dependent on its frequency. The Copenhagen interpretation of Niels Bohr became widely accepted, in the mid-1920s, developments in quantum mechanics led to its becoming the standard formulation for atomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the old quantum theory, out of deference to their particle-like behavior in certain processes and measurements, light quanta came to be called photons. From Einsteins simple postulation was born a flurry of debating, theorizing, thus, the entire field of quantum physics emerged, leading to its wider acceptance at the Fifth Solvay Conference in 1927
33.
Hebrew
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Hebrew is a language native to Israel, spoken by over 9 million people worldwide, of whom over 5 million are in Israel. Historically, it is regarded as the language of the Israelites and their ancestors, the earliest examples of written Paleo-Hebrew date from the 10th century BCE. Hebrew belongs to the West Semitic branch of the Afroasiatic language family, Hebrew is the only living Canaanite language left, and the only truly successful example of a revived dead language. Hebrew had ceased to be a spoken language somewhere between 200 and 400 CE, declining since the aftermath of the Bar Kokhba revolt. Aramaic and to a lesser extent Greek were already in use as international languages, especially among elites and it survived into the medieval period as the language of Jewish liturgy, rabbinic literature, intra-Jewish commerce, and poetry. Then, in the 19th century, it was revived as a spoken and literary language, and, according to Ethnologue, had become, as of 1998, the language of 5 million people worldwide. After Israel, the United States has the second largest Hebrew-speaking population, with 220,000 fluent speakers, Modern Hebrew is one of the two official languages of the State of Israel, while premodern Hebrew is used for prayer or study in Jewish communities around the world today. Ancient Hebrew is also the tongue of the Samaritans, while modern Hebrew or Arabic is their vernacular. For this reason, Hebrew has been referred to by Jews as Leshon Hakodesh, the modern word Hebrew is derived from the word Ivri, one of several names for the Israelite people. It is traditionally understood to be a based on the name of Abrahams ancestor, Eber. This name is based upon the root ʕ-b-r meaning to cross over. Interpretations of the term ʕibrim link it to this verb, cross over, in the Bible, the Hebrew language is called Yәhudit because Judah was the surviving kingdom at the time of the quotation. In Isaiah 19,18 it is called the Language of Canaan, Hebrew belongs to the Canaanite group of languages. In turn, the Canaanite languages are a branch of the Northwest Semitic family of languages, according to Avraham ben-Yosef, Hebrew flourished as a spoken language in the Kingdoms of Israel and Judah during about 1200 to 586 BCE. Scholars debate the degree to which Hebrew was a vernacular in ancient times following the Babylonian exile. In July 2008 Israeli archaeologist Yossi Garfinkel discovered a ceramic shard at Khirbet Qeiyafa which he claimed may be the earliest Hebrew writing yet discovered, dating around 3000 years ago. The Gezer calendar also dates back to the 10th century BCE at the beginning of the Monarchic Period, classified as Archaic Biblical Hebrew, the calendar presents a list of seasons and related agricultural activities. The Gezer calendar is written in an old Semitic script, akin to the Phoenician one that through the Greeks, the Gezer calendar is written without any vowels, and it does not use consonants to imply vowels even in the places where later Hebrew spelling requires it
34.
Kabbalah
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Kabbalah is an esoteric method, discipline, and school of thought that originated in Judaism. A traditional Kabbalist in Judaism is called a Mekubbal, Kabbalah is a set of esoteric teachings meant to explain the relationship between an unchanging, eternal, and mysterious Ein Sof and the mortal and finite universe. While it is used by some denominations, it is not a religious denomination in itself. It forms the foundations of religious interpretation. Kabbalah seeks to define the nature of the universe and the human being, the nature and purpose of existence and it also presents methods to aid understanding of the concepts and thereby attain spiritual realisation. Kabbalah originally developed within the realm of Jewish tradition, and kabbalists often use classical Jewish sources to explain, traditional practitioners believe its earliest origins pre-date world religions, forming the primordial blueprint for Creations philosophies, religions, sciences, arts, and political systems. Safed Rabbi Isaac Luria is considered the father of contemporary Kabbalah and it was popularised in the form of Hasidic Judaism from the 18th century onwards. According to the Zohar, a text for kabbalistic thought. These four levels are called pardes from their initial letters, peshat, the direct interpretations of meaning. Derash, midrashic meanings, often with imaginative comparisons with similar words or verses, sod, the inner, esoteric meanings, expressed in kabbalah. Kabbalah is considered by its followers as a part of the study of Torah – the study of Torah being an inherent duty of observant Jews. A third tradition, related but more shunned, involves the magical aims of Practical Kabbalah and they can be readily distinguished by their basic intent with respect to God, The Theosophical tradition of Theoretical Kabbalah seeks to understand and describe the divine realm. Consequently, it formed a minor tradition shunned from Kabbalah. According to traditional belief, early kabbalistic knowledge was transmitted orally by the Patriarchs, prophets, According to this view, early kabbalah was, in around the 10th century BC, an open knowledge practiced by over a million people in ancient Israel. Foreign conquests drove the Jewish spiritual leadership of the time to hide the knowledge and make it secret and it is hard to clarify with any degree of certainty the exact concepts within kabbalah. There are several different schools of thought with different outlooks, however. From the Renaissance onwards Jewish Kabbalah texts entered non-Jewish culture, where they were studied and translated by Christian Hebraists, syncretic traditions of Christian Kabbalah and Hermetic Qabalah developed independently of Jewish Kabbalah, reading the Jewish texts as universal ancient wisdom. Both adapted the Jewish concepts freely from their Judaic understanding, to merge with other theologies, religious traditions, with the decline of Christian Cabala in the Age of Reason, Hermetic Qabalah continued as a central underground tradition in Western esotericism
35.
Torah
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The Torah is the central reference of Judaism. It has a range of meanings and it can most specifically mean the first five books of the twenty-four books of the Tanakh, and it usually includes the rabbinic commentaries. In rabbinic literature the word Torah denotes both the five books and the Oral Torah, the Oral Torah consists of interpretations and amplifications which according to rabbinic tradition have been handed down from generation to generation and are now embodied in the Talmud and Midrash. According to the Midrash, the Torah was created prior to the creation of the world, traditionally, the words of the Torah are written on a scroll by a scribe in Hebrew. A Torah portion is read publicly at least once every three days in the presence of a congregation, reading the Torah publicly is one of the bases for Jewish communal life. The word Torah in Hebrew is derived from the root ירה, the meaning of the word is therefore teaching, doctrine, or instruction, the commonly accepted law gives a wrong impression. Other translational contexts in the English language include custom, theory, guidance, the earliest name for the first part of the Bible seems to have been The Torah of Moses. This title, however, is neither in the Torah itself. It appears in Joshua and Kings, but it cannot be said to refer there to the entire corpus, in contrast, there is every likelihood that its use in the post-Exilic works was intended to be comprehensive. Other early titles were The Book of Moses and The Book of the Torah, Christian scholars usually refer to the first five books of the Hebrew Bible as the Pentateuch, a term first used in the Hellenistic Judaism of Alexandria, meaning five books, or as the Law. The Torah starts from the beginning of Gods creating the world, through the beginnings of the people of Israel, their descent into Egypt, and it ends with the death of Moses, just before the people of Israel cross to the promised land of Canaan. Interspersed in the narrative are the teachings given explicitly or implicitly embedded in the narrative. This is followed by the story of the three patriarchs, Joseph and the four matriarchs, God gives to the patriarchs a promise of the land of Canaan, but at the end of Genesis the sons of Jacob end up leaving Canaan for Egypt due to a regional famine. They had heard there was a grain storage and distribution facility in Egypt. Exodus begins the story of Gods revelation to his people of Israel through Moses, Moses receives the Torah from God, and teaches His laws and Covenant to the people of Israel. It also talks about the first violation of the covenant when the Golden Calf was constructed, Exodus includes the instructions on building the Tabernacle and concludes with its actual construction. Leviticus begins with instructions to the Israelites on how to use the Tabernacle, leviticus 26 provides a detailed list of rewards for following Gods commandments and a detailed list of punishments for not following them. Numbers tells how Israel consolidated itself as a community at Sinai, set out from Sinai to move towards Canaan, even Moses sins and is told he would not live to enter the land
36.
Boeing
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The Boeing Company is an American multinational corporation that designs, manufactures, and sells airplanes, rotorcraft, rockets, and satellites worldwide. The company also provides leasing and product support services, Boeing stock is a component of the Dow Jones Industrial Average. The Boeing Companys corporate headquarters are located in Chicago and the company is led by President, Boeing is organized into five primary divisions, Boeing Commercial Airplanes, Boeing Defense, Space & Security, Engineering, Operations & Technology, Boeing Capital, and Boeing Shared Services Group. Boeing bought Heaths shipyard in Seattle on the Duwamish River, which became his first airplane factory. Boeing was incorporated in Seattle by William Boeing, on July 15,1916, Boeing was later incorporated in Delaware, the original Certificate of Incorporation was filed with the Secretary of State of Delaware on July 19,1934. Boeing, who studied at Yale University, worked initially in the timber industry and this knowledge proved invaluable in his subsequent design and assembly of airplanes. The company stayed in Seattle to take advantage of the supply of spruce wood. William Boeing founded his company a few months after the June 15 maiden flight of one of the two B&W seaplanes built with the assistance of George Conrad Westervelt, a U. S. Navy engineer. Boeing and Westervelt decided to build the B&W seaplane after having flown in a Curtiss aircraft, Boeing bought a Glenn Martin Flying Birdcage seaplane and was taught to fly by Glenn Martin himself. Boeing soon crashed the Birdcage and when Martin informed Boeing that replacement parts would not become available for months, Westervelt agreed to build a better airplane and soon produced the B&W Seaplane. This first Boeing airplane was assembled in a hangar located on the northeast shore of Seattles Lake Union. Many of Boeings early planes were seaplanes, on April 6,1917, the U. S. declared War on Germany and later in the year entered World War I. On May 9,1917, the became the Boeing Airplane Company. With the U. S. entering the war, Boeing knew that the U. S. Navy needed seaplanes for training, so Boeing shipped two new Model Cs to Pensacola, Florida, where the planes were flown for the Navy. The Navy liked the Model C and ordered 50 more, the company moved its operations to a larger former shipbuilding facility known as Boeing Plant 1, located on the lower Duwamish River, Washington state. Others, including Boeing, started selling other products, Boeing built dressers, counters, and furniture, along with flat-bottom boats called Sea Sleds. In 1919 the Boeing B-1, flying boat made its first flight and it accommodated one pilot and two passengers and some mail. Over the course of eight years, it made international airmail flights from Seattle to Victoria, on May 24,1920, the Boeing Model 8 made its first flight
37.
C-137 Stratoliner
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The Boeing C-137 Stratoliner was a VIP transport aircraft derived from the Boeing 707 jet airliner used by the United States Air Force. Other nations also bought new and used 707s for military service, primarily as VIP or tanker transports. In addition, the 707 served as the basis for several specialized versions, the designation C-18 covers several later variants based on the 707-320B/C series. USAF procurement of the Boeing 707 was very limited, amounting to three Model 707-153s designated VC-137A. When delivered in 1959 these had four 13,500 lb dry thrust Pratt & Whitney J57 turbojets, Two further non-presidential C-137C aircraft were later added. To supplement its VC-137s, the USAF converted several C-135 airframes to VC-135 VIP standard, the C-18 is the US military designation for the conversions of the 707-320B series. C-18B One C-18A modified with instrumentation and equipment to support the Military Strategic, eC-18B Four C-18As modified alongside examples of the C-135 for Advanced Range Instrumentation Aircraft missions in support of the Apollo space program. The designation E-7 was originally applied to modified Boeing 707s before being replaced by the EC-18 designation, eC-18C Original designation for two prototype J-STAR aircraft, later redesignated E-8A. EC-18D Two C-18As modified as a Cruise Missile Mission Control Aircraft, tC-18E Two second-hand 707-331 aircraft modified for E-3 pilot and crew training. TC-18F Two second-hand 707-382 aircraft modified for E-6 pilot training, VC-137B The three VC-137As re-engined with four Pratt & Whitney JT3D-3 engines, operated by the 89th Military Airlift Wing, redesignated C-137B. C-137B The three VC-137Bs redesignated when downgraded from VIP role, vC-137C Two 707-353Bs were purchased by the USAF for service as presidential transports with call signs SAM26000 and SAM27000, later redesignated C-137C. C-137C The two VC-137Cs were redesignated when downgraded from presidential use, Two further C-137Cs were acquired by the USAF, one 707-396C and one 707-382B bought second hand in 1987. EC-137D Two aircraft built as Early Warning and Control System prototypes, a further second-hand 707-355C aircraft was acquired and configured as an airborne special operations command post. Boeing E-3 Sentry Airborne warning and control aircraft that provides all-weather surveillance, command, control and communications, to the United States, NATO. Based on the 707-320B, production ended in 1992 after 68 had been built, Boeing E-6 Mercury A version of the 707-320, it operates as an airborne command post and communications center, relaying instructions from the National Command Authority. Its role in relaying to the ballistic missile submarines, known as Take Charge and Move Out. Only one version of the E-6 currently exists, the E-6B, cT-49A NATO Trainer-Cargo Aircraft operated to support E-3A AWACS training and air transport/cargo for NATO based on Boeing 707-320B. CC-137 Husky Canadian Forces designation for the 707-347C, five were purchased new in 1970
38.
Cargo aircraft
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A cargo aircraft is a fixed-wing aircraft that is designed or converted for the carriage of cargo rather than passengers. Such aircraft usually do not incorporate passenger amenities and generally one or more large doors for loading cargo. Freighters may be operated by passenger or cargo airlines, by private individuals or by the armed forces of individual countries. Cargo aircraft represent a small proportion of the air freight market. The majority is carried in special ULD containers in the holds of normal passenger aircraft. Aircraft were put to use carrying cargo in the form of air mail as early as 1911, although the earliest aircraft were not designed primarily as cargo carriers, by the mid-1920s aircraft manufacturers were designing and building dedicated cargo aircraft. The Vickers Vernon, a development of the Vickers Vimy Commercial, in February 1923 this was put to use by the RAFs Iraq Command who flew nearly 500 Sikh troops from Kingarban to Kirkuk in the first ever strategic airlift of troops. The Victorians also helped to pioneer air routes for Imperial Airways Handley Page HP.42 airliners, the World War II German design, the Arado Ar 232 was the first purpose built cargo aircraft. The Ar 232 was intended to supplant the earlier Junkers Ju 52 freighter conversions, most other forces used freighter versions of airliners in the cargo role as well, most notably the C-47 Skytrain version of the Douglas DC-3, which served with practically every Allied nation. This aircraft, like most of its era, used tail-dragger landing gear caused the aircraft to have a decided rearward tilt when landed. A similar rear loading ramp even appeared in a different form on the nosewheel gear-equipped. Postwar Europe also served to play a role in the development of the modern air cargo. To rapidly supply the numbers of aircraft, many older types. In operation it was found that it took as long or longer to unload these older designs as the much larger tricycle landing gear Douglas C-54 Skymaster which was easier to move about in when landed. The C-47s were quickly removed from service, and from then on flat-decks were a requirement of all new cargo designs, in the years following the war era a number of new custom-built cargo aircraft were introduced, often including some experimental features. For instance, the USs C-82 Packet featured a cargo area. Although larger, smaller and faster designs have been proposed for many years and these designs offer the ability to carry the heaviest loads, even main battle tanks, at global ranges. The Boeing 747 was originally designed to the specification as the C-5
39.
Boeing 707
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The Boeing 707 is a mid-sized, long-range, narrow-body, four-engine jet airliner built by Boeing Commercial Airplanes from 1958 to 1979. Its name is pronounced as seven oh seven. Versions of the aircraft have a capacity from 140 to 219 passengers, developed as Boeings first jet airliner, the 707 is a swept-wing design with podded engines. Although it was not the first jetliner in service, the 707 was the first to be commercially successful, dominating passenger air transport in the 1960s and remaining common through the 1970s, the 707 is generally credited with ushering in the Jet Age. It established Boeing as one of the largest manufacturers of passenger aircraft, the later 720,727,737, and 757 share elements of the 707s fuselage design. The 707 was developed from the Boeing 367-80, a prototype jet first flown in 1954, a larger fuselage cross-section and other modifications resulted in the initial-production 707-120, powered by Pratt & Whitney JT3C turbojet engines, which first flew on December 20,1957. Pan American World Airways began regular 707 service on October 26,1958, later derivatives included the shortened long-range 707-138 and the stretched 707-320, both of which entered service in 1959. A smaller short-range variant, the 720, was introduced in 1960, the 707 has been used on domestic, transcontinental, and transatlantic flights, and for cargo and military applications. A convertible passenger-freighter model, the 707-320C, entered service in 1963, military derivatives include the E-3 Sentry airborne reconnaissance aircraft and the C-137 Stratoliner VIP transports. Boeing produced and delivered 1,011 airliners including the smaller 720 series, ten Boeing 707s were in commercial service in July 2013. During and after World War II, Boeing was known for its military aircraft, the company had produced innovative and important bombers, from the B-17 Flying Fortress and B-29 Superfortress, to the jet-powered B-47 Stratojet and B-52 Stratofortress. The companys civil aviation department lagged far behind Douglas and other competitors, during 1949–1950, Boeing embarked on studies for a new jet transport, realizing that any design must be aimed at both the military and civilian markets. At the time, aerial refueling was becoming a standard technique for military aircraft, with the advent of the Jet Age, a new tanker was required to meet the USAFs fleet of jet-powered bombers, this was where Boeings new design would potentially win military orders. Boeing studied numerous wing and engine layouts for its new transport/tanker, some of which were based on the B-47 and C-97, before settling on 367–80. The Dash 80 took less than two years from launch in 1952 to rollout on May 14,1954, then first flew on July 15,1954. The prototype was an aircraft for both military and civilian use. The United States Air Force was the first customer, using it as the basis for the KC-135 Stratotanker aerial refueling platform, whether the passenger 707 would be profitable was far from certain. In a demonstration flight over Lake Washington outside Seattle, on August 7,1955, the 132-inch wide fuselage of the Dash 80 was large enough for four-abreast seating like the Stratocruiser
40.
United States Air Force
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The United States Air Force is the aerial warfare service branch of the United States Armed Forces and one of the seven American uniformed services. Initially part of the United States Army, the USAF was formed as a branch of the military on 18 September 1947 under the National Security Act of 1947. It is the most recent branch of the U. S. military to be formed, the U. S. Air Force is a military service organized within the Department of the Air Force, one of the three military departments of the Department of Defense. The Air Force is headed by the civilian Secretary of the Air Force, who reports to the Secretary of Defense, the U. S. Air Force provides air support for surface forces and aids in the recovery of troops in the field. As of 2015, the service more than 5,137 military aircraft,406 ICBMs and 63 military satellites. It has a $161 billion budget with 313,242 active duty personnel,141,197 civilian employees,69,200 Air Force Reserve personnel, and 105,500 Air National Guard personnel. According to the National Security Act of 1947, which created the USAF and it shall be organized, trained, and equipped primarily for prompt and sustained offensive and defensive air operations. The stated mission of the USAF today is to fly, fight, and win in air, space and we will provide compelling air, space, and cyber capabilities for use by the combatant commanders. We will excel as stewards of all Air Force resources in service to the American people, while providing precise and reliable Global Vigilance, Reach and it should be emphasized that the core functions, by themselves, are not doctrinal constructs. The purpose of Nuclear Deterrence Operations is to operate, maintain, in the event deterrence fails, the US should be able to appropriately respond with nuclear options. Dissuading others from acquiring or proliferating WMD, and the means to deliver them, moreover, different deterrence strategies are required to deter various adversaries, whether they are a nation state, or non-state/transnational actor. Nuclear strike is the ability of forces to rapidly and accurately strike targets which the enemy holds dear in a devastating manner. Should deterrence fail, the President may authorize a precise, tailored response to terminate the conflict at the lowest possible level, post-conflict, regeneration of a credible nuclear deterrent capability will deter further aggression. Finally, the Air Force regularly exercises and evaluates all aspects of operations to ensure high levels of performance. Nuclear surety ensures the safety, security and effectiveness of nuclear operations, the Air Force, in conjunction with other entities within the Departments of Defense or Energy, achieves a high standard of protection through a stringent nuclear surety program. The Air Force continues to pursue safe, secure and effective nuclear weapons consistent with operational requirements, adversaries, allies, and the American people must be highly confident of the Air Forces ability to secure nuclear weapons from accidents, theft, loss, and accidental or unauthorized use. This day-to-day commitment to precise and reliable nuclear operations is the cornerstone of the credibility of the NDO mission, positive nuclear command, control, communications, effective nuclear weapons security, and robust combat support are essential to the overall NDO function. OCA is the method of countering air and missile threats, since it attempts to defeat the enemy closer to its source
41.
Royal Air Force
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The Royal Air Force is the United Kingdoms aerial warfare force. Formed towards the end of the First World War on 1 April 1918, following victory over the Central Powers in 1918 the RAF emerged as, at the time, the largest air force in the world. The RAF describe its mission statement as, an agile, adaptable and capable Air Force that, person for person, is second to none, and that makes a decisive air power contribution in support of the UK Defence Mission. The mission statement is supported by the RAFs definition of air power, Air power is defined as the ability to project power from the air and space to influence the behaviour of people or the course of events. Today the Royal Air Force maintains a fleet of various types of aircraft. The majority of the RAFs rotary-wing aircraft form part of the tri-service Joint Helicopter Command in support of ground forces, most of the RAFs aircraft and personnel are based in the UK, with many others serving on operations or at long-established overseas bases. It was founded on 1 April 1918, with headquarters located in the former Hotel Cecil, during the First World War, by the amalgamation of the Royal Flying Corps, at that time it was the largest air force in the world. The RAFs naval aviation branch, the Fleet Air Arm, was founded in 1924, the RAF developed the doctrine of strategic bombing which led to the construction of long-range bombers and became its main bombing strategy in the Second World War. The RAF underwent rapid expansion prior to and during the Second World War, under the British Commonwealth Air Training Plan of December 1939, the air forces of British Commonwealth countries trained and formed Article XV squadrons for service with RAF formations. Many individual personnel from countries, and exiles from occupied Europe. By the end of the war the Royal Canadian Air Force had contributed more than 30 squadrons to serve in RAF formations, additionally, the Royal Australian Air Force represented around nine percent of all RAF personnel who served in the European and Mediterranean theatres. In the Battle of Britain in 1940, the RAF defended the skies over Britain against the numerically superior German Luftwaffe, the largest RAF effort during the war was the strategic bombing campaign against Germany by Bomber Command. Following victory in the Second World War, the RAF underwent significant re-organisation, during the early stages of the Cold War, one of the first major operations undertaken by the Royal Air Force was in 1948 and the Berlin Airlift, codenamed Operation Plainfire. Before Britain developed its own nuclear weapons the RAF was provided with American nuclear weapons under Project E and these were initially armed with nuclear gravity bombs, later being equipped with the Blue Steel missile. Following the development of the Royal Navys Polaris submarines, the nuclear deterrent passed to the navys submarines on 30 June 1969. With the introduction of Polaris, the RAFs strategic nuclear role was reduced to a tactical one and this tactical role was continued by the V bombers into the 1980s and until 1998 by Tornado GR1s. For much of the Cold War the primary role of the RAF was the defence of Western Europe against potential attack by the Soviet Union, with many squadrons based in West Germany. With the decline of the British Empire, global operations were scaled back, despite this, the RAF fought in many battles in the Cold War period
42.
No. 137 Squadron RAF
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No.137 Squadron RAF existed briefly as a day bomber unit in World War I but it never became operational. During World War II it flew as one of the two Whirlwind squadrons before converting to Hurricane Mk. IV fighter-bombers and later the Hawker Typhoon in the same role, the squadron was disbanded in August 1945. No.137 Squadron RAF existed briefly as a working up to be a day bomber unit on Airco DH. 9s during World War I. It was formed at Shawbury on 1 April 1918 and was disbanded there on 4 July 1918, plans to reinstate the squadron in September as laid out in Air Organisation Memorandum 939 of 13 July 1918 came to nought as Air Organisation Memorandum 999 of 17 August 1918 cancelled these. The squadron was reformed at Charmy Down on 20 September 1941, the squadron became operational with them on 20 October and flew its first mission four days afterwards. Unfortunately the new CO, S/Ldr Sample, was killed four days after this in a collision with a new pilot. Two days later another pilot crashed into the sea, after this bad start, No.137 became non-operational for a period before resuming with coastal missions on 11 November. On one such mission on 12 February 1942, to escort destroyers, they met by accident the fighter screen around the Scharnhorst. 137 flew this new fighter-bomber operationally from 8 February 1944 until 25 August 1945, list of Royal Air Force aircraft squadrons History of squadron at RAF. mod. uk RAFWeb - Air of Authority
43.
VFA-137
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Strike Fighter Squadron 137, also known as the Kestrels, are a United States Navy F/A-18E Super Hornet strike fighter squadron stationed at Naval Air Station Lemoore, California. Strike Fighter Squadron 137 was established on July 2,1985 and they received their first Lot VIII F/A-18A Hornet on November 25,1985 and in October 1986 the squadron was awarded the Silver Anchor for new construction squadrons. In the course of their 23-year history, they have a safety record that includes over 90,000 mishap-free flight hours, in 1987-1988 the squadron made its first deployment to the Mediterranean Sea embarked on the USS Coral Sea, as part of Carrier Air Wing Thirteen. That year the squadron was recognized with the Commander Naval Air Forces, in October 1990, the squadron transferred to Carrier Air Wing Six on board USS Forrestal, completing an accelerated work up cycle and their third deployment. On cruise, the squadron flew sorties over Iraq in support of Operation Provide Comfort, in September 1992, the squadron completed a homeport change to NAS Lemoore and transitioned to the night attack capable Lot XV F/A-18C. In May 1993, the squadron joined Carrier Air Wing Two, on this deployment, and the 1997 deployment, the squadron patrolled the skies over Iraq, enforcing the United Nations no-fly zone in support of Operation Southern Watch. In 1999 and again in 2001, VFA-137 employed precision-guided ordnance against Iraq as part of a Coalition Forces response to repeated violations of the no-fly zone, in November 2002, VFA-137 deployed to the Persian Gulf on board USS Constellation for her final deployment. The squadron participated in operations in the skies over Iraq, initially in support of Operation Southern Watch. During the course of the conflict, the squadron flew over 500 combat sorties, the squadron returned home in June 2003, and began the transition to the new Lot XXV F/A-18E Super Hornet. After completing the Safe for Flight certification, they became the third F/A-18E squadron in the U. S. Navy, in April 2004, Commander, Naval Air Force, U. S. Pacific Fleet awarded the Battle “E” for calendar year 2003, subsequently, Commander, Naval Air Force awarded the 2003 Captain Michael J. Estocin Award for exceptional operational performance and flight safety. In March 2006, the squadron deployed with CVW2 aboard USS Abraham Lincoln for a 5-month WestPac. The deployment included port calls in Hong Kong, Thailand, Singapore and Sasebo, Japan, and was marked by participation in Exercises Foal Eagle, Valiant Shield, VFA-137 returned from deployment in August 2006. After a work-up cycle that included 2 detachments to NAS Fallon and 3 underway periods on board USS Abraham Lincoln, following 7 months at sea, including 5 months in the Persian Gulf supporting Operations Iraqi Freedom and Enduring Freedom, the squadron returned home in October 2008. On March 15,2010, two VFA-137 aircraft were involved in a collision while training at NAS Fallon. Both pilots survived with one managing to land his plane, while the pilot ejected and was rescued by helicopter. An investigation determined that pilot error was to blame for the collision, the responsible pilots name was redacted from the report released to the public. Naval aviation Modern US Navy carrier air operations List of United States Navy aircraft squadrons List of Inactive United States Navy aircraft squadrons VFA-137s Official Webpage
44.
United States Navy
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The United States Navy is the naval warfare service branch of the United States Armed Forces and one of the seven uniformed services of the United States. The U. S. Navy is the largest, most capable navy in the world, the U. S. Navy has the worlds largest aircraft carrier fleet, with ten in service, two in the reserve fleet, and three new carriers under construction. The service has 323,792 personnel on duty and 108,515 in the Navy Reserve. It has 274 deployable combat vessels and more than 3,700 operational aircraft as of October 2016, the U. S. Navy traces its origins to the Continental Navy, which was established during the American Revolutionary War and was effectively disbanded as a separate entity shortly thereafter. It played a role in the American Civil War by blockading the Confederacy. It played the role in the World War II defeat of Imperial Japan. The 21st century U. S. Navy maintains a global presence, deploying in strength in such areas as the Western Pacific, the Mediterranean. The Navy is administratively managed by the Department of the Navy, the Department of the Navy is itself a division of the Department of Defense, which is headed by the Secretary of Defense. The Chief of Naval Operations is an admiral and the senior naval officer of the Department of the Navy. The CNO may not be the highest ranking officer in the armed forces if the Chairman or the Vice Chairman of the Joint Chiefs of Staff. The mission of the Navy is to maintain, train and equip combat-ready Naval forces capable of winning wars, deterring aggression, the United States Navy is a seaborne branch of the military of the United States. The Navys three primary areas of responsibility, The preparation of naval forces necessary for the prosecution of war. The development of aircraft, weapons, tactics, technique, organization, U. S. Navy training manuals state that the mission of the U. S. Armed Forces is to prepare and conduct prompt and sustained combat operations in support of the national interest, as part of that establishment, the U. S. Navys functions comprise sea control, power projection and nuclear deterrence, in addition to sealift duties. It follows then as certain as that night succeeds the day, that without a decisive naval force we can do nothing definitive, the Navy was rooted in the colonial seafaring tradition, which produced a large community of sailors, captains, and shipbuilders. In the early stages of the American Revolutionary War, Massachusetts had its own Massachusetts Naval Militia, the establishment of a national navy was an issue of debate among the members of the Second Continental Congress. Supporters argued that a navy would protect shipping, defend the coast, detractors countered that challenging the British Royal Navy, then the worlds preeminent naval power, was a foolish undertaking. Commander in Chief George Washington resolved the debate when he commissioned the ocean-going schooner USS Hannah to interdict British merchant ships, and reported the captures to the Congress
45.
F/A-18E Super Hornet
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The Boeing F/A-18E and F/A-18F Super Hornet are twin-engine carrier-capable multirole fighter aircraft variants based on the McDonnell Douglas F/A-18 Hornet. The F/A-18E single-seat and F/A-18F tandem-seat variants are larger and more advanced derivatives of the F/A-18C, the Super Hornet has an internal 20 mm M61 rotary cannon and can carry air-to-air missiles and air-to-surface weapons. Additional fuel can be carried in up to five fuel tanks. Designed and initially produced by McDonnell Douglas, the Super Hornet first flew in 1995, full-rate production began in September 1997, after the merger of McDonnell Douglas and Boeing the previous month. The Super Hornet entered service with the United States Navy in 1999, replacing the Grumman F-14 Tomcat, which was retired in 2006, the Super Hornet serves alongside the original Hornet. The Royal Australian Air Force, which has operated the F/A-18A as its main fighter since 1984, RAAF Super Hornets entered service in December 2010. The Super Hornet is a redesign of the McDonnell Douglas F/A-18 Hornet. The Super Hornets unique wing and tail configuration can be traced back to an internal Northrop project P-530,1965, this had started as a substantial rework of the lightweight F-5E with a larger wing, twin tail fins and a distinctive leading edge root extension. The Hornet proved to be effective but limited in combat radius, the concept of an enlarged Hornet was first proposed in the 1980s, which was marketed by McDonnell Douglas as Hornet 2000. The Hornet 2000 concept was an advanced F/A-18 with a larger wing, the end of the Cold War led to a period of military budget cuts and considerable restructuring. At the same time, U. S. Naval Aviation faced a number of problems, the McDonnell Douglas A-12 Avenger II was canceled in 1991 after the program ran into serious problems, it was intended to replace the obsolete Grumman A-6 Intruder and LTV A-7 Corsair II. The Navy considered updating an existing design as an attractive approach to a clean-sheet program. The next-generation Hornet design proved more attractive than Grummans Quick Strike upgrade to the F-14 Tomcat, at the time, the Grumman F-14 Tomcat was the Navys primary air superiority fighter and fleet defense interceptor. In 1992, the Navy canceled the Navy Advanced Tactical Fighter, the Super Hornet was first ordered by the U. S. Navy in 1992. The Navy retained the F/A-18 designation to help sell the program to Congress as a low-risk derivative, the Hornet and Super Hornet share many characteristics, including avionics, ejection seats, radar, armament, mission computer software, and maintenance/operating procedures. The initial F/A-18E/F retained most of the systems from the F/A-18C/Ds configuration at the time. The design would be expanded in the Super Hornet with an empty weight slightly greater than the F-15C, the Super Hornet first flew on 29 November 1995. Initial production on the F/A-18E/F began in 1995, flight testing started in 1996 with the F/A-18E/Fs first carrier landing in 1997
46.
Naval Air Station Lemoore
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Naval Air Station Lemoore or NAS Lemoore is a United States Navy base, located in Kings County and Fresno County, California. Lemoore Station, California, a place, is located inside the bases borders. NAS Lemoore is the Navys newest and largest Master Jet Base, Strike Fighter Wing Pacific, along with its associated squadrons, is home ported there. NAS Lemoore also hosts four Carrier Air Wings, Carrier Air Wing Two, Carrier Air Wing Nine, Carrier Air Wing Eleven, and Carrier Air Wing Seventeen. Commissioned in 1961, NAS Lemoore, as seen from an aircraft flying above, looks significant and stands out from the farmlands of Central California, NAS Lemoore is the newest and largest Master Jet Base in the U. S. Navy. It has two parallel runways 4,600 feet apart. Aircraft parking and maintenance hangars are aligned between the 13, 500-foot runways, separated from the hangars by underpasses beneath taxiways A & C, the remainder of the air operations area is located directly southeast. In July 1998, NAS Lemoore was selected as the West Coast site for the Navy’s newest strike-fighter aircraft and this action brought approximately 92 additional aircraft,1,850 additional active duty personnel and 3,000 family members to NAS Lemoore and several associated facility additions or improvements. The Navy also brought four new fleet squadrons to Naval Air Station Lemoore over the period 2001-2004, originally, the Officer In Charge of Construction for building the base was Commander Dennis K. Culp CEC/USN, who was the first Naval officer in Lemoore. With the transfer of NAS Miramar to the United States Marine Corps, NAS Lemoore was built from the ground up as a Master Jet Base, and has several operational advantages, and relatively few constraints, as a result. Strike Fighter Wing Pacific with its facilities is home ported here. The primary aircraft based at NAS Lemoore is the F/A-18 Hornet Strike Fighter, currently, there are a total of 175 Hornets and Super Hornets home-based at NAS Lemoore operating from one Fleet Replacement Squadron and fifteen Fleet Squadrons. FAA Airport Master Record for NLC DoD Lodging Worldwide http, //www. cnic. navy. mil/Lemoore/index. htm Resources for this U. S
47.
California
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California is the most populous state in the United States and the third most extensive by area. Located on the western coast of the U. S, California is bordered by the other U. S. states of Oregon, Nevada, and Arizona and shares an international border with the Mexican state of Baja California. Los Angeles is Californias most populous city, and the second largest after New York City. The Los Angeles Area and the San Francisco Bay Area are the nations second- and fifth-most populous urban regions, California also has the nations most populous county, Los Angeles County, and its largest county by area, San Bernardino County. The Central Valley, an agricultural area, dominates the states center. What is now California was first settled by various Native American tribes before being explored by a number of European expeditions during the 16th and 17th centuries, the Spanish Empire then claimed it as part of Alta California in their New Spain colony. The area became a part of Mexico in 1821 following its war for independence. The western portion of Alta California then was organized as the State of California, the California Gold Rush starting in 1848 led to dramatic social and demographic changes, with large-scale emigration from the east and abroad with an accompanying economic boom. If it were a country, California would be the 6th largest economy in the world, fifty-eight percent of the states economy is centered on finance, government, real estate services, technology, and professional, scientific and technical business services. Although it accounts for only 1.5 percent of the states economy, the story of Calafia is recorded in a 1510 work The Adventures of Esplandián, written as a sequel to Amadis de Gaula by Spanish adventure writer Garci Rodríguez de Montalvo. The kingdom of Queen Calafia, according to Montalvo, was said to be a land inhabited by griffins and other strange beasts. This conventional wisdom that California was an island, with maps drawn to reflect this belief, shortened forms of the states name include CA, Cal. Calif. and US-CA. Settled by successive waves of arrivals during the last 10,000 years, various estimates of the native population range from 100,000 to 300,000. The Indigenous peoples of California included more than 70 distinct groups of Native Americans, ranging from large, settled populations living on the coast to groups in the interior. California groups also were diverse in their organization with bands, tribes, villages. Trade, intermarriage and military alliances fostered many social and economic relationships among the diverse groups, the first European effort to explore the coast as far north as the Russian River was a Spanish sailing expedition, led by Portuguese captain Juan Rodríguez Cabrillo, in 1542. Some 37 years later English explorer Francis Drake also explored and claimed a portion of the California coast in 1579. Spanish traders made unintended visits with the Manila galleons on their trips from the Philippines beginning in 1565
48.
USNS Mission Santa Ana (T-AO-137)
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USNS Mission Santa Ana was a Mission Buenaventura-class oiler that served in the United States Navy. The ship was intended as USS Concho for the U. S. Navy. The ship, a Type T2-SE-A3 tanker, was completed as SS Mission Santa Ana, the tanker was acquired by the U. S. Navy in 1948 as USS Mission Santa Ana, but was transferred to the Military Sea Transport Service upon its creation in 1949. The ship was named for the Santa Ana Estancia, she was the only U. S. Naval Vessel to bear the name, D. J. Johnson, and delivered on 25 October 1945. Acquired by the Navy on 9 January 1948 and chartered to Pacific Tankers Inc. for operations and she served with MSTS until 3 April 1950 when she was taken out of service and berthed in the San Diego group of the Pacific Reserve Fleet. She lay at San Diego, California in reserve until 27 January 1955 when she was transferred to the Maritime Administration and laid up in the Maritime Reserve Fleet at Olympia and she was struck from the Naval Vessel Register on 22 June 1955. Reacquired by the Navy on 3 July 1956 she was again placed in service with MSTS and operated, under charter. The ships final disposition is unknown and this article incorporates text from the public domain Dictionary of American Naval Fighting Ships. Dictionary of American Naval Fighting Ships, aO-137 / T-AO-137 Mission Santa Ana. Archived from the original on March 5,2005
49.
World War II
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World War II, also known as the Second World War, was a global war that lasted from 1939 to 1945, although related conflicts began earlier. It involved the vast majority of the worlds countries—including all of the great powers—eventually forming two opposing alliances, the Allies and the Axis. It was the most widespread war in history, and directly involved more than 100 million people from over 30 countries. Marked by mass deaths of civilians, including the Holocaust and the bombing of industrial and population centres. These made World War II the deadliest conflict in human history, from late 1939 to early 1941, in a series of campaigns and treaties, Germany conquered or controlled much of continental Europe, and formed the Axis alliance with Italy and Japan. Under the Molotov–Ribbentrop Pact of August 1939, Germany and the Soviet Union partitioned and annexed territories of their European neighbours, Poland, Finland, Romania and the Baltic states. In December 1941, Japan attacked the United States and European colonies in the Pacific Ocean, and quickly conquered much of the Western Pacific. The Axis advance halted in 1942 when Japan lost the critical Battle of Midway, near Hawaii, in 1944, the Western Allies invaded German-occupied France, while the Soviet Union regained all of its territorial losses and invaded Germany and its allies. During 1944 and 1945 the Japanese suffered major reverses in mainland Asia in South Central China and Burma, while the Allies crippled the Japanese Navy, thus ended the war in Asia, cementing the total victory of the Allies. World War II altered the political alignment and social structure of the world, the United Nations was established to foster international co-operation and prevent future conflicts. The victorious great powers—the United States, the Soviet Union, China, the United Kingdom, the Soviet Union and the United States emerged as rival superpowers, setting the stage for the Cold War, which lasted for the next 46 years. Meanwhile, the influence of European great powers waned, while the decolonisation of Asia, most countries whose industries had been damaged moved towards economic recovery. Political integration, especially in Europe, emerged as an effort to end pre-war enmities, the start of the war in Europe is generally held to be 1 September 1939, beginning with the German invasion of Poland, Britain and France declared war on Germany two days later. The dates for the beginning of war in the Pacific include the start of the Second Sino-Japanese War on 7 July 1937, or even the Japanese invasion of Manchuria on 19 September 1931. Others follow the British historian A. J. P. Taylor, who held that the Sino-Japanese War and war in Europe and its colonies occurred simultaneously and this article uses the conventional dating. Other starting dates sometimes used for World War II include the Italian invasion of Abyssinia on 3 October 1935. The British historian Antony Beevor views the beginning of World War II as the Battles of Khalkhin Gol fought between Japan and the forces of Mongolia and the Soviet Union from May to September 1939, the exact date of the wars end is also not universally agreed upon. It was generally accepted at the time that the war ended with the armistice of 14 August 1945, rather than the formal surrender of Japan
50.
Minesweeper (ship)
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A minesweeper is a small naval warship designed to engage in minesweeping. Using various mechanisms intended to counter the threat posed by naval mines, although naval warfare has a long history, the earliest known usage of the naval mine dates to the Ming dynasty. Dedicated minesweepers, however, only appear in the record several centuries later, to the Crimean War. In the Crimean War, minesweepers consisted of British rowboats trailing grapnels to snag the mines, despite the use of mines in the American Civil War, there are no records of effective minesweeping being used. Officials in the Union Army attempted to create the first minesweeper but were plagued by flawed designs, minesweeping technology picked up in the Russo-Japanese War, using aging torpedo boats as minesweepers. In Britain, naval leaders recognized before the outbreak of World War I that the development of sea mines was a threat to the nations shipping, sir Arthur Wilson noted the real threat of the time was blockade aided by mines and not invasion. A Trawler Section of the Royal Navy Reserve became the predecessor of the mine sweeping forces with specially designed ships and these reserve Trawler Section fishermen and their trawlers were activated, supplied with mine gear, rifles, uniforms and pay as the first minesweepers. The dedicated, purpose-built minesweeper first appeared during World War I with the Flower-class minesweeping sloop, by the end of the War, naval mine technology had grown beyond the ability of minesweepers to detect and remove. Minesweeping made significant advancements during World War II, combatant nations quickly adapted ships to the task of minesweeping, including Australias 35 civilian ships that became Auxiliary Minesweepers. Both Allied and Axis countries made heavy use of minesweepers throughout the war, historian Gordon Williamson wrote that Germanys minesweepers alone formed a massive proportion of its total strength, and are very much the unsung heroes of the Kriegsmarine. Naval mines remained a threat even after the war ended, after the Second World War, allied countries worked on new classes of minesweepers ranging from 120-ton designs for clearing estuaries to 735-ton oceangoing vessels. The United States Navy even used specialized Mechanized Landing Craft to sweep shallow harbors in, as of June 2012, the U. S. Navy had four minesweepers deployed to the Persian Gulf to address regional instabilities. Minesweepers are equipped with mechanical or electrical devices, known as sweeps, mechanical sweeps are devices designed to cut the anchoring cables of moored mines, and preferably attach a tag to help the subsequent localization and neutralization. They are towed behind the minesweeper, and use a body to maintain the sweep at the desired depth. Influence sweeps are equipment, often towed, that emulate a particular ship signature, the most common such sweeps are magnetic and acoustic generators. There are two modes of operating an influence sweep, MSM and TSM, MSM sweeping is founded on intelligence on a given type of mine, and produces the output required for detonation of this mine. If such intelligence is unavailable, the TSM sweeping instead reproduces the influence of the ship that is about to transit through the area. TSM sweeping thus clears mines directed at this ship without knowledge of the mines, however, mines directed at other ships might remain
51.
USS Ascella (AK-137)
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USS Ascella was a Crater-class cargo ship commissioned by the US Navy for service in World War II. Ascella was named after Ascella, a star in the constellation Sagittarius and she was responsible for delivering troops, goods and equipment to locations in the Asiatic-Pacific Theater. Ascella was laid down 7 January 1943, under a Maritime Commission contract,708, as the Liberty ship SS George C. Yount, by California Shipbuilding Corporation, Terminal Island, Los Angeles, California, launched 4 February 1943, two days after commissioning, the cargo ship arrived at the Naval Supply Depot, Oakland, California, to load stores, provisions, and ammunition. Following brief shakedown training, she departed San Francisco, California, nine days later, Ascella entered port at Pearl Harbor and began discharging her cargo. On 3 February, she shifted berths and began loading supplies bound for the US Army occupation garrison on newly won Kwajalein in the Marshall Islands, a week later, the vessel put to sea and, after a nine-day voyage, entered the lagoon at Kwajalein. She spent the remainder of February unloading her cargo before departing Kwajalein on 3 March, after interrupting her voyage at Pearl Harbor to drop off three landing craft for repairs, the ship returned to the Naval Supply Depot, Oakland, on 23 March. There she took on another load of supplies, embarked 83 Navy men for passage to Hawaii and she entered Pearl Harbor on 10 April, and began a four-day visit during which her passengers disembarked and she loaded ammunition and armory equipment. On 14 April, Ascella set sail for the Marshall Islands with another 44 passengers embarked, upon her arrival in Majuro lagoon, the cargo ship began replenishing the warships of Task Force 58. During her sojourn there, she also provided berthing spaces for her passengers until the middle of the first week in May. On 6 June, she took on board 47 U. S, marines for passage to Roi Island at Kwajalein, where the ship remained and loaded defective ammunition and empty shell cases until 21 June. On that day, Ascella embarked 51 Navy passengers and weighed anchor for Hawaii and she stopped at Oahu from 30 June to 3 July, to debark 24 of her passengers and unload her cargo. Another eight days at sea preceded her 11 July, arrival back at San Francisco, after disembarking the remaining 27 passengers, the ship started loading dry stores and provisions bound for the fleet in the Central Pacific. She got underway on 24 July, and reached Pearl Harbor on 1 August, during the next two days, the cargo ship debarked passengers and took on mail bound for the Central Pacific. Returning to sea on 3 August, Ascella resumed the voyage west and stood into the lagoon at Eniwetok Atoll on 15 August, in addition to serving as station stores ship issuing supplies to various units of the fleet, she also provided berthing spaces for transient sailors. After transferring what remained of her cargo to Silica on 11 September, Ascella embarked 53 hospital patients for transportation to Hawaii on 16 September and she reached Pearl Harbor on 25 September, exchanged her patient-passengers for 56 California-bound sailors, and continued on her way on 27 September. On 6 October, the ship pulled into San Pedro, California, three weeks of voyage repairs and cargo loading operations followed her return to the California coast. She got underway again on 27 October, to carry supplies, Ascella made a stop at Pearl Harbor to take on fuel and water before continuing on to her first destination, Finschhafen, New Guinea
52.
USS Bowie (APA-137)
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USS Bowie was a Haskell-class attack transport acquired by the U. S. Navy during World War II for the task of transporting troops to and from combat areas. Outfitting, shakedown, and amphibious training occupied Bowie until the week in February 1945. After post-shakedown availability at Terminal Island, she loaded cargo at the Naval Supply Depot, Oakland, California and she made a refueling stop at Eniwetok in the Marshalls before arriving at Guam on 10 March. The attack transport completed cargo operations there on 16 March and then moved to Saipan on the 17th to embark casualties and she put to sea for Hawaii that same day and entered Pearl Harbor on 27 March. The ship conducted operations in Hawaiian waters and engaged in upkeep in Pearl Harbor until mid-April. At that time, she began loading elements of the 10th Army bound for duty in the Okinawa campaign. Bowie stood out of Pearl Harbor on 17 April in a convoy and she arrived off the Hagushi beaches on Okinawa on 10 May. The troops went ashore immediately, and the transport began unloading cargo. During her stay in the Ryūkyūs, Bowie witnessed a number of air raids, on 15 May, the attack transport left Okinawa in a Hawaii-bound convoy. She made two stops, one at Ulithi and the other at Guam, before arriving back in Pearl Harbor on 3 June and she remained there overnight and, on the 4th, headed for the west coast. Bowie reached San Francisco, California, on 10 June and disembarked the casualties, later in the month, she loaded cargo and took on troops. The ship loosed her moorings on 17 June and stood out of San Francisco Bay, on her way across the Pacific Ocean to the Philippines, Bowie stopped at Eniwetok and Ulithi for fuel. She arrived at Tacloban, on Leyte, on 9 July and began discharging cargo, five days later, the attack transport headed back to Hawaii. Bowie spent almost two months in the Hawaiian Islands, when not in port at either Pearl Harbor or Honolulu, she conducted rehearsal landings at various locations in the islands. On 1 September, she left Pearl Harbor in a convoy bound ultimately for Japan and she stopped at Saipan to take on fuel and provisions from 13 to 16 September and arrived at Sasebo, Japan, on the 22d. Her troops went ashore on the 24th, and Bowie cleared Sasebo the next day and she took on boats at Subic Bay on 30 September and then moved to Manila. The attack transport moved to Lingayen Gulf on 2 and 3 October and she departed Lingayen Gulf in convoy on 9 October and arrived in Sasebo on the 14th. She did not, however, disembark her passengers until 18 October, on the 22d, Bowie departed Sasebo and proceeded to Guam where she stopped on the 27th