1.
150 (number)
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150 is the natural number following 149 and preceding 151. 150 is the sum of eight consecutive primes, given 150, the Mertens function returns 0. The sum of Eulers totient function φ over the first twenty-two integers is 150,150 is a Harshad number and an abundant number. The last numbered Psalm in the Bible, Psalm 150, perhaps the one most often set to music,150 is also, The number of degrees in the quincunx astrological aspect explored by Johannes Kepler
2.
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
3.
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
4.
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
5.
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
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.
Vickers Type 143
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The Vickers Type 143 or Bolivian Scout was a British single-seat fighter biplane designed and built by Vickers in 1929-1930. Six were built for Bolivia in 1930, which used the survivors in the Chaco War against Paraguay and it was an all-metal, single-seat, biplane aircraft, with single-bay wings. The Type 143 first flew on 11 June 1929, and successfully met all performance criteria, One of the six aircraft was evaluated by the Aeroplane and Armament Experimental Establishment at Martlesham Heath before delivery to Bolivia. Delivery of the six Type 143s to Bolivia began in January 1930, while the type proved popular in Bolivian service, three of the six had been written off by the time the border disputes between Bolivia and Paraguay escalated into the Chaco War. The three remaining Type 143s continued to serve in the Chaco War until superseded by Curtiss Hawks, Vickers Type 143 Six aircraft for Bolivia, powered by 450 hp Bristol Jupiter VIA engine. Vickers Type 177 One prototype Naval Fighter, evaluated for Fleet Air Arm, Bolivia Bolivian Air Force received six aircraft. United Kingdom Fleet Air Arm tested one prototype.29 lb/ft² Power/mass,0
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United Kingdom
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The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom or Britain, is a sovereign country in western Europe. Lying off the north-western coast of the European mainland, the United Kingdom includes the island of Great Britain, Northern Ireland is the only part of the United Kingdom that shares a land border with another sovereign state—the Republic of Ireland. The Irish Sea lies between Great Britain and Ireland, with an area of 242,500 square kilometres, the United Kingdom is the 78th-largest sovereign state in the world and the 11th-largest in Europe. It is also the 21st-most populous country, with an estimated 65.1 million inhabitants, together, this makes it the fourth-most densely populated country in the European Union. The United Kingdom is a monarchy with a parliamentary system of governance. The monarch is Queen Elizabeth II, who has reigned since 6 February 1952, other major urban areas in the United Kingdom include the regions of Birmingham, Leeds, Glasgow, Liverpool and Manchester. The United Kingdom consists of four countries—England, Scotland, Wales, the last three have devolved administrations, each with varying powers, based in their capitals, Edinburgh, Cardiff and Belfast, respectively. The relationships among the countries of the UK have changed over time, Wales was annexed by the Kingdom of England under the Laws in Wales Acts 1535 and 1542. A treaty between England and Scotland resulted in 1707 in a unified Kingdom of Great Britain, which merged in 1801 with the Kingdom of Ireland to form the United Kingdom of Great Britain and Ireland. Five-sixths of Ireland seceded from the UK in 1922, leaving the present formulation of the United Kingdom of Great Britain, there are fourteen British Overseas Territories. These are the remnants of the British Empire which, at its height in the 1920s, British influence can be observed in the language, culture and legal systems of many of its former colonies. The United Kingdom is a country and has the worlds fifth-largest economy by nominal GDP. The UK is considered to have an economy and is categorised as very high in the Human Development Index. It was the worlds first industrialised country and the worlds foremost power during the 19th, the UK remains a great power with considerable economic, cultural, military, scientific and political influence internationally. It is a nuclear weapons state and its military expenditure ranks fourth or fifth in the world. The UK has been a permanent member of the United Nations Security Council since its first session in 1946 and it has been a leading member state of the EU and its predecessor, the European Economic Community, since 1973. However, on 23 June 2016, a referendum on the UKs membership of the EU resulted in a decision to leave. The Acts of Union 1800 united the Kingdom of Great Britain, Scotland, Wales and Northern Ireland have devolved self-government
21.
Biplane
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A biplane is a fixed-wing aircraft with two main wings stacked one above the other. The first powered, controlled aeroplane to fly, the Wright Flyer, used a biplane wing arrangement, while a biplane wing structure has a structural advantage over a monoplane, it produces more drag than a similar unbraced or cantilever monoplane wing. Improved structural techniques, better materials and the quest for greater speed made the biplane configuration obsolete for most purposes by the late 1930s. Biplanes offer several advantages over conventional cantilever monoplane designs, they permit lighter wing structures, low wing loading, however, interference between the airflow over each wing increases drag substantially, and biplanes generally need extensive bracing, which causes additional drag. Biplanes are distinguished from tandem wing arrangements, where the wings are placed forward and aft, instead of above, the term is also occasionally used in biology, to describe the wings of some flying animals. In a biplane aircraft, two wings are placed one above the other, either or both of the main wings can support ailerons, while flaps are more usually positioned on the lower wing. Bracing is nearly always added between the upper and lower wings, in the form of wires and/or slender interplane struts positioned symmetrically on either side of the fuselage. The primary advantage of the biplane over the traditional single plane or monoplane is to combine great stiffness with light weight. A braced monoplane wing must support itself fully, while the two wings of a help to stiffen each other. The biplane is therefore inherently stiffer than the monoplane, also, the structural forces in the spars of a biplane wing tend to be lower, so the wing can use less material to obtain the same overall strength and is therefore much lighter. A disadvantage of the biplane was the need for extra struts to space the wings apart, the low power supplied by the engines available in the first years of aviation meant that aeroplanes could only fly slowly. This required an even lower stalling speed, which in turn required a low wing loading, combining both large wing area with light weight. A biplane wing of a span and chord has twice the area of a monoplane the same size and so can fly more slowly. Alternatively, a wing of the same area as a monoplane has lower span and chord, reducing the structural forces. Biplanes suffer aerodynamic interference between the two planes and this means that a biplane does not in practice obtain twice the lift of the similarly-sized monoplane. The farther apart the wings are spaced the less the interference, given the slow speed and low power of early aircraft, the drag penalty of the wires and struts and the mutual interference of airflows were relatively minor and acceptable factors. The smaller biplane wing also allows greater maneuverability, during World War One, this further enhanced the dominance of the biplane and, despite the need for speed, military aircraft were among the last to abandon the biplane form. Specialist sports Aerobatic biplanes are still occasionally made, biplanes were originally designed with the wings positioned directly one above the other
22.
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
23.
143d Airlift Wing
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The 143d Airlift Wing is a unit of the Rhode Island Air National Guard, stationed at Quonset Point Air National Guard Station, Rhode Island. If activated to service, the Wing is gained by the United States Air Force Air Mobility Command. The 143d Airlift Squadron assigned to the Wings 143d Operations Group, is a descendant organization of the 152d Observation Squadron and it is one of the 29 original National Guard Observation Squadrons of the United States Army National Guard formed before World War II. The 143d Special Operations Group was established by the National Guard Bureau, other squadrons assigned into the group were the 143d Headquarters, 143d Material Squadron, 143d Combat Support Squadron, and the 143d USAF Dispensary. The Grumman SA-16 Albatross flown by 143d pilots since 1955 was replaced in 1968 with a version of the Albatross. With twice the cargo capability and range, the HU-16 opened up new avenues of opportunity as was demonstrated in 1970. The unit would work in the Special Operations field for seven years, during which the HU-16 aircraft were eventually retired in 1972. In 1975 as part of a program to upgrade Air National Guard units the 143d was redesignated as a Tactical Airlift Group. In 1980 the 143d Tactical Airlift Group moved from T. F, green airport to its new home at Quonset Air National Guard Base. As global airlifters, Rhode Island Herks were found in all parts of the United States, Europe, Africa, South America, in 1989, the 143d was selected for conversion to the C-130E Model. In 1990 unit volunteers provided support during Operation Desert Shield, in September, unit members flew out of Rhein-Main Air Base, Germany to support operational missions from Turkey and Saudi Arabia. The second group of volunteers arrived at RAF Mildenhall, England in January 1991 and was in the theater of operations when Operation Desert Shield turned into Operation Desert Storm. With the defeat of the Iraqi forces and the end of the Gulf War, as part of Air Mobility Command the unit continued to be called upon to support State, Federal, and UN activities throughout the world. On 1 October 1995 the group was elevated to Wing status, in 1998 the Air Force formed the Expeditionary Air Force, smaller sized war fighting packages able to rapidly respond to regional conflicts. The Wing has participated in five AEF cycles, supporting Operation Joint Forge in the Balkans, Operation Southern Watch in Southwest Asia and Coronet Oak in South America. On 11 September 2001, the 143d responded to the again, deploying unit members to Ground Zero, to US bases for homeland security. The 143d AW has supported the Global War on Terror by not only becoming a bridge to and from the theater, the 143d AW also provided and continues to provide the much needed troop support within Southwest Asia and many other areas of the world. In December 2001, the 143d received its first C-130J-30, the Wing became the first in the Air Force to receive the stretch version of the J model
24.
Quonset Point
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Quonset Point /ˈkwɒnsᵻt/, also known simply as Quonset, is a small peninsula in Narragansett Bay in the U. S. state of Rhode Island. It is contained entirely within the town of North Kingstown and its name is widely known from the Quonset hut, which was first manufactured there. Quonset is a Native American word likely meaning small long place, Quonset Point was the location of Naval Air Station Quonset Point, a large United States Navy base. The peninsula is now used for purposes and is partially abandoned. A major industrial tenant is a hull-fabrication and outfitting facility for Electric Boat Corporation, Rhode Island Route 403 is a freeway branching from Route 4 that serves the area, Quonset is also served by a railroad spur from Amtraks Northeast Corridor. Quonset Point is the birthplace of former White House Secretary Dee Dee Myers, it’s a former Navy surveillance ship acquired by the NOAA and converted into a deep sea research vessel. Inc. and consists of approximately 14 miles of track in two branches, •The Quonset Business Park benefits from convenient access to Interstate 95 via a 4-lane limited-access highway. •Ferry service to and from Oak Bluffs, Marthas Vineyard is provided by Rhode Island Fast Ferry, •The Rhode Island Public Transportation authority currently has bus stops at Electric Boat, The Gateway and on Post Road on the border of the Quonset Business Park. ĈĈ The ferry dock at Quonset Point is the terminal for the Marthas Vineyard Fast Ferry Millennium to Oak Bluffs. A shuttle bus every hour before the ferry departs, and after the ferry arrives, a bus travels to the Providence Airport. The Rhode Island Air Show is held annually by the Rhode Island National Guard and is perhaps the most well known event to place on Quonset Point. Tucker, John Klatt, and Michael Goulian as well as the GEICO Skytypers, attendance in 2011 was so high that the show was sold out after parking locations filled up. The 2012 show yielded a similar audience and each year had a normal attendance of over 200,000. Without involvement by the Blue Angels or Thunderbirds it is unlikely that a show will take place at Quonset. To the shock of air show Fans, on January 4,2014 the Rhode Island Air National Guard Open House and Air Show was announced to take place on that year after a two-year hiatus in between. Although the Cherry Point Air Show has since terminated its cancellation and will take place, during the 1950s, Quonset Point was home port for the aircraft carriers, the USS Antietam, USS Tarawa, and the USS Leyte. During the 1960s and early 1970s, four aircraft carriers used Quonset Point as their home port, the carriers were the USS Lake Champlain, the USS Essex, the USS Wasp, and the USS Intrepid. BASE, Advancing a Post-Military Landscape An extensive photographic survey of the Quonset Point & Davisville Naval Bases completed in 2000 by Erik Carlson & Erica Carpenter
25.
Rhode Island
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Rhode Island, officially the State of Rhode Island and Providence Plantations, is a state in the New England region of the northeastern United States. Rhode Island is the smallest in area, the eighth least populous, and its official name is also the longest of any state in the Union. Rhode Island is bordered by Connecticut to the west, Massachusetts to the north and east, the state also shares a short maritime border with New York. It boycotted the 1787 convention that drew up the United States Constitution, on May 29,1790, Rhode Island became the 13th and last state to ratify the Constitution. Rhode Islands official nickname is The Ocean State, a reference to the fact that the state has several large bays, Rhode Island covers 1,214 square miles, of which 1,045 square miles are land. Despite its name, most of Rhode Island is located on the mainland of the United States, the official name of the state is State of Rhode Island and Providence Plantations, which is derived from the merger of four settlements. Rhode Island is now commonly called Aquidneck Island, the largest of several islands in Narragansett Bay, Providence Plantation was the name of the colony founded by Roger Williams in the area now known as the city of Providence. This was adjoined by the settlement of Warwick, hence the plural Providence Plantations and it is unclear how Aquidneck Island came to be known as Rhode Island, although there are two popular theories. Explorer Giovanni da Verrazzano noted the presence of an island near the mouth of Narragansett Bay in 1524, subsequent European explorers were unable to precisely identify the island that Verrazzano had named, but the Pilgrims who later colonized the area assumed that it was Aquidneck. A second theory concerns the fact that Adriaen Block passed by Aquidneck during his expeditions in the 1610s, historians have theorized that this reddish appearance resulted from either red autumn foliage or red clay on portions of the shore. The earliest documented use of the name Rhode Island for Aquidneck was in 1637 by Roger Williams, the name was officially applied to the island in 1644 with these words, Aquethneck shall be henceforth called the Isle of Rodes or Rhode-Island. The name Isle of Rodes is used in a document as late as 1646. Dutch maps as early as 1659 call the island Red Island, Williams was a theologian forced out of the Massachusetts Bay Colony. Seeking religious and political tolerance, he and others founded Providence Plantation as a proprietary colony. Providence referred to the concept of providence, and plantation was an English term for a colony. State of Rhode Island and Providence Plantations is the longest official name of any state in the Union, advocates for excising plantation asserted that the word specifically referred to the British colonial practice of establishing settlements which disenfranchised native people. Advocates for retaining the name argued that plantation was simply an archaic English synonym for colony, the referendum election was held on November 2,2010, and the people voted overwhelmingly to retain the entire original name. It shares a maritime border with New York State between Block Island and Long Island