1.
Integer
–
An integer is a number that can be written without a fractional component. For example,21,4,0, and −2048 are integers, while 9.75, 5 1⁄2, the set of integers consists of zero, the positive natural numbers, also called whole numbers or counting numbers, and their additive inverses. This is often denoted by a boldface Z or blackboard bold Z standing for the German word Zahlen, ℤ is a subset of the sets of rational and real numbers and, like the natural numbers, is countably infinite. The integers form the smallest group and the smallest ring containing the natural numbers, in algebraic number theory, the integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, the integers are the integers that are also rational numbers. Like the natural numbers, Z is closed under the operations of addition and multiplication, that is, however, with the inclusion of the negative natural numbers, and, importantly,0, Z is also closed under subtraction. The integers form a ring which is the most basic one, in the following sense, for any unital ring. This universal property, namely to be an object in the category of rings. Z is not closed under division, since the quotient of two integers, need not be an integer, although the natural numbers are closed under exponentiation, the integers are not. The following lists some of the properties of addition and multiplication for any integers a, b and c. In the language of algebra, the first five properties listed above for addition say that Z under addition is an abelian group. As a group under addition, Z is a cyclic group, in fact, Z under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to Z. The first four properties listed above for multiplication say that Z under multiplication is a commutative monoid. However, not every integer has an inverse, e. g. there is no integer x such that 2x =1, because the left hand side is even. This means that Z under multiplication is not a group, all the rules from the above property table, except for the last, taken together say that Z together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of algebraic structure. Only those equalities of expressions are true in Z for all values of variables, note that certain non-zero integers map to zero in certain rings. The lack of zero-divisors in the means that the commutative ring Z is an integral domain
Integer
–
Algebraic structure → Group theory
Group theory
2.
Negative number
–
In mathematics, a negative number is a real number that is less than zero. If positive represents movement to the right, negative represents movement to the left, if positive represents above sea level, then negative represents below level. If positive represents a deposit, negative represents a withdrawal and they are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, if a quantity may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. In the medical context of fighting a tumor, an expansion could be thought of as a negative shrinkage, negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common idea of an opposite is reflected in arithmetic. For example, − −3 =3 because the opposite of an opposite is the original thing, negative numbers are usually written with a minus sign in front. For example, −3 represents a quantity with a magnitude of three, and is pronounced minus three or negative three. To help tell the difference between a subtraction operation and a number, occasionally the negative sign is placed slightly higher than the minus sign. Conversely, a number that is greater than zero is called positive, the positivity of a number may be emphasized by placing a plus sign before it, e. g. +3. In general, the negativity or positivity of a number is referred to as its sign, every real number other than zero is either positive or negative. The positive whole numbers are referred to as natural numbers, while the positive and negative numbers are referred to as integers. In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, Liu Hui established rules for adding and subtracting negative numbers. By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers, islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients. Western mathematicians accepted the idea of numbers by the 17th century. Prior to the concept of numbers, mathematicians such as Diophantus considered negative solutions to problems false. Negative numbers can be thought of as resulting from the subtraction of a number from a smaller. For example, negative three is the result of subtracting three from zero,0 −3 = −3, in general, the subtraction of a larger number from a smaller yields a negative result, with the magnitude of the result being the difference between the two numbers
Negative number
–
This thermometer is indicating a negative
Fahrenheit temperature (−4°F).
3.
100 (number)
–
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
100 (number)
–
The
U.S. hundred-dollar bill, Series 2009.
4.
Factorization
–
In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 ×5, in all cases, a product of simpler objects is obtained. The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viètes formulas relate the coefficients of a polynomial to its roots, the opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms. Integer factorization for large integers appears to be a difficult problem, there is no known method to carry it out quickly. Its complexity is the basis of the security of some public key cryptography algorithms. A matrix can also be factorized into a product of matrices of special types, One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types, QR decomposition, LQ, QL, RQ and this situation is generalized by factorization systems. By the fundamental theorem of arithmetic, every integer greater than 1 has a unique prime factorization. Given an algorithm for integer factorization, one can factor any integer down to its constituent primes by repeated application of this algorithm, for very large numbers, no efficient classical algorithm is known. Modern techniques for factoring polynomials are fast and efficient, but use sophisticated mathematical ideas and these techniques are used in the construction of computer routines for carrying out polynomial factorization in Computer algebra systems. This article is concerned with classical techniques. While the general notion of factoring just means writing an expression as a product of simpler expressions, when factoring polynomials this means that the factors are to be polynomials of smaller degree. Thus, while x 2 − y = is a factorization of the expression, another issue concerns the coefficients of the factors. It is not always possible to do this, and a polynomial that can not be factored in this way is said to be irreducible over this type of coefficient, thus, x2 -2 is irreducible over the integers and x2 +4 is irreducible over the reals. In the first example, the integers 1 and -2 can also be thought of as real numbers, and if they are, then x 2 −2 = shows that this polynomial factors over the reals. Similarly, since the integers 1 and 4 can be thought of as real and hence complex numbers, x2 +4 splits over the complex numbers, i. e. x 2 +4 =. The fundamental theorem of algebra can be stated as, Every polynomial of n with complex number coefficients splits completely into n linear factors
Factorization
–
A visual representation of the factorization of cubes using volumes. For a sum of cubes, simply substitute z=-y.
5.
Divisor
–
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
Divisor
–
The divisors of 10 illustrated with
Cuisenaire rods: 1, 2, 5, and 10
6.
Greek numerals
–
Greek numerals are a system of writing numbers using the letters of the Greek alphabet. These alphabetic numerals are known as Ionic or Ionian numerals, Milesian numerals. In modern Greece, they are used for ordinal numbers. For ordinary cardinal numbers, however, Greece uses Arabic numerals, attic numerals, which were later adopted as the basis for Roman numerals, were the first alphabetic set. They were acrophonic, derived from the first letters of the names of the numbers represented and they ran =1, =5, =10, =100, =1000, and =10000. 50,500,5000, and 50000 were represented by the letter with minuscule powers of ten written in the top right corner, the same system was used outside of Attica, but the symbols varied with the local alphabets, in Boeotia, was 1000. The present system probably developed around Miletus in Ionia, 19th-century classicists placed its development in the 3rd century BC, the occasion of its first widespread use. The present system uses the 24 letters adopted by Euclid as well as three Phoenician and Ionic ones that were not carried over, digamma, koppa, and sampi. The position of characters within the numbering system imply that the first two were still in use while the third was not. Greek numerals are decimal, based on powers of 10, the units from 1 to 9 are assigned to the first nine letters of the old Ionic alphabet from alpha to theta. Each multiple of one hundred from 100 to 900 was then assigned its own separate letter as well and this alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total. For example,241 was represented as, in ancient and medieval manuscripts, these numerals were eventually distinguished from letters using overbars, α, β, γ, etc. In medieval manuscripts of the Book of Revelation, the number of the Beast 666 is written as χξϛ, although the Greek alphabet began with only majuscule forms, surviving papyrus manuscripts from Egypt show that uncial and cursive minuscule forms began early. These new letter forms sometimes replaced the ones, especially in the case of the obscure numerals. The old Q-shaped koppa began to be broken up and simplified, the numeral for 6 changed several times. During antiquity, the letter form of digamma came to be avoided in favor of a special numerical one. By the Byzantine era, the letter was known as episemon and this eventually merged with the sigma-tau ligature stigma. In modern Greek, a number of changes have been made
Greek numerals
–
Numeral systems
Greek numerals
–
A
Constantinopolitan map of the British Isles from
Ptolemy 's
Geography (c. 1300), using Greek numerals for its
graticule: 52–63°N of the
equator and 6–33°E from Ptolemy's
Prime Meridian at the
Fortunate Isles.
7.
Roman numerals
–
The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet, Roman numerals, as used today, are based on seven symbols, The use of Roman numerals continued long after the decline of the Roman Empire. The numbers 1 to 10 are usually expressed in Roman numerals as follows, I, II, III, IV, V, VI, VII, VIII, IX, Numbers are formed by combining symbols and adding the values, so II is two and XIII is thirteen. Symbols are placed left to right in order of value. Named after the year of its release,2014 as MMXIV, the year of the games of the XXII Olympic Winter Games The standard forms described above reflect typical modern usage rather than a universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval, Roman inscriptions, especially in official contexts, seem to show a preference for additive forms such as IIII and VIIII instead of subtractive forms such as IV and IX. Both methods appear in documents from the Roman era, even within the same document, double subtractives also occur, such as XIIX or even IIXX instead of XVIII. Sometimes V and L are not used, with such as IIIIII. Such variation and inconsistency continued through the period and into modern times. Clock faces that use Roman numerals normally show IIII for four o’clock but IX for nine o’clock, however, this is far from universal, for example, the clock on the Palace of Westminster in London uses IV. Similarly, at the beginning of the 20th century, different representations of 900 appeared in several inscribed dates. For instance,1910 is shown on Admiralty Arch, London, as MDCCCCX rather than MCMX, although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used
Roman numerals
–
Entrance to section LII (52) of the
Colosseum, with numerals still visible
Roman numerals
–
Numeral systems
Roman numerals
–
A typical
clock face with Roman numerals in
Bad Salzdetfurth, Germany
Roman numerals
–
An inscription on
Admiralty Arch, London. The number is 1910, for which MCMX would be more usual
8.
Binary number
–
The base-2 system is a positional notation with a radix of 2. Because of its implementation in digital electronic circuitry using logic gates. Each digit is referred to as a bit, the modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de lArithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions, the method used for ancient Egyptian multiplication is also closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, the I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique and it is based on taoistic duality of yin and yang. Eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, the Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, Pingalas Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingalas system increases towards the right, the residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Africa, sets of binary combinations similar to the I Ching have also been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been applied in sub-Saharan Africa. Leibnizs system uses 0 and 1, like the modern binary numeral system, Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own beliefs as a Christian. Binary numerals were central to Leibnizs theology and he believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. Is not easy to impart to the pagans, is the ex nihilo through Gods almighty power. In 1854, British mathematician George Boole published a paper detailing an algebraic system of logic that would become known as Boolean algebra
Binary number
–
Numeral systems
Binary number
–
Arithmetic values represented by parts of the Eye of Horus
Binary number
–
Gottfried Leibniz
Binary number
–
George Boole
9.
Ternary numeral system
–
The ternary numeral system has three as its base. Analogous to a bit, a digit is a trit. One trit is equivalent to bits of information. Representations of integer numbers in ternary do not get uncomfortably lengthy as quickly as in binary, for example, decimal 365 corresponds to binary 101101101 and to ternary 111112. However, they are far less compact than the corresponding representations in bases such as decimal – see below for a compact way to codify ternary using nonary. The value of a number with n bits that are all 1 is 2n −1. Then N = M, N = /, and N = bd −1, for a three-digit ternary number, N =33 −1 =26 =2 ×32 +2 ×31 +2 ×30 =18 +6 +2. Nonary or septemvigesimal can be used for representation of ternary. A base-three system is used in Islam to keep track of counting Tasbih to 99 or to 100 on a hand for counting prayers. In certain analog logic, the state of the circuit is often expressed ternary and this is most commonly seen in Transistor–transistor logic using 7406 open collector logic. The output is said to either be low, high, or open, in this configuration the output of the circuit is actually not connected to any voltage reference at all. Where the signal is usually grounded to a reference, or at a certain voltage level. Thus, the voltage level is sometimes unpredictable. A rare ternary point is used to denote fractional parts of an inning in baseball, since each inning consists of three outs, each out is considered one third of an inning and is denoted as.1. For example, if a player pitched all of the 4th, 5th and 6th innings, plus 2 outs of the 7th inning, his Innings pitched column for that game would be listed as 3.2, meaning 3⅔. In this usage, only the part of the number is written in ternary form. Ternary numbers can be used to convey self-similar structures like the Sierpinski triangle or the Cantor set conveniently, additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed. The Cantor set consists of the points from 0 to 1 that have an expression that does not contain any instance of the digit 1
Ternary numeral system
–
Numeral systems
10.
Quaternary numeral system
–
Quaternary is the base-4 numeral system. It uses the digits 0,1,2 and 3 to represent any real number. Four is the largest number within the range and one of two numbers that is both a square and a highly composite number, making quaternary a convenient choice for a base at this scale. Despite being twice as large, its economy is equal to that of binary. However, it no better in the localization of prime numbers. See decimal and binary for a discussion of these properties, as with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system. Each radix 4,8 and 16 is a power of 2, so the conversion to and from binary is implemented by matching each digit with 2,3 or 4 binary digits, for example, in base 4,302104 =11001001002. Although octal and hexadecimal are widely used in computing and computer programming in the discussion and analysis of binary arithmetic and logic, by analogy with byte and nybble, a quaternary digit is sometimes called a crumb. There is a surviving list of Ventureño language number words up to 32 written down by a Spanish priest ca, the Kharosthi numerals have a partial base 4 counting system from 1 to decimal 10. Quaternary numbers are used in the representation of 2D Hilbert curves, here a real number between 0 and 1 is converted into the quaternary system. Every single digit now indicates in which of the respective 4 sub-quadrants the number will be projected, parallels can be drawn between quaternary numerals and the way genetic code is represented by DNA. The four DNA nucleotides in order, abbreviated A, C, G and T, can be taken to represent the quaternary digits in numerical order 0,1,2. With this encoding, the complementary digit pairs 0↔3, and 1↔2 match the complementation of the pairs, A↔T and C↔G. For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010, quaternary line codes have been used for transmission, from the invention of the telegraph to the 2B1Q code used in modern ISDN circuits
Quaternary numeral system
–
Numeral systems
11.
Quinary
–
Quinary is a numeral system with five as the base. A possible origination of a system is that there are five fingers on either hand. The base five is stated from 0–4, in the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100, today, the main usage of base 5 is as a biquinary system, which is decimal using five as a sub-base. Another example of a system, is sexagesimal, base 60. Each quinary digit has log25 bits of information, many languages use quinary number systems, including Gumatj, Nunggubuyu, Kuurn Kopan Noot, Luiseño and Saraveca. Gumatj is a true 5–25 language, in which 25 is the group of 5. The Gumatj numerals are shown below, In the video game Riven and subsequent games of the Myst franchise, a decimal system with 2 and 5 as a sub-bases is called biquinary, and is found in Wolof and Khmer. Roman numerals are a biquinary system, the numbers 1,5,10, and 50 are written as I, V, X, and L respectively. Eight is VIII and seventy is LXX, most versions of the abacus use a biquinary system to simulate a decimal system for ease of calculation. Urnfield culture numerals and some tally mark systems are also biquinary, units of currencies are commonly partially or wholly biquinary. A vigesimal system with 4 and 5 as a sub-bases is found in Nahuatl, pentimal system Quibinary Yan Tan Tethera References, Quinary Base Conversion, includes fractional part, from Math Is Fun Media related to Quinary numeral system at Wikimedia Commons
Quinary
–
Numeral systems
12.
Senary
–
The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
Senary
–
Numeral systems
Senary
–
34 senary = 22 decimal, in senary finger counting
Senary
13.
Octal
–
The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping binary digits into groups of three. For example, the representation for decimal 74 is 1001010. Two zeroes can be added at the left,1001010, corresponding the octal digits 112, in the decimal system each decimal place is a power of ten. For example,7410 =7 ×101 +4 ×100 In the octal system each place is a power of eight. The Yuki language in California and the Pamean languages in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves and it has been suggested that the reconstructed Proto-Indo-European word for nine might be related to the PIE word for new. Based on this, some have speculated that proto-Indo-Europeans used a number system. In 1716 King Charles XII of Sweden asked Emanuel Swedenborg to elaborate a number based on 64 instead of 10. Swedenborg however argued that for people with less intelligence than the king such a big base would be too difficult, in 1718 Swedenborg wrote a manuscript, En ny rekenkonst som om vexlas wid Thalet 8 i stelle then wanliga wid Thalet 10. The numbers 1-7 are there denoted by the l, s, n, m, t, f, u. Thus 8 = lo,16 = so,24 = no,64 = loo,512 = looo etc, numbers with consecutive consonants are pronounced with vowel sounds between in accordance with a special rule. Writing under the pseudonym Hirossa Ap-Iccim in The Gentlemans Magazine, July 1745, Hugh Jones proposed a system for British coins, weights. In 1801, James Anderson criticized the French for basing the Metric system on decimal arithmetic and he suggested base 8 for which he coined the term octal. In the mid 19th century, Alfred B. Taylor concluded that Our octonary radix is, therefore, so, for example, the number 65 would be spoken in octonary as under-un. Taylor also republished some of Swedenborgs work on octonary as an appendix to the above-cited publications, in the 2009 film Avatar, the language of the extraterrestrial Navi race employs an octal numeral system, probably due to the fact that they have four fingers on each hand. In the TV series Stargate SG-1, the Ancients, a race of beings responsible for the invention of the Stargates, in the tabletop game series Warhammer 40,000, the Tau race use an octal number system. Octal became widely used in computing systems such as the PDP-8, ICL1900. Octal was an abbreviation of binary for these machines because their word size is divisible by three
Octal
–
Numeral systems
14.
Duodecimal
–
The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written by a rotated 2 and this notation was introduced by Sir Isaac Pitman. These digit forms are available as Unicode characters on computerized systems since June 2015 as ↊ and ↋, other notations use A, T, or X for ten and B or E for eleven. The number twelve is written as 10 in duodecimal, whereas the digit string 12 means 1 dozen and 2 units. Similarly, in duodecimal 100 means 1 gross,1000 means 1 great gross, the number twelve, a superior highly composite number, is the smallest number with four non-trivial factors, and the smallest to include as factors all four numbers within the subitizing range. As a result, duodecimal has been described as the number system. Of its factors,2 and 3 are prime, which means the reciprocals of all 3-smooth numbers have a representation in duodecimal. In particular, the five most elementary fractions all have a terminating representation in duodecimal. This all makes it a convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary. Although the trigesimal and sexagesimal systems do even better in respect, this is at the cost of unwieldy multiplication tables. In this section, numerals are based on decimal places, for example,10 means ten,12 means twelve. Languages using duodecimal number systems are uncommon, germanic languages have special words for 11 and 12, such as eleven and twelve in English. However, they are considered to come from Proto-Germanic *ainlif and *twalif, historically, units of time in many civilizations are duodecimal. There are twelve signs of the zodiac, twelve months in a year, traditional Chinese calendars, clocks, and compasses are based on the twelve Earthly Branches. There are 12 inches in a foot,12 troy ounces in a troy pound,12 old British pence in a shilling,24 hours in a day. The Romans used a system based on 12, including the uncia which became both the English words ounce and inch. The importance of 12 has been attributed to the number of cycles in a year. It is possible to count to 12 with the acting as a pointer
Duodecimal
–
Numeral systems
Duodecimal
–
A duodecimal multiplication table
15.
Hexadecimal
–
In mathematics and computing, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, Hexadecimal numerals are widely used by computer system designers and programmers. As each hexadecimal digit represents four binary digits, it allows a more human-friendly representation of binary-coded values, one hexadecimal digit represents a nibble, which is half of an octet or byte. For example, a byte can have values ranging from 00000000 to 11111111 in binary form. In a non-programming context, a subscript is typically used to give the radix, several notations are used to support hexadecimal representation of constants in programming languages, usually involving a prefix or suffix. The prefix 0x is used in C and related languages, where this value might be denoted as 0x2AF3, in contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers expressed in other bases. There are several conventions for expressing values unambiguously, a numerical subscript can give the base explicitly,15910 is decimal 159,15916 is hexadecimal 159, which is equal to 34510. Some authors prefer a text subscript, such as 159decimal and 159hex, or 159d and 159h. example. com/name%20with%20spaces where %20 is the space character, thus ’, represents the right single quotation mark, Unicode code point number 2019 in hex,8217. In the Unicode standard, a value is represented with U+ followed by the hex value. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #, white, CSS allows 3-hexdigit abbreviations with one hexdigit per component, #FA3 abbreviates #FFAA33. *nix shells, AT&T assembly language and likewise the C programming language, to output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h, some assembly languages use the notation HABCD. Ada and VHDL enclose hexadecimal numerals in based numeric quotes, 16#5A3#, for bit vector constants VHDL uses the notation x5A3. Verilog represents hexadecimal constants in the form 8hFF, where 8 is the number of bits in the value, the Smalltalk language uses the prefix 16r, 16r5A3 PostScript and the Bourne shell and its derivatives denote hex with prefix 16#, 16#5A3. For PostScript, binary data can be expressed as unprefixed consecutive hexadecimal pairs, in early systems when a Macintosh crashed, one or two lines of hexadecimal code would be displayed under the Sad Mac to tell the user what went wrong. Common Lisp uses the prefixes #x and #16r, setting the variables *read-base* and *print-base* to 16 can also used to switch the reader and printer of a Common Lisp system to Hexadecimal number representation for reading and printing numbers. Thus Hexadecimal numbers can be represented without the #x or #16r prefix code, MSX BASIC, QuickBASIC, FreeBASIC and Visual Basic prefix hexadecimal numbers with &H, &H5A3 BBC BASIC and Locomotive BASIC use & for hex. TI-89 and 92 series uses a 0h prefix, 0h5A3 ALGOL68 uses the prefix 16r to denote hexadecimal numbers, binary, quaternary and octal numbers can be specified similarly
Hexadecimal
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Numeral systems
Hexadecimal
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Bruce Alan Martin's hexadecimal notation proposal
Hexadecimal
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Hexadecimal finger-counting scheme.
16.
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
Vigesimal
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Numeral systems
Vigesimal
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The
Maya numerals are a base-20 system.
17.
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
Base 36
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Numeral systems
Base 36
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34 senary = 22 decimal, in senary finger counting
Base 36
18.
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
Natural number
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The
Ishango bone (on exhibition at the
Royal Belgian Institute of Natural Sciences) is believed to have been used 20,000 years ago for natural number arithmetic.
Natural number
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Natural numbers can be used for counting (one
apple, two apples, three apples, …)
19.
Even number
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Parity is a mathematical term that describes the property of an integers inclusion in one of two categories, even or odd. An integer is even if it is divisible by two and odd if it is not even. For example,6 is even there is no remainder when dividing it by 2. By contrast,3,5,7,21 leave a remainder of 1 when divided by 2, examples of even numbers include −4,0,8, and 1738. In particular, zero is an even number, some examples of odd numbers are −5,3,9, and 73. Parity does not apply to non-integer numbers and this classification applies only to integers, i. e. non-integers like 1/2,4.201, or infinity are neither even nor odd. The sets of even and odd numbers can be defined as following and that is, if the last digit is 1,3,5,7, or 9, then it is odd, otherwise it is even. The same idea will work using any even base, in particular, a number expressed in the binary numeral system is odd if its last digit is 1 and even if its last digit is 0. In an odd base, the number is according to the sum of its digits – it is even if. The following laws can be verified using the properties of divisibility and they are a special case of rules in modular arithmetic, and are commonly used to check if an equality is likely to be correct by testing the parity of each side. As with ordinary arithmetic, multiplication and addition are commutative and associative in modulo 2 arithmetic, however, subtraction in modulo 2 is identical to addition, so subtraction also possesses these properties, which is not true for normal integer arithmetic. The structure is in fact a field with just two elements, the division of two whole numbers does not necessarily result in a whole number. For example,1 divided by 4 equals 1/4, which is neither even nor odd, since the concepts even, but when the quotient is an integer, it will be even if and only if the dividend has more factors of two than the divisor. The ancient Greeks considered 1, the monad, to be neither odd nor fully even. It is this, that two relatively different things or ideas there stands always a third, in a sort of balance. Thus, there is here between odd and even numbers one number which is neither of the two, similarly, in form, the right angle stands between the acute and obtuse angles, and in language, the semi-vowels or aspirants between the mutes and vowels. A thoughtful teacher and a pupil taught to think for himself can scarcely help noticing this, integer coordinates of points in Euclidean spaces of two or more dimensions also have a parity, usually defined as the parity of the sum of the coordinates. For instance, the cubic lattice and its higher-dimensional generalizations
Even number
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Rubik's Revenge in solved state
20.
Composite number
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A composite number is a positive integer that can be formed by multiplying together two smaller positive integers. Equivalently, it is an integer that has at least one divisor other than 1. Every positive integer is composite, prime, or the unit 1, so the numbers are exactly the numbers that are not prime. For example, the integer 14 is a number because it is the product of the two smaller integers 2 ×7. Likewise, the integers 2 and 3 are not composite numbers because each of them can only be divided by one, every composite number can be written as the product of two or more primes. For example, the composite number 299 can be written as 13 ×23, and the composite number 360 can be written as 23 ×32 ×5, furthermore and this fact is called the fundamental theorem of arithmetic. There are several known primality tests that can determine whether a number is prime or composite, one way to classify composite numbers is by counting the number of prime factors. A composite number with two prime factors is a semiprime or 2-almost prime, a composite number with three distinct prime factors is a sphenic number. In some applications, it is necessary to differentiate between composite numbers with an odd number of prime factors and those with an even number of distinct prime factors. For the latter μ =2 x =1, while for the former μ =2 x +1 = −1, however, for prime numbers, the function also returns −1 and μ =1. For a number n with one or more repeated prime factors, if all the prime factors of a number are repeated it is called a powerful number. If none of its factors are repeated, it is called squarefree. For example,72 =23 ×32, all the factors are repeated. 42 =2 ×3 ×7, none of the factors are repeated. Another way to classify composite numbers is by counting the number of divisors, all composite numbers have at least three divisors. In the case of squares of primes, those divisors are, a number n that has more divisors than any x < n is a highly composite number. Composite numbers have also been called rectangular numbers, but that name can refer to the pronic numbers, numbers that are the product of two consecutive integers. Table of prime factors Integer factorization Canonical representation of a positive integer Sieve of Eratosthenes Fraleigh, a First Course In Abstract Algebra, Reading, Addison-Wesley, ISBN 0-201-01984-1 Herstein, I. N
Composite number
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Overview
21.
Sphenic number
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In number theory, a sphenic number is a positive integer that is the product of three distinct prime numbers. A sphenic number is a product pqr where p, q and this definition is more stringent than simply requiring the integer to have exactly three prime factors. For instance,60 =22 ×3 ×5 has exactly 3 prime factors, the smallest sphenic number is 30 =2 ×3 ×5, the product of the smallest three primes. The first few numbers are 30,42,66,70,78,102,105,110,114,130,138,154,165. As of January 2016 the largest known number is × ×. It is the product of the three largest known primes, all sphenic numbers have exactly eight divisors. If we express the number as n = p ⋅ q ⋅ r, where p, q. For example,24 is not a number, but it has exactly eight divisors. All sphenic numbers are by definition squarefree, because the factors must be distinct. The Möbius function of any number is −1. The cyclotomic polynomials Φ n, taken over all sphenic numbers n, the first case of two consecutive sphenic integers is 230 = 2×5×23 and 231 = 3×7×11. The first case of three is 1309 = 7×11×17,1310 = 2×5×131, and 1311 = 3×19×23, there is no case of more than three, because every fourth consecutive positive integer is divisible by 4 = 2×2 and therefore not squarefree. The numbers 2013,2014, and 2015 are all sphenic, the next three consecutive sphenic years will be 2665,2666 and 2667. Semiprimes, products of two prime numbers
Sphenic number
–
Overview
22.
Abundant number
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In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. The integer 12 is the first abundant number and its proper divisors are 1,2,3,4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance, the number 12 has an abundance of 4, for example. A number n for which the sum of divisors σ>2n, or, equivalently, the sum of proper divisors s>n. The first 28 abundant numbers are,12,18,20,24,30,36,40,42,48,54,56,60,66,70,72,78,80,84,88,90,96,100,102,104,108,112,114,120, …. For example, the divisors of 24 are 1,2,3,4,6,8. Because 36 is more than 24, the number 24 is abundant and its abundance is 36 −24 =12. The smallest odd abundant number is 945, the smallest abundant number not divisible by 2 or by 3 is 5391411025 whose distinct prime factors are 5,7,11,13,17,19,23, and 29. An algorithm given by Iannucci in 2005 shows how to find the smallest abundant number not divisible by the first k primes. If A represents the smallest abundant number not divisible by the first k primes then for all ϵ >0 we have,2 − ϵ < ln A <2 + ϵ for sufficiently large k, infinitely many even and odd abundant numbers exist. The set of abundant numbers has a natural density, marc Deléglise showed in 1998 that the natural density of the set of abundant numbers and perfect numbers is between 0.2474 and 0.2480. Every multiple of a number is abundant. For example, every multiple of 6 is abundant because the divisors include 1, n/2, n/3, every multiple of an abundant number is abundant. For example, every multiple of 20 is abundant because n/2 + n/4 + n/5 + n/10 + n/20 = n + n/10, every integer greater than 20161 can be written as the sum of two abundant numbers. An abundant number which is not a number is called a weird number. An abundant number with abundance 1 is called a quasiperfect number, numbers whose sum of proper factors equals the number itself are called perfect numbers, while numbers whose sum of proper factors is less than the number itself are called deficient numbers. The abundancy index of n is the ratio σ/n, distinct numbers n1, n2. with the same abundancy index are called friendly numbers. The sequence of least numbers n such that σ > kn, in which a2 =12 corresponds to the first abundant number, if p = is a list of primes, then p is termed abundant if some integer composed only of primes in p is abundant
Abundant number
–
Overview
23.
12 (number)
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12 is the natural number following 11 and preceding 13. The product of the first three factorials, twelve is a highly composite number, divisible by 2,3,4. It is central to systems of counting, including the Western calendar and units of time. The word twelve is the largest number with a name in English. Such uses gradually disappeared with the introduction of Arabic numerals during the 12th-century Renaissance and it derives from the Old English twelf and tuelf, first attested in the 10th-century Lindisfarne Gospels Book of John. It has cognates in every Germanic language, whose Proto-Germanic ancestor has been reconstructed as *twaliƀi, from *twa and suffix *-lif- or *-liƀ- of uncertain meaning. It is sometimes compared with the Lithuanian dvýlika, although -lika is used as the suffix for all numbers from 11 to 19, every other Indo-European language instead uses a form of two+ten, such as the Latin duōdecim. The usual ordinal form is twelfth but dozenth or duodecimal is also used in some contexts, similarly, a group of twelve things is usually a dozen but may also be referred to as a duodecad. The adjective referring to a group of twelve is duodecuple, as with eleven, the earliest forms of twelve are often considered to be connected with Proto-Germanic *liƀan or *liƀan, with the implicit meaning that two is left after having already counted to ten. The Lithuanian suffix is also considered to share a similar development, the suffix *-lif- has also been connected with reconstructions of the Proto-Germanic for ten. While, as mentioned above,12 has its own name in Germanic languages such as English and German, it is a number in many other languages, e. g. Italian dodici. In Germany, according to an old tradition, the numbers 0 through 12 were spelt out, the Duden now calls this tradition outdated and no longer valid, but many writers still follow it. Another system spells out all numbers written in one or two words, Twelve is a composite number, the smallest number with exactly six divisors, its divisors being 1,2,3,4,6 and 12. Twelve is also a composite number, the next one being twenty-four. Twelve is also a highly composite number, the next one being sixty. It is the first composite number of the form p2q, a square-prime,12 has an aliquot sum of 16. Accordingly,12 is the first abundant number and demonstrates an 8-member aliquot sequence,12 is the 3rd composite number in the 3-aliquot tree, the only number which has 12 as its aliquot sum is the square 121. Only 2 other square primes are abundant, Twelve is a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number
12 (number)
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12 stars are featured on the
Flag of Europe
24.
Asteroid belt
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The asteroid belt is the circumstellar disc in the Solar System located roughly between the orbits of the planets Mars and Jupiter. It is occupied by numerous irregularly shaped bodies called asteroids or minor planets, the asteroid belt is also termed the main asteroid belt or main belt to distinguish it from other asteroid populations in the Solar System such as near-Earth asteroids and trojan asteroids. About half the mass of the belt is contained in the four largest asteroids, Ceres, Vesta, Pallas, the total mass of the asteroid belt is approximately 4% that of the Moon, or 22% that of Pluto, and roughly twice that of Plutos moon Charon. Ceres, the belts only dwarf planet, is about 950 km in diameter, whereas Vesta, Pallas. The remaining bodies range down to the size of a dust particle, the asteroid material is so thinly distributed that numerous unmanned spacecraft have traversed it without incident. Nonetheless, collisions between large asteroids do occur, and these can form a family whose members have similar orbital characteristics. Individual asteroids within the belt are categorized by their spectra. The asteroid belt formed from the solar nebula as a group of planetesimals. Planetesimals are the precursors of the protoplanets. Between Mars and Jupiter, however, gravitational perturbations from Jupiter imbued the protoplanets with too much energy for them to accrete into a planet. Collisions became too violent, and instead of fusing together, the planetesimals, as a result,99. 9% of the asteroid belts original mass was lost in the first 100 million years of the Solar Systems history. Some fragments eventually found their way into the inner Solar System, Asteroid orbits continue to be appreciably perturbed whenever their period of revolution about the Sun forms an orbital resonance with Jupiter. At these orbital distances, a Kirkwood gap occurs as they are swept into other orbits. Classes of small Solar System bodies in other regions are the objects, the centaurs, the Kuiper belt objects, the scattered disc objects, the sednoids. On 22 January 2014, ESA scientists reported the detection, for the first definitive time, of water vapor on Ceres, the detection was made by using the far-infrared abilities of the Herschel Space Observatory. The finding was unexpected because comets, not asteroids, are considered to sprout jets. According to one of the scientists, The lines are becoming more and more blurred between comets and asteroids. This pattern, now known as the Titius–Bode law, predicted the semi-major axes of the six planets of the provided one allowed for a gap between the orbits of Mars and Jupiter
Asteroid belt
–
By far the largest object within the belt is
Ceres. The total mass of the asteroid belt is significantly less than
Pluto 's, and approximately twice that of Pluto's moon
Charon.
Asteroid belt
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Sun Jupiter trojans Orbits of
planets
Asteroid belt
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Giuseppe Piazzi, discoverer of
Ceres, the largest object in the asteroid belt. For several decades after its discovery Ceres was known as a planet, after which it was reclassified as asteroid number 1. In 2006 it was recognized to be a dwarf planet.
Asteroid belt
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951 Gaspra, the first asteroid imaged by a spacecraft, as viewed during
Galileo ' s 1991 flyby; colors are exaggerated
25.
Asteroid
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Asteroids are minor planets, especially those of the inner Solar System. The larger ones have also been called planetoids and these terms have historically been applied to any astronomical object orbiting the Sun that did not show the disc of a planet and was not observed to have the characteristics of an active comet. As minor planets in the outer Solar System were discovered and found to have volatile-based surfaces that resemble those of comets, in this article, the term asteroid refers to the minor planets of the inner Solar System including those co-orbital with Jupiter. There are millions of asteroids, many thought to be the remnants of planetesimals. The large majority of known asteroids orbit in the belt between the orbits of Mars and Jupiter, or are co-orbital with Jupiter. However, other orbital families exist with significant populations, including the near-Earth objects, individual asteroids are classified by their characteristic spectra, with the majority falling into three main groups, C-type, M-type, and S-type. These were named after and are identified with carbon-rich, metallic. The size of asteroids varies greatly, some reaching as much as 1000 km across, asteroids are differentiated from comets and meteoroids. In the case of comets, the difference is one of composition, while asteroids are composed of mineral and rock, comets are composed of dust. In addition, asteroids formed closer to the sun, preventing the development of the aforementioned cometary ice, the difference between asteroids and meteoroids is mainly one of size, meteoroids have a diameter of less than one meter, whereas asteroids have a diameter of greater than one meter. Finally, meteoroids can be composed of either cometary or asteroidal materials, only one asteroid,4 Vesta, which has a relatively reflective surface, is normally visible to the naked eye, and this only in very dark skies when it is favorably positioned. Rarely, small asteroids passing close to Earth may be visible to the eye for a short time. As of March 2016, the Minor Planet Center had data on more than 1.3 million objects in the inner and outer Solar System, the United Nations declared June 30 as International Asteroid Day to educate the public about asteroids. The date of International Asteroid Day commemorates the anniversary of the Tunguska asteroid impact over Siberia, the first asteroid to be discovered, Ceres, was found in 1801 by Giuseppe Piazzi, and was originally considered to be a new planet. In the early half of the nineteenth century, the terms asteroid. Asteroid discovery methods have improved over the past two centuries. This task required that hand-drawn sky charts be prepared for all stars in the band down to an agreed-upon limit of faintness. On subsequent nights, the sky would be charted again and any moving object would, hopefully, the expected motion of the missing planet was about 30 seconds of arc per hour, readily discernible by observers
Asteroid
–
253 Mathilde, a
C-type asteroid measuring about 50 kilometres (30 mi) across, covered in craters half that size. Photograph taken in 1997 by the
NEAR Shoemaker probe.
Asteroid
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2013 EC, shown here in radar images, has a provisional designation
Asteroid
–
⚵
Asteroid
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243 Ida and its moon Dactyl. Dactyl is the first satellite of an asteroid to be discovered.
26.
Variable star
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For the astronomical object, see Variable star. Variable Star is a 2006 novel written by Spider Robinson based on the seven pages of an eight-page 1955 novel outline by the late Robert A. Heinlein. The book is set in a divergent offshoot of Heinleins Future History and contains references to works by Heinlein. It describes the coming of age of a musician who signs on to the crew of a starship as a way of escaping from a failed romance. Robinson posted a note on his website in 2009 noting that his agent had sold a trilogy of sequels based on the novel, Robinson states in an appendix to the book that he was working from an outline that lacked an ending. He was told by his publisher that they wanted him to write in his own style, not Heinleins, Heinleins original title for Variable Star was The Stars are a Clock. Eighteen-year-old aspiring musician and composer Joel Johnston, a Ganymedean on Earth for his education, both are orphans, and virtually penniless. When Jinny decides their relationship is ready for marriage, she reveals that she is actually Jinnia Conrad, Joel learns that Conrad has already mapped out his future, he is to be groomed for a role in the family business and to produce children to continue the dynasty. Preferring to pursue his own destiny, he flees the Conrad estate with the help of Jinnys cousin, to escape the Conrads and their vast reach, Joel joins the crew of the RSS Charles Sheffield. The ship is headed to a distant star on a 20-year voyage to establish a colony, with experience from his family farm, Joel works as a farmer for the ships crew of 500 and as a part-time musician. He regularly corresponds with Evelyn through the twins on board who maintain contact with Earth via telepathy with their siblings, six relativists are essential to the voyage, controlling the ships quantum ramjet drive with their minds. The drive has to run continuously, at speeds, it is nearly impossible to restart it. Each relativist can only stand the strain reliably for six hours a day, five years into the voyage, one is killed and another mentally incapacitated, leaving only four and no margin for error. The next year, the Sheffield learns through its telepaths that the Sun has gone nova, a wavefront of deadly gamma radiation is expanding at lightspeed, threatening the colonies that are all that is left of humanity. The crew is able to warn one in time, the rest are doomed. The Sun going nova is contrary to all theories, and because over 90% of the suns mass was converted into energy. Unable to bear the catastrophe, one of the relativists commits suicide, despite the other threes efforts, the quantum ramjet drive soon shuts down. The Sheffield will not be able to stop, it will coast by its destination at 97. 6% of the speed of light
Variable star
–
Variable Star
Variable star
27.
174th Air Refueling Squadron
–
The 174th Air Refueling Squadron is a unit of the Iowa Air National Guard 185th Air Refueling Wing. It is assigned to Sioux City Air National Guard Base, Iowa and is equipped with the KC-135R Stratotanker aircraft, established on 27 April 1943 at Richmond Army Air Base, Virginia, as the 386th Fighter Squadron, equipped with P-47 Thunderbolts. Deployed to the European Theater of Operations, and assigned to Ninth Air Force in England, arrived at RAF Gosfield, Essex on 23 December 1943. Their first combat air field training resumed for two months, the squadron was instrumental in determining the maximum bomb loads for the P-47. Two one-thousand pound bombs and a fuel tank on the Billy Rack. They were the first group to fly a mission with that bomb load. Their firepower was eight fifty caliber machine guns and their total arsenal included rockets and this armament was standard for all thirteen P-47 fighter-bomber groups shortly after the D-Day Invasion on 6 June 1944. Assigned to the IX Tactical Air Command, the squadron flew in support of General Hodges First Army. Protect the ground forces from air attack and destroy any. On two occasions to support Pattons Third Army, the first was shortly after 1 August 1944. The second was during the last months of the Battle of the Bulge, the squadron was active against specific targets on D-Day before, during and following. This was the first company breakthrough in the Battle of the Bulge in taking Germany, the squadron was part of the first group to move into Germany on 17 March 1945 at Aachen and the first to fly a combat mission off a German soil. The 386th Fighter Squadron flew combat from 22 February 1944 through 4 May 1945 and they flew combat from eleven air fields or air strips moving more times than any other fighter-bomber group in the Ninth Air Force. Assigned to the Sioux Gateway Regional Airport, a training field during World War II used to train B-17 Flying Fortress aircrews. Was assigned to the Iowa ANG 132d Fighter Wing, which consisted of the 124th, along with the 123d Fighter Squadron at Des Moines, and the Nebraska ANG 173d Fighter Squadron at Lincoln, Nebraska. The initial component of the unit included 9 rated officers,7 non-rated officers, today, the 185th consists of nearly 1,000 traditional and full-time military members as well as over 300 air technicians and state contract employees. Engaged in routine training exercises, and was upgraded to F-84B Thunderjet jet aircraft in early 1948, the 132d was moved to Alexandria AFB, Louisiana in May 1952 again with F-51s replacing the federalized Oklahoma ANG 137th Fighter-Bomber Wing which was deployed to France. Performed training as a fighter unit until relieved from active service
174th Air Refueling Squadron
–
174th Air Refueling Squadron - KC-135R Stratotankers at Sioux City AGB IA
174th Air Refueling Squadron
–
174th Tactical Fighter Squadron A-7K 81-1073
174th Air Refueling Squadron
–
174th Tactical Fighter Squadron F-16C 85-568
28.
Iowa Air National Guard
–
The Iowa Air National Guard is the air force militia of the State of Iowa, United States of America. It is, along with the Iowa Army National Guard, an element of the Iowa National Guard, as state militia units, the units in the Iowa Air National Guard are not in the normal United States Air Force chain of command. They are under the jurisdiction of the Governor of Iowa through the office of the Iowa Adjutant General unless they are federalized by order of the President of the United States. The Iowa Air National Guard is headquartered at Camp Dodge, Johnston, under the Total Force concept, Iowa Air National Guard units are considered to be Air Reserve Components of the United States Air Force. Iowa ANG units are trained and equipped by the Air Force and are gained by a Major Command of the USAF if federalized. State missions include disaster relief in times of earthquakes, hurricanes, floods and forest fires, search and rescue, protection of public services. These unit designations were allotted and transferred to various State National Guard bureaus to provide them unit designations to re-establish them as Air National Guard units. The Iowa Air National Guard origins date to the formation of the 132d Fighter Group at Des Moines Municipal Airport, Des Moines and it was equipped with F-51D Mustangs and its mission was the air defense of the state. In addition, the 174th Fighter Squadron was formed at Sioux Gateway Airport, Sioux City, on 1 October 1962 the 174th Tactical Fighter Squadron was expanded to a Group level, and the 185th Tactical Fighter Group received federal recognition and was activated. The 185th Air Refueling Wing provides mid-air refueling and mobility sustainment in support of the global mission of the Air Force. After the September 11th,2001 terrorist attacks on the United States, also, Iowa ANG units have been deployed overseas as part of Operation Enduring Freedom in Afghanistan and Operation Iraqi Freedom in Iraq as well as other locations as directed. Iowa State Guard Iowa Wing Civil Air Patrol This article incorporates public domain material from the Air Force Historical Research Agency website http, Iowa Air National Guard 132nd Fighter Wing 185th Air Refueling Wing
Iowa Air National Guard
–
124th Fighter Squadron - General Dynamics F-16C Block 25C Fighting Falcon 84-1230, Des Moines AGB. The 124th FS is the oldest unit in the Iowa Air National Guard, having over 60 years of service to the state and nation
Iowa Air National Guard
–
Iowa Air National Guard Republic F-84E Thunderjet at Des Moines Municipal Airport, 1956
29.
Canadian Expeditionary Force
–
The Canadian Expeditionary Force was the designation of the field force created by Canada for service overseas in the First World War. The force fielded several combat formations on the Western Front in France and Belgium, the Canadian Cavalry Brigade and the Canadian Independent Force, which were independent of the Canadian Corps, also fought on the Western Front. The CEF also had a reserve and training organization in England. The Germans went so far as to call them storm troopers for their combat efficiency. In August 1918, the CEFs Canadian Siberian Expeditionary Force travelled to revolution-torn Russia and it reinforced an anti-Bolshevik garrison in Vladivostok during the winter of 1918–19. At this time, another force of Canadian soldiers were placed in Archangel, the Canadian Expeditionary Force was mostly volunteers, as conscription was not enforced until the end of the war when call-ups began in January 1918. Ultimately, only 24,132 conscripts arrived in France before the end of the war, Canada was the senior Dominion in the British Empire and automatically at war with Germany upon the British declaration. According to Canadian historian Dr. Serge Durflinger at the Canadian War Museum, of the first contingent formed at Valcartier, Quebec in 1914, fully two-thirds were men born in the United Kingdom. By the end of the war in 1918, at least fifty per cent of the CEF consisted of British-born men, many British nationals from the United Kingdom or other territories who were resident in Canada also joined the CEF. As several CEF battalions were posted to the Bermuda Garrison before proceeding to France, although the Bermuda Militia Artillery and Bermuda Volunteer Rifle Corps both sent contingents to the Western Front, the first would not arrive there til June 1915. By then, many Bermudians had already been serving on the Western Front in the CEF for months, Bermudians in the CEF enlisted under the same terms as Canadians, and all male British Nationals resident in Canada became liable for conscription under the Military Service Act,1917. Two tank battalions were raised in 1918 but did not see service, most of the infantry battalions were broken up and used as reinforcements, with a total of fifty being used in the field, including the mounted rifle units, which were re-organized as infantry. The artillery and engineering units underwent significant re-organization as the war progressed, a distinct entity within the Canadian Expeditionary Force was the Canadian Machine Gun Corps. It consisted of several machine gun battalions, the Eatons, Yukon, and Borden Motor Machine Gun Batteries. During the summer of 1918, these units were consolidated into four machine gun battalions, the Canadian Corps with its four infantry divisions comprised the main fighting force of the CEF. The Canadian Cavalry Brigade also served in France, the 1915 Battle of Ypres, the first engagement of Canadian forces in the Great War, changed the Canadian perspective on war. Ypres exposed Canadian soldiers and their commanders to modern war and they had already experienced the effects of shellfire and developed a reputation for aggressive trench raiding despite their lack of formal training and generally inferior equipment. In April 1915, they were introduced to yet another facet of modern war, the Germans employed chlorine gas to create a hole in the French lines adjacent to the Canadian force and poured troops into the gap
Canadian Expeditionary Force
–
26th Battalion of the Second Canadian Expeditionary Force, 1915
Canadian Expeditionary Force
Canadian Expeditionary Force
–
Private Joseph Pappin, 130 Battalion, Canadian Expeditionary Force.
30.
World War I
–
World War I, also known as the First World War, the Great War, or the War to End All Wars, was a global war originating in Europe that lasted from 28 July 1914 to 11 November 1918. More than 70 million military personnel, including 60 million Europeans, were mobilised in one of the largest wars in history and it was one of the deadliest conflicts in history, and paved the way for major political changes, including revolutions in many of the nations involved. The war drew in all the worlds great powers, assembled in two opposing alliances, the Allies versus the Central Powers of Germany and Austria-Hungary. These alliances were reorganised and expanded as more nations entered the war, Italy, Japan, the trigger for the war was the assassination of Archduke Franz Ferdinand of Austria, heir to the throne of Austria-Hungary, by Yugoslav nationalist Gavrilo Princip in Sarajevo on 28 June 1914. This set off a crisis when Austria-Hungary delivered an ultimatum to the Kingdom of Serbia. Within weeks, the powers were at war and the conflict soon spread around the world. On 25 July Russia began mobilisation and on 28 July, the Austro-Hungarians declared war on Serbia, Germany presented an ultimatum to Russia to demobilise, and when this was refused, declared war on Russia on 1 August. Germany then invaded neutral Belgium and Luxembourg before moving towards France, after the German march on Paris was halted, what became known as the Western Front settled into a battle of attrition, with a trench line that changed little until 1917. On the Eastern Front, the Russian army was successful against the Austro-Hungarians, in November 1914, the Ottoman Empire joined the Central Powers, opening fronts in the Caucasus, Mesopotamia and the Sinai. In 1915, Italy joined the Allies and Bulgaria joined the Central Powers, Romania joined the Allies in 1916, after a stunning German offensive along the Western Front in the spring of 1918, the Allies rallied and drove back the Germans in a series of successful offensives. By the end of the war or soon after, the German Empire, Russian Empire, Austro-Hungarian Empire, national borders were redrawn, with several independent nations restored or created, and Germanys colonies were parceled out among the victors. During the Paris Peace Conference of 1919, the Big Four imposed their terms in a series of treaties, the League of Nations was formed with the aim of preventing any repetition of such a conflict. This effort failed, and economic depression, renewed nationalism, weakened successor states, and feelings of humiliation eventually contributed to World War II. From the time of its start until the approach of World War II, at the time, it was also sometimes called the war to end war or the war to end all wars due to its then-unparalleled scale and devastation. In Canada, Macleans magazine in October 1914 wrote, Some wars name themselves, during the interwar period, the war was most often called the World War and the Great War in English-speaking countries. Will become the first world war in the sense of the word. These began in 1815, with the Holy Alliance between Prussia, Russia, and Austria, when Germany was united in 1871, Prussia became part of the new German nation. Soon after, in October 1873, German Chancellor Otto von Bismarck negotiated the League of the Three Emperors between the monarchs of Austria-Hungary, Russia and Germany
World War I
–
Clockwise from the top: The aftermath of shelling during the
Battle of the Somme,
Mark V tanks cross the
Hindenburg Line,
HMS Irresistible sinks after hitting a
mine in the
Dardanelles, a British
Vickers machine gun crew wears
gas masks during the Battle of the Somme,
Albatros D.III fighters of
Jagdstaffel 11
World War I
–
Sarajevo citizens reading a poster with the proclamation of the
Austrian annexation in 1908.
World War I
–
This picture is usually associated with the arrest of
Gavrilo Princip, although some believe it depicts Ferdinand Behr, a bystander.
World War I
–
Serbian Army
Blériot XI "Oluj", 1915.
31.
174th Fighter Wing
–
The 174th Attack Wing is a unit of the New York Air National Guard, stationed at Hancock Field Air National Guard Base, Syracuse, New York. If activated to service, the Wing is gained by the United States Air Force Air Combat Command. The 174th Attack Wing currently operates the MQ-9 Reaper Remotely Piloted Aircraft, received federal recognition by the National Guard Bureau and activated on 1 September 1962 as the 174th Tactical Fighter Group. The group was stationed at Hancock Field, Syracuse, New York, and allocated to Tactical Air Command. Other squadrons assigned into the group were the 174th Headquarters, 174th Material Squadron, 174th Combat Support Squadron, the 138th TFS was equipped with the F-86H Sabre. The squadron engaged normal peacetime training and exercises, in the summer of 1965, the squadron took part in Exercise Oneida Bear II at Fort Drum, which involved some 6 500 soldiers of the regular Army, the Army Reserve and the National Guard. 138th TFS aircraft from Syracuse provided close air support to both aggressor and Friendly Forces during the exercise, and were engaged in tactical air strikes. In the exercise, conducted by the First Army, the Second Brigade of the Armys Fifth Infantry was opposed by a force of selected Army National Guard. The 174th Groups pilots flew 77 sorties for a total of 114 hours without a single abort, the squadron trained at Ramey AFB, Puerto Rico, in early 1967 in an all service amphibious and airborne exercise. A detachment of unit pilots and support personnel participated, twelve F-86H aircraft participated with three C-130 Hercules for equipment and personnel support. All types of air missions were flown. Total sorties were 213 with total hours flown,308, special firepowers demonstration was accomplished with 20 sorties delivering 40 and 2000 rounds of 20 mm fired. Later in 1967, Operation Sentry Post I was held in August and this was a joint Air National Guard – TAC Exercise. Twelve F-86Hs were flown and squadron pilots worked with radar flying air-to-air and air-to-ground gunnery with, a total of 204 sorties and 245 hours were flown in this operation. In 1968, the 174th TFG was federalized and placed on active duty, the Group was alerted for active duty on 11 April 1968, partially mobilized on 13 May and deployed to Cannon Air Force Base, Clovis, New Mexico. The mission of the 174th was to train Forward Air Controllers for service in Vietnam, the FAC flew a light observation aircraft at low altitudes, visually observing enemy installations and movements and providing on-the-spot directions for fighters and bombers. The FAC dictated the type of ordnance to be delivered, observes the strike, on arrival at Cannon AFB along with the Maryland ANG 175th Tactical Fighter Squadron, they comprised the 140th Tactical Fighter Wing. Originally based in Denver, Colorado, headquarters of the 140th moved to Cannon AFB with the deployment of the 140th Tactical Fighter Group to active duty in Vietnam, not all members of the 174th Tactical Fighter Group were mobilized, however
174th Fighter Wing
–
General Atomics MQ-9A Reaper of the 138th Attack Squadron
174th Fighter Wing
–
138th Tactical Fighter Squadron F-86H Sabre 53-1519 about 1966 in Vietnam War camouflage
174th Fighter Wing
–
138th TFS Cessna A-37B Dragonfly 69-6423, 1974
174th Fighter Wing
–
A 138th TFS A-10A Thunderbolt II 78-0670
32.
Syracuse Hancock International Airport
–
Syracuse Hancock International Airport is a city owned, joint civil-military airport five miles northeast of downtown Syracuse, in Onondaga County, New York. The airport is off Interstate 81 near Mattydale, New York, the main terminal complex is at the east end of Colonel Eileen Collins Boulevard. The National Plan of Integrated Airport Systems for 2011–2015 called it a commercial service airport. Federal Aviation Administration records say the airport had 1,105,143 passenger boardings in calendar year 2008,1,016,571 in 2009 and 1,024,505 in 2010, in 1927 Syracuse mayor Charles Hanna felt his city needed an airport. A location at Amboy in the town of Camillus, New York was purchased for $50,000, and by 1928, at the end of World War II the United States Army Air Corps leased their bomber base near Mattydale, New York to the city. On September 17,1949 the Clarence E. Hancock Airport opened to the using a renovated machine shop as a terminal. The airport had three runways,5, 500-foot long and 300-foot wide. American, Buffalo, Colonial and Robinson Airlines were the first airlines at the airport, in 2004 Syracuse Mayor Matthew Driscoll created a television and internet campaign, Fly Syracuse, hoping to lower fares and increase passenger traffic at the airport. The airport has experienced growth thanks to the efforts of local business contributions toward the campaign. The airport covers 2,000 acres at an elevation of 421 feet and it has two asphalt runways, 10/28 is 9,003 by 150 feet and 15/33 is 7,500 by 150 feet. The east-west instrument runway was extended from its original 5500 feet by the mid-1950s to 6863 feet, in 1958 the instrument landing system to runway 28 was augmented with a 3000 foot high-intensity approach lighting system. With the use of the Century series fighter aircraft by the Air Force, around 1960 the main east-west runway was extended again, the runway was strengthened in the early 1960s for the heavier Boeing 707. In the 1960s runway centerline lighting was added to the main runway, around the time of building the new terminal building, runway 6-24 was shortened to 3261 feet and continued to be a general aviation runway into the 1970s, and was abandoned after that. Runway 14-32 was lengthened in the 1960s to 6000 feet, another extension brought it to 6480 feet and sometime around 1980 to its present length of 7500 feet. The crosswind runway was renumbered from 14-32 to 15-33, an instrument landing system was added to runway 10 with medium intensity approach lighting with runway alignment indicator lights. Runway 15 got a medium intensity approach lighting system, in the year ending September 30,2011 the airport had 72,113 aircraft operations, average 197 per day, 45% air taxi, 24% airline, 20% military, and 12% general aviation. 93 aircraft were based at this airport, 55% single-engine, 26% military, 10% multi-engine, 8% jet. Syracuse receives an average 124 inches of snow annually, most of any city in the United States
Syracuse Hancock International Airport
–
Syracuse Hancock International Airport
Syracuse Hancock International Airport
–
United Airlines Boeing 737 at SYR in 1993
Syracuse Hancock International Airport
–
An
American Airlines McDonnell Douglas MD-80 being
deiced at Terminal B. In the background is a
Northwest Airlines DC-9 parked at Terminal A.
33.
Syracuse, New York
–
Syracuse is a city in, and the county seat of, Onondaga County, New York, in the United States. It is the largest U. S. city with the name Syracuse, and is the fifth most populous city in the state of New York following New York City, Buffalo, Rochester, and Yonkers. At the 2010 census, the city population was 145,170 and it is the economic and educational hub of Central New York, a region with over a million inhabitants. Syracuse is also well-provided with convention sites, with a convention complex. Syracuse was named after the original Greek city Syracuse, a city on the eastern coast of the Italian island of Sicily. The city has functioned as a crossroads over the last two centuries, first between the Erie Canal and its branch canals, then of the railway network. Today, Syracuse is located at the intersection of Interstates 81 and 90, Syracuse is home to Syracuse University, a major research university, as well as Le Moyne College, a nationally recognized liberal arts college. In 2010, Forbes rated Syracuse 4th in the top 10 places in the U. S. to raise a family, the Syracuse area was first seen by Europeans when French missionaries came to the area in the 1600s. Marie de Gannentaha, on the northeast shore of Onondaga Lake, Jesuit missionaries visiting the Syracuse region in the mid 1600s reported salty brine springs around the southern end of Salt Lake, known today as Onondaga Lake. It is the north flowing brine from Tully that is the source of salt for the salty springs found along the shoreline of Onondaga lake, the rapid development of this industry in the 18th and 19th centuries led to the nicknaming of Syracuse as The Salt City. In 1847, the city was named after Syracuse, Sicily. In 1861, he developed the process for the manufacture of soda ash from brine wells dug in the southern end of Tully valley. The process was an improvement over the earlier Leblanc process, the Syracuse Solvay plant was the incubator for a large chemical industry complex owned by Allied Signal in Syracuse, the result of which made Onondaga Lake the most polluted in the nation. The salt industry declined after the Civil War, but a new manufacturing industry arose in its place, the Geneva Medical College was founded in 1834. It is now known as Upstate Medical University, one of four medical colleges in the State University of New York system. The first New York State Fair was held in Syracuse in 1841, world War II sparked significant industrial expansion in the area, specialty steel, fasteners, custom machining. After the war, two of the Big Three automobile manufacturers had major operations in the area, Syracuse was headquarters for Carrier Corporation, and Crouse-Hinds manufactured traffic signals in Syracuse. General Electric had its television manufacturing plant at Electronics Parkway in Syracuse
Syracuse, New York
–
A view of the downtown Syracuse skyline
Syracuse, New York
–
View of the Boulevard c. 1908
Syracuse, New York
–
A view of
Downtown Syracuse from
University Hill
Syracuse, New York
–
Onondaga Creek as it flows near
Franklin Square
34.
174th Infantry Brigade (United States)
–
The 174th Infantry Brigade is an infantry brigade of the United States Army based at Fort Drum, New York. A U. S. Army Reserve training unit, the brigade provides operational training readiness for units in the First Army, tracing its lineage back to the American Civil War, the brigade was deployed for both World War I and World War II. As such, many personnel in the brigade are instructors who are combat veterans of Operation Iraqi Freedom. The brigade is a unit of the First Army. As a separate Reserve brigade, it does not report to a division level headquarters. The brigade is made up of six battalions and its Headquarters and Headquarters Detachment is located at Fort Dix, New Jersey. Assigned to the brigade are the 1st Battalion, 314th Infantry Regiment, the 2nd Battalion, 313th Regiment, and the 3rd Battalion, 314th Regiment, which are also headquartered at Fort Drum. Additionally, the contains the 2nd Battalion, 310th Regiment, and 3rd Battalion, 313th Regiment. The 3rd Battalion, 309th Regiment, also part of the brigade, is headquartered at Syracuse, the brigade draws its origins back to the 174th New York Volunteer Infantry Regiment, a unit that served during the American Civil War. The regiment sailed to Louisiana that December, upon arrival, it was assigned to the 2nd brigade of Major General William Emorys division. After the fall of Port Hudson it engaged Confederate forces at Coxs plantation, in the end, the unit lost 54 soldiers,18 killed,29 wounded and 7 missing. This was the heaviest loss sustained by any regiment in the action, the remainder of the year was spent by the regiment in post and garrison duty at Baton Rouge, and on 8 February 1864, the regiment was consolidated with the 162nd New York Infantry. The 174th Infantry Brigade was first constituted on 5 August 1917 in the National Army and it was organized on 25 August 1917 at Camp Dix, New Jersey, and assigned to the 87th Division. It never saw combat in World War I, like the other units of the 87th Division, the brigade was used for labor duties and it received a campaign streamer for World War I without an inscription. After the war, it was demobilized on 23 May 1919 at Camp Dix, reorganized in December 1921 at Shreveport, Louisiana, the brigade was redesignated on 23 March 1925 as the 174th Brigade. It was again redesignated on 24 August 1936 as the 174th Infantry Brigade, on 13 February 1942, the unit was converted and redesignated as 3rd platoon, 87th Reconnaissance Troop, still assigned to the 87th Division. This consolidation also occurred to the 173rd Infantry Brigade and that December, the unit was ordered into active military service and reorganized along with the rest of the division at Camp McCain, Mississippi, which became an Infantry division. It was then mechanized the next year, the 87th Infantry Division arrived in Scotland on 22 October 1944, and trained in England until the end of November
174th Infantry Brigade (United States)
–
174th Infantry Brigade shoulder sleeve insignia
174th Infantry Brigade (United States)
–
Distinctive unit insignia
174th Infantry Brigade (United States)
–
A soldier of the 174th Infantry Brigade trains a reservist on convoy duty at Fort Drum, New York.
35.
United States Army
–
The United States Army is the largest branch of the United States Armed Forces and performs land-based military operations. After the Revolutionary War, the Congress of the Confederation created the United States Army on 3 June 1784, the United States Army considers itself descended from the Continental Army, and dates its institutional inception from the origin of that armed force in 1775. As a uniformed service, the Army is part of the Department of the Army. As a branch of the forces, the mission of the U. S. The branch participates in conflicts worldwide and is the major ground-based offensive and defensive force of the United States, the United States Army serves as the land-based branch of the U. S. Section 3062 of Title 10, U. S, the army was initially led by men who had served in the British Army or colonial militias and who brought much of British military heritage with them. As the Revolutionary War progressed, French aid, resources, a number of European soldiers came on their own to help, such as Friedrich Wilhelm von Steuben, who taught Prussian Army tactics and organizational skills. The army fought numerous pitched battles and in the South in 1780–81 sometimes used the Fabian strategy and hit-and-run tactics, hitting where the British were weakest, to wear down their forces. Washington led victories against the British at Trenton and Princeton, but lost a series of battles in the New York and New Jersey campaign in 1776, with a decisive victory at Yorktown, and the help of the French, the Continental Army prevailed against the British. After the war, though, the Continental Army was quickly given land certificates, State militias became the new nations sole ground army, with the exception of a regiment to guard the Western Frontier and one battery of artillery guarding West Points arsenal. However, because of continuing conflict with Native Americans, it was realized that it was necessary to field a trained standing army. The War of 1812, the second and last war between the United States and Great Britain, had mixed results. After taking control of Lake Erie in 1813, the U. S. Army seized parts of western Upper Canada, burned York and defeated Tecumseh, which caused his Western Confederacy to collapse. Following U. S. victories in the Canadian province of Upper Canada, British troops, were able to capture and burn Washington, which was defended by militia, in 1814. Two weeks after a treaty was signed, Andrew Jackson defeated the British in the Battle of New Orleans and Siege of Fort St. Philip, U. S. troops and sailors captured HMS Cyane, Levant, and Penguin in the final engagements of the war. Per the treaty, both sides, the United States and Great Britain, returned to the status quo. Both navies kept the warships they had seized during the conflict, the armys major campaign against the Indians was fought in Florida against Seminoles. It took long wars to defeat the Seminoles and move them to Oklahoma
United States Army
–
Storming of Redoubt #10 in the
Siege of Yorktown during the
American Revolutionary War prompted the British government to begin negotiations, resulting in the
Treaty of Paris and British recognition of the United States of America.
United States Army
–
Emblem of the United States Department of the Army
United States Army
–
General
Andrew Jackson stands on the parapet of his makeshift defenses as his troops repulse attacking
Highlanders during the
defense of New Orleans, the final major battle of the War of 1812
United States Army
–
The
Battle of Gettysburg, the turning point of the American Civil War
36.
Fort Drum
–
Fort Drum is a U. S. Army military reservation and a census-designated place in Jefferson County, New York, United States. The population was 12,955 at the 2010 census and it is home to the 10th Mountain Division. Fort Drum consists of 107,265 acres and temperatures can reach as low as −30 °F and this section of the article incorporates text taken from a public-domain document prepared by the US military. A portion of the present Fort Drum was purchased for use as a training site since 1908. However, the presence in the North Country may be traced back to the early 19th century. In 1809 a company of soldiers was stationed at Sacketts Harbor to enforce the Embargo Act. Following the outbreak of the War of 1812, Sacketts Harbor became the center of United States naval and military activity for the Upper St. Lawrence River valley and Lake Ontario. During the 1830s and 1840s, the Lower Canada Rebellion in Canada prompted a new round of military preparations, in 1908, Major General Frederick Dent Grant was sent to the Pine Camp region to train with 2,000 regulars and 8,000 militia. Grant, the son of former United States president and Civil War general Ulysses S. Grant, in 1909 the military allocated funds to purchase land to form Pine Camp, and summer training continued here through the years. The camps first introduction to the spotlight came in 1935 when the largest peacetime maneuvers were held on Pine Plains. Approximately 36,500 soldiers came from throughout the Northeast to take part in the exercise, some soldiers traveled by trains which arrived in town every 15 minutes, coming from as far away as Buffalo, New York and New York City. For 36 hours, young men from offices, factories, the maneuvers were judged to be most successful and the War Department purchased an additional 9,000 acres of land. The LeRay Mansion, built in the early 19th century, was named after James LeRay de Chaumont, throughout the years the mansion served as a post commanders quarters, visiting dignitaries quarters and a location for formal military receptions. Today the mansion is used to high ranking visitors, which has encouraged the continued upkeep of the mansion. The LeRay Mansion is registered with the National Register of Historic Places, with the outbreak of World War II, Pine Camp was selected for a major expansion. An additional 75,000 acres of land was purchased, displacing 525 local families, five entire villages were eliminated, while others were reduced from one-third to one-half their size. By Labor Day,1941,100 tracts of land were taken over, three thousand buildings, including 24 schools, six churches and a post office, were abandoned. Contractors then went to work, and in a period of 10 months at a cost of $20 million, construction workers paid the price, as the winter of 1941-42 was one of the coldest in North Country history
Fort Drum
–
Marksmanship training at Fort Drum
37.
New York (state)
–
New York is a state in the northeastern United States, and is the 27th-most extensive, fourth-most populous, and seventh-most densely populated U. S. state. New York is bordered by New Jersey and Pennsylvania to the south and Connecticut, Massachusetts, and Vermont to the east. With an estimated population of 8.55 million in 2015, New York City is the most populous city in the United States, the New York Metropolitan Area is one of the most populous urban agglomerations in the world. New York City makes up over 40% of the population of New York State, two-thirds of the states population lives in the New York City Metropolitan Area, and nearly 40% lives on Long Island. Both the state and New York City were named for the 17th-century Duke of York, the next four most populous cities in the state are Buffalo, Rochester, Yonkers, and Syracuse, while the state capital is Albany. New York has a diverse geography and these more mountainous regions are bisected by two major river valleys—the north-south Hudson River Valley and the east-west Mohawk River Valley, which forms the core of the Erie Canal. Western New York is considered part of the Great Lakes Region and straddles Lake Ontario, between the two lakes lies Niagara Falls. The central part of the state is dominated by the Finger Lakes, New York had been inhabited by tribes of Algonquian and Iroquoian-speaking Native Americans for several hundred years by the time the earliest Europeans came to New York. The first Europeans to arrive were French colonists and Jesuit missionaries who arrived southward from settlements at Montreal for trade, the British annexed the colony from the Dutch in 1664. The borders of the British colony, the Province of New York, were similar to those of the present-day state, New York is home to the Statue of Liberty, a symbol of the United States and its ideals of freedom, democracy, and opportunity. In the 21st century, New York has emerged as a node of creativity and entrepreneurship, social tolerance. On April 17,1524 Verrazanno entered New York Bay, by way of the now called the Narrows into the northern bay which he named Santa Margherita. Verrazzano described it as a vast coastline with a delta in which every kind of ship could pass and he adds. This vast sheet of water swarmed with native boats and he landed on the tip of Manhattan and possibly on the furthest point of Long Island. Verrazannos stay was interrupted by a storm which pushed him north towards Marthas Vineyard, in 1540 French traders from New France built a chateau on Castle Island, within present-day Albany, due to flooding, it was abandoned the next year. In 1614, the Dutch under the command of Hendrick Corstiaensen, rebuilt the French chateau, Fort Nassau was the first Dutch settlement in North America, and was located along the Hudson River, also within present-day Albany. The small fort served as a trading post and warehouse, located on the Hudson River flood plain, the rudimentary fort was washed away by flooding in 1617, and abandoned for good after Fort Orange was built nearby in 1623. Henry Hudsons 1609 voyage marked the beginning of European involvement with the area, sailing for the Dutch East India Company and looking for a passage to Asia, he entered the Upper New York Bay on September 11 of that year
New York (state)
–
British general
John Burgoyne surrenders at
Saratoga in 1777.
New York (state)
–
Flag
New York (state)
–
1800 map of New York from
Low's Encyclopaedia
New York (state)
–
The
Erie Canal at
Lockport, New York in 1839
38.
United States
–
Forty-eight of the fifty states and the federal district are contiguous and located in North America between Canada and Mexico. The state of Alaska is in the northwest corner of North America, bordered by Canada to the east, the state of Hawaii is an archipelago in the mid-Pacific Ocean. The U. S. territories are scattered about the Pacific Ocean, the geography, climate and wildlife of the country are extremely diverse. At 3.8 million square miles and with over 324 million people, the United States is the worlds third- or fourth-largest country by area, third-largest by land area. It is one of the worlds most ethnically diverse and multicultural nations, paleo-Indians migrated from Asia to the North American mainland at least 15,000 years ago. European colonization began in the 16th century, the United States emerged from 13 British colonies along the East Coast. Numerous disputes between Great Britain and the following the Seven Years War led to the American Revolution. On July 4,1776, during the course of the American Revolutionary War, the war ended in 1783 with recognition of the independence of the United States by Great Britain, representing the first successful war of independence against a European power. The current constitution was adopted in 1788, after the Articles of Confederation, the first ten amendments, collectively named the Bill of Rights, were ratified in 1791 and designed to guarantee many fundamental civil liberties. During the second half of the 19th century, the American Civil War led to the end of slavery in the country. By the end of century, the United States extended into the Pacific Ocean. The Spanish–American War and World War I confirmed the status as a global military power. The end of the Cold War and the dissolution of the Soviet Union in 1991 left the United States as the sole superpower. The U. S. is a member of the United Nations, World Bank, International Monetary Fund, Organization of American States. The United States is a developed country, with the worlds largest economy by nominal GDP. It ranks highly in several measures of performance, including average wage, human development, per capita GDP. While the U. S. economy is considered post-industrial, characterized by the dominance of services and knowledge economy, the United States is a prominent political and cultural force internationally, and a leader in scientific research and technological innovations. In 1507, the German cartographer Martin Waldseemüller produced a map on which he named the lands of the Western Hemisphere America after the Italian explorer and cartographer Amerigo Vespucci
United States
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Native Americans meeting with Europeans, 1764
United States
–
Flag
United States
–
The signing of the
Mayflower Compact, 1620.
United States
–
The
Declaration of Independence: the
Committee of Five presenting their draft to the
Second Continental Congress in 1776
39.
Radar
–
Radar is an object-detection system that uses radio waves to determine the range, angle, or velocity of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, Radio waves from the transmitter reflect off the object and return to the receiver, giving information about the objects location and speed. Radar was developed secretly for military use by several nations in the period before, the term RADAR was coined in 1940 by the United States Navy as an acronym for RAdio Detection And Ranging or RAdio Direction And Ranging. The term radar has since entered English and other languages as a common noun, high tech radar systems are associated with digital signal processing, machine learning and are capable of extracting useful information from very high noise levels. Other systems similar to make use of other parts of the electromagnetic spectrum. One example is lidar, which uses ultraviolet, visible, or near infrared light from lasers rather than radio waves, as early as 1886, German physicist Heinrich Hertz showed that radio waves could be reflected from solid objects. In 1895, Alexander Popov, an instructor at the Imperial Russian Navy school in Kronstadt. The next year, he added a spark-gap transmitter, in 1897, while testing this equipment for communicating between two ships in the Baltic Sea, he took note of an interference beat caused by the passage of a third vessel. In his report, Popov wrote that this phenomenon might be used for detecting objects, the German inventor Christian Hülsmeyer was the first to use radio waves to detect the presence of distant metallic objects. In 1904, he demonstrated the feasibility of detecting a ship in dense fog and he obtained a patent for his detection device in April 1904 and later a patent for a related amendment for estimating the distance to the ship. He also got a British patent on September 23,1904 for a radar system. It operated on a 50 cm wavelength and the radar signal was created via a spark-gap. In 1915, Robert Watson-Watt used radio technology to advance warning to airmen. Watson-Watt became an expert on the use of direction finding as part of his lightning experiments. As part of ongoing experiments, he asked the new boy, Arnold Frederic Wilkins, Wilkins made an extensive study of available units before selecting a receiver model from the General Post Office. Its instruction manual noted that there was fading when aircraft flew by, in 1922, A. Hoyt Taylor and Leo C. Taylor submitted a report, suggesting that this might be used to detect the presence of ships in low visibility, eight years later, Lawrence A. Australia, Canada, New Zealand, and South Africa followed prewar Great Britain, and Hungary had similar developments during the war. Hugon, began developing a radio apparatus, a part of which was installed on the liner Normandie in 1935
Radar
–
Long-range radar
antenna, used to track space objects and ballistic missiles.
Radar
–
Radar of the type used for detection of aircraft. It rotates steadily, sweeping the airspace with a narrow beam.
Radar
–
Experimental radar antenna, US
Naval Research Laboratory, Anacostia, D. C., late 1930s
Radar
–
A
Chain Home tower in Great Baddow, United Kingdom
40.
Helicopter
–
A helicopter is a type of rotorcraft in which lift and thrust are supplied by rotors. This allows the helicopter to take off and land vertically, to hover, and to fly forward, backward and these attributes allow helicopters to be used in congested or isolated areas where fixed-wing aircraft and many forms of VTOL aircraft cannot perform. English language nicknames for helicopter include chopper, copter, helo, heli, Helicopters were developed and built during the first half-century of flight, with the Focke-Wulf Fw 61 being the first operational helicopter in 1936. Some helicopters reached limited production, but it was not until 1942 that a helicopter designed by Igor Sikorsky reached full-scale production, with 131 aircraft built. Though most earlier designs used more than one rotor, it is the single main rotor with anti-torque tail rotor configuration that has become the most common helicopter configuration. Tandem rotor helicopters are also in use due to their greater payload capacity. Coaxial helicopters, tiltrotor aircraft, and compound helicopters are all flying today, quadcopter helicopters pioneered as early as 1907 in France, and other types of multicopter have been developed for specialized applications such as unmanned drones. The earliest references for vertical flight came from China, since around 400 BC, Chinese children have played with bamboo flying toys. This bamboo-copter is spun by rolling a stick attached to a rotor, the spinning creates lift, and the toy flies when released. The 4th-century AD Daoist book Baopuzi by Ge Hong reportedly describes some of the ideas inherent to rotary wing aircraft, designs similar to the Chinese helicopter toy appeared in Renaissance paintings and other works. In the 18th and early 19th centuries Western scientists developed flying machines based on the Chinese toy. It was not until the early 1480s, when Leonardo da Vinci created a design for a machine that could be described as an aerial screw, that any recorded advancement was made towards vertical flight. His notes suggested that he built flying models, but there were no indications for any provision to stop the rotor from making the craft rotate. As scientific knowledge increased and became accepted, people continued to pursue the idea of vertical flight. In July 1754, Russian Mikhail Lomonosov had developed a small coaxial modeled after the Chinese top but powered by a spring device. It was powered by a spring, and was suggested as a method to lift meteorological instruments. Sir George Cayley, influenced by a fascination with the Chinese flying top, developed a model of feathers, similar to that of Launoy and Bienvenu. By the end of the century, he had progressed to using sheets of tin for rotor blades and his writings on his experiments and models would become influential on future aviation pioneers
Helicopter
–
A police department
Bell 206 helicopter
Helicopter
–
A decorated Japanese taketombo bamboo-copter
Helicopter
–
Leonardo's "aerial screw"
Helicopter
–
Prototype created by
M. Lomonosov, 1754
41.
Attack Squadron 174 (United States Navy)
–
Attack Squadron 174 also known as the Hellrazors was a United States Navy attack squadron based at Naval Air Station Cecil Field, Florida, and were attached to Light Attack Wing One. The unit has evolved several times throughout its history dates back to 1944. When it was established in March 1944 the unit was designated VB-81 flying the SB2C Helldiver and it was redesignated VA-13A on 15 November 1946. The unit was redesignated VA-134 on 2 August 1948 flying F-4U Corsairs, the Hellrazors received their final designation VA-174 on 1 July 1966 after becoming the first US Navy squadron to receive the A-7A Corsair II. It was the squadron to bear the VA-174 designation, the first VA-174 was disestablished on 25 January 1950. The squadron was disestablished on 30 June 1988, VB-81 was redesignated VF-13 in November 1946 while the squadron was embarked on USS Princeton. In 1949 the squadron transferred to the East Coast, arriving in Naval Air Station Jacksonville the squadron was redesignated to VF-134 and later VF-174. Operating aboard the USS Coral Sea with Carrier Air Group Seventeen, VF-174 participated in operations Protex and it returned to Jacksonville to transition to the F9F-6 Cougar and then made a short cruise to Guantanamo Bay in May and June 1951 aboard the USS Midway. The squadron returned from the Mediterranean in February 1952 and participated in operations Mainbase, in preparation for a globe-circling cruise, VF-174 deployed twice to Guantanamo Bay, Cuba for intensive gunnery training. Both time the squadron was cited for Outstanding Performance, after returning from their second Gitmo trip in early 1954, the squadron moved to its present home at Naval Air Station Cecil Field and joined Carrier Air Group One. In late 1954 the USS Midway became the first American carrier to visit the British port of Cape Town, while in the Pacific the carrier operated with the Seventh Fleet near Formosa and VF-174 participated in the evacuation of the Tachen Island in December 1954. Immediately after their return to Cecil Field in August 1955, VF-174 transitioned to the FJ-3 FURY, the squadron operated with the new Furies for only a few months and then transitioned to the F9F-8 Cougar in early 1956. With the new Cougars an attack syllabus was added to the fighter operations. Acting as both and attack and fighter squadron, the Hellrazors deployed to the Far East in October 1956 aboard the USS Bennington as a weapons squadron with Air Task Group One Eighty One. The squadron returned to Cecil Field in May 1957, in January 1958, VF-174 transitioned to the F8U-1 Crusader and in March 1958 began training pilots in F8Us for Atlantic Fleet squadrons. On 1 May 1958 the squadron relinquished its role and was officially designated the Atlantic Fleet F8U replacement pilot training squadron. During the next eight years until 1 July 1966, VF-174 excelled in all areas, the squadron evaluated the Mark IV Full Pressure Suit, the Delmar Missile and Gunnery Target System, and the two-seater TF-8A Crusader. The squadron assumed an all weather fighter capability with the arrival of the F8U-2N in November 1960, the squadron received the Aviation Safety Award in 1960 and again in 1962, and the Delmar Target System Award for top efficiency in gunnery exercises in 1963
Attack Squadron 174 (United States Navy)
–
VA-174 Insignia
Attack Squadron 174 (United States Navy)
–
An
A-7 Corsair II from VA-174 loaded with weapons.
Attack Squadron 174 (United States Navy)
–
Corsair II of VA-174 in 1976 wearing a large version of the squadron's insignia
Attack Squadron 174 (United States Navy)
–
An VA-174 TA-7C at NAS Dallas in 1988.
42.
United States Navy
–
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
United States Navy
United States Navy
–
United States Navy portal
United States Navy
–
USS Constellation vs L'Insurgente during the
Quasi-War
United States Navy
–
USS Constitution vs HMS Guerriere during the
War of 1812
43.
Naval Air Station Cecil Field
–
Naval Air Station Cecil Field or NAS Cecil Field was a United States Navy air base, located in Duval County, Florida. Prior to October 1999, NAS Cecil Field was the largest military base in terms of acreage in the Jacksonville, Florida area. Including nearly 2,500 acres at OLF Whitehouse, the NAS Cecil Field complex consisted of 22,939 acres, in addition and it is now a civilian, public-use, joint civil-military airfield and industrial park known as Cecil Commerce Center and Cecil Airport. NAS Cecil Field was named in honor of Commander Henry Barton Cecil, USN, who died in 1933 in the crash of the Navy airship USS Akron. Shortly before the United States entry into World War II, a 2,600 acre tract of land was purchased in western Duval County and construction began on the U. S. Naval Auxiliary Air Station, Cecil Field. The base got its start in June 1941 as a field of NAS Jacksonville. From 1943 until the war ended, NAAS Cecil Field was a pilots last stop before assignment to combat in either the Atlantic Fleet or Pacific Fleet and it operated at full capacity during the war years and after the war. Disestablished as NAAS Cecil Field at the end of World War II, the station was rejuvenated as an operating base for fleet aircraft squadrons and air groups, ushering in the jet age for Naval Aviation in the Jacksonville area. In 1951, the area of NAS Cecil Field was increased to 4,600 acres and additional new buildings. Naval Air Station Cecil Field occupied 19,664 acres, and was projected to be Navys largest Master Jet Base. S, Squadrons from NAS Cecil Field were aboard every Atlantic Fleet aircraft carrier deployed to Southeast Asia during the Vietnam War. During this period, thirteen NAS Cecil Field pilots were listed as POW or MIA, the POW/MIA memorial located behind the base chapel has become the chosen site for many retiring officers and enlisted personnel to hold their retirement ceremonies. The first Atlantic Fleet Squadrons to fly the A-7 Corsair II, the F/A-18 Hornet, the S-3A and S-3B Viking, and the ES-3A Shadow were all based at NAS Cecil Field. NAS Cecil Field squadrons again made history during the Gulf War, marking the final deployment for the A-7E Corsair II. The first weather observations were recorded at NAS Cecil Field in May 1949, in those days, weather observing and forecasting services were provided by the Meteorology Division of the Air Operations Department. In September 1979, almost 14 years later, the changed to Naval Oceanography Command Detachment. Naval Air Station Cecil Field was identified for closure by the 1993 federal Base Realignment and Closure Commission and approved by the U. S. Congress and President Bill Clinton in July 1993. There have been efforts to see the base returned as a Naval Air Station, the FLARNG operates CH-47 Chinook, UH-60 Blackhawk, UH-72 Lakota and C-12 Huron aircraft from AASF #1 at Cecil Field. Also located at Cecil Field is Coast Guard Air Facility Jacksonville, which supports the U. S. Coast Guards Helicopter Interdiction Tactical Squadron and its MH-65C Dolphin helicopters
Naval Air Station Cecil Field
–
NAS Cecil Field
Naval Air Station Cecil Field
–
An
FJ-3 from VF-62 at NAS Cecil Field, 1956.
Naval Air Station Cecil Field
–
Two
F8U-1s of VF-62 over NAS Cecil Field, 1962.
Naval Air Station Cecil Field
–
Lockheed S-3A Viking of
VS-31 Squadron at Cecil Field in 1976
44.
Florida
–
Florida /ˈflɒrᵻdə/ is a state located in the southeastern region of the United States. It is bordered to the west by the Gulf of Mexico, to the north by Alabama and Georgia, to the east by the Atlantic Ocean, Florida is the 22nd-most extensive, the 3rd-most populous, and the 8th-most densely populated of the U. S. states. Jacksonville is the most populous municipality in the state and is the largest city by area in the contiguous United States, the Miami metropolitan area is Floridas most populous urban area. The city of Tallahassee is the state capital, much of the state is at or near sea level and is characterized by sedimentary soil. The climate varies from subtropical in the north to tropical in the south, the American alligator, American crocodile, Florida panther, and manatee can be found in the Everglades National Park. It was a location of the Seminole Wars against the Native Americans. Today, Florida is distinctive for its large Cuban expatriate community and high population growth, the states economy relies mainly on tourism, agriculture, and transportation, which developed in the late 19th century. Florida is also renowned for amusement parks, orange crops, the Kennedy Space Center, Florida has attracted many writers such as Marjorie Kinnan Rawlings, Ernest Hemingway and Tennessee Williams, and continues to attract celebrities and athletes. It is internationally known for golf, tennis, auto racing, by the 16th century, the earliest time for which there is a historical record, major Native American groups included the Apalachee, the Timucua, the Ais, the Tocobaga, the Calusa and the Tequesta. Florida was the first part of the continental United States to be visited and settled by Europeans, the earliest known European explorers came with the Spanish conquistador Juan Ponce de León. Ponce de León spotted and landed on the peninsula on April 2,1513 and he named the region La Florida. The story that he was searching for the Fountain of Youth is a myth, in May 1539, Conquistador Hernando de Soto skirted the coast of Florida, searching for a deep harbor to land. He described seeing a wall of red mangroves spread mile after mile, some reaching as high as 70 feet. Very soon, many smokes appeared along the whole coast, billowing against the sky, the Spanish introduced Christianity, cattle, horses, sheep, the Spanish language, and more to Florida. Both the Spanish and French established settlements in Florida, with varying degrees of success, in 1559, Don Tristán de Luna y Arellano established a settlement at present-day Pensacola, making it the first attempted settlement in Florida, but it was abandoned by 1561. Spain maintained tenuous control over the region by converting the tribes to Christianity. The area of Spanish Florida diminished with the establishment of English settlements to the north, the English attacked St. Augustine, burning the city and its cathedral to the ground several times. Florida attracted numerous Africans and African-Americans from adjacent British colonies who sought freedom from slavery, in 1738, Governor Manuel de Montiano established Fort Gracia Real de Santa Teresa de Mose near St
Florida
–
St. Augustine is the oldest city in the U.S., established in 1565 by Spain.
Florida
–
Flag
Florida
–
Aerial view of
Castillo De San Marcos (Florida).
Florida
–
The five flags of Florida from the right,
Spain (1565–1763), the
Kingdom of Great Britain, Spain (1784–1821), the
Confederacy, and the United States. France (flag not shown) also controlled part of Florida.
45.
Vietnam War
–
It was the second of the Indochina Wars and was officially fought between North Vietnam and the government of South Vietnam. The war is considered a Cold War-era proxy war. As the war continued, the actions of the Viet Cong decreased as the role. U. S. and South Vietnamese forces relied on air superiority and overwhelming firepower to conduct search and destroy operations, involving ground forces, artillery, in the course of the war, the U. S. conducted a large-scale strategic bombing campaign against North Vietnam. The North Vietnamese government and the Viet Cong were fighting to reunify Vietnam and they viewed the conflict as a colonial war and a continuation of the First Indochina War against forces from France and later on the United States. The U. S. government viewed its involvement in the war as a way to prevent a communist takeover of South Vietnam and this was part the domino theory of a wider containment policy, with the stated aim of stopping the spread of communism. Beginning in 1950, American military advisors arrived in what was then French Indochina, U. S. involvement escalated in the early 1960s, with troop levels tripling in 1961 and again in 1962. Regular U. S. combat units were deployed beginning in 1965, despite the Paris Peace Accord, which was signed by all parties in January 1973, the fighting continued. In the U. S. and the Western world, a large anti-Vietnam War movement developed as part of a larger counterculture, the war changed the dynamics between the Eastern and Western Blocs, and altered North–South relations. Direct U. S. military involvement ended on 15 August 1973, the capture of Saigon by the North Vietnamese Army in April 1975 marked the end of the war, and North and South Vietnam were reunified the following year. The war exacted a huge human cost in terms of fatalities, estimates of the number of Vietnamese soldiers and civilians killed vary from 966,000 to 3.8 million. Some 240, 000–300,000 Cambodians,20, 000–62,000 Laotians, and 58,220 U. S. service members died in the conflict. Various names have applied to the conflict. Vietnam War is the most commonly used name in English and it has also been called the Second Indochina War and the Vietnam Conflict. As there have been several conflicts in Indochina, this conflict is known by the names of its primary protagonists to distinguish it from others. In Vietnamese, the war is known as Kháng chiến chống Mỹ. It is also called Chiến tranh Việt Nam, France began its conquest of Indochina in the late 1850s, and completed pacification by 1893. The 1884 Treaty of Huế formed the basis for French colonial rule in Vietnam for the seven decades
Vietnam War
–
Clockwise, from top left: U.S. combat operations in
Ia Drang, ARVN Rangers defending
Saigon during the 1968
Tet Offensive, two
Douglas A-4C Skyhawks en route for airstrikes against North Vietnam after the
Gulf of Tonkin incident, ARVN recapture
Quảng Trị during the 1972
Easter Offensive, civilians fleeing the
1972 Battle of Quảng Trị, burial of 300 victims of the 1968
Huế Massacre.
Vietnam War
–
A Japanese naval officer surrenders his sword to a British Lieutenant in Saigon on 13 September 1945.
Vietnam War
–
The
Geneva Conference, 1954
Vietnam War
–
U.S. President
Dwight D. Eisenhower and Secretary of State
John Foster Dulles greet President
Ngô Đình Diệm of
South Vietnam in Washington, 8 May 1957.
46.
USS Colquitt (AK-174)
–
USS Colquitt was an Alamosa-class cargo ship commissioned by the US Navy for service in World War II. She was responsible for delivering troops, goods and equipment to locations in the war zone, Colquitt was transferred to the US Coast Guard two days later and served until decommissioned 11 March 1946, on which date her transfer to the Coast Guard became permanent. She was renamed and reclassified Kukui, by the Coast Guard, the Coast Guard at that time needed a large cargo vessel to supply the equipment and personnel needed for the construction and logistical support of the Pacific LORAN chain. Her name was changed to Kukui, a name taken from a tender that had just been decommissioned. She was converted to Coast Guard specifications at the Coast Guard Yard in Curtis Bay, during her Coast Guard career she was based out of Honolulu, Hawaii. Through 1960 she was responsible for constructing the entire Philippine LORAN system, all construction of this system was done by sailors of Kukui. Their dual role as seamen and construction workers was one of the most unique assignments in the armed forces and she carried on her decks two LCMs to ferry men and equipment to shore and also had three bulldozers, several trucks and a few jeeps stashed in her holds. Seven months a year she was underway providing necessary support to members of the Coast Guard LORAN chain throughout the western Pacific. During this time she delivered everything from toothpicks to antenna poles and she also carried the complex electronic equipment necessary to set up the LORAN system. As a Coast Guard public affairs release noted, The men and they not only sailed the ship but they operated bulldozers, landing craft, trucks and jeeps. A typical voyage would cover over 18,000 nmi and Kukui would deliver 2,500,000 short tons of cargo to the many Coast Guard operated LORAN stations throughout the western Pacific. In all she would make over 20 stops at stations and ports, including Yokosuka, Japan. On 15 June 1953 she rendered assistance to a civilian workman injured at Batan LORAN station. In 1957 the crew of the Kukui observed a lack of books in the Philippine school districts they visited, the following year they got up a collection of 400 books to give to needy schoolchildren. Through hard work and perseverance they increased the total to 45,000 books within the three years. She also delivered relief supplies to the island of Batan after it was hit by Typhoon Elaine, on 1 December 1969, French Frigate Shoals LORAN Station was hit by a tidal wave, forcing the crew to evacuate and destroying much of the station. Kukui was sent to the island the month and was responsible for her reconstruction and rehabilitation. On 24 June 1970 she collided with the M/V Myoriki Maru No.25 six miles from Yokosuka, Japan, in January 1972, the Kukui received word that as part of a move to reduce Coast Guard spending, she would be decommissioned
USS Colquitt (AK-174)
–
USCGC Kukui (WAK-186) ex-USS Colquitt (AK-174) underway off the Coast Guard Yard at Curtis Bay, MD., 16 March 1946. Kukui was one of two ships of this class transferred to the Coast Guard in 1946.
USS Colquitt (AK-174)
–
USCGC Kukui (WAK-186) underway, date and location unknown.
47.
Cargo ship
–
A cargo ship or freighter is any sort of ship or vessel that carries cargo, goods, and materials from one port to another. Thousands of cargo carriers ply the worlds seas and oceans each year, cargo ships are usually specially designed for the task, often being equipped with cranes and other mechanisms to load and unload, and come in all sizes. Today, they are almost always built by welded steel, cargo ships/freighters can be divided into five groups, according to the type of cargo they carry. Tankers carry petroleum products or other liquid cargo, dry bulk carriers carry coal, grain, ore and other similar products in loose form. Multi-purpose vessels, as the name suggests, carry different classes of cargo – e. g. liquid, a Reefer ship is specifically designed and used for shipping perishable commodities which require temperature-controlled, mostly fruits, meat, fish, vegetables, dairy products and other foodstuffs. Specialized types of cargo vessels include ships and bulk carriers. Cargo ships fall into two categories that reflect the services they offer to industry, liner and tramp services. Those on a published schedule and fixed tariff rates are cargo liners. Tramp ships do not have fixed schedules, users charter them to haul loads. Generally, the shipping companies and private individuals operate tramp ships. Cargo liners run on fixed schedules published by the shipping companies, each trip a liner takes is called a voyage. However, some cargo liners may carry passengers also, a cargo liner that carries 12 or more passengers is called a combination or passenger-cum-cargo line. The desire to trade routes over longer distances, and throughout more seasons of the year. Before the middle of the 19th century, the incidence of piracy resulted in most cargo ships being armed, sometimes heavily, as in the case of the Manila galleons. They were also escorted by warships. Piracy is still common in some waters, particularly in the Malacca Straits. In 2004, the governments of three nations agreed to provide better protection for the ships passing through the Straits. The waters off Somalia and Nigeria are also prone to piracy, while smaller vessels are also in danger along parts of the South American, Southeast Asian coasts, the words cargo and freight have become interchangeable in casual usage
Cargo ship
–
The
Colombo Express, one of the largest container ships in the world (when she was built in 2005), owned and operated by
Hapag-Lloyd of
Germany
Cargo ship
–
Loading of a general cargo vessel in 1959
Cargo ship
–
A Delmas container ship unloading at the Zanzibar port in Tanzania
48.
World War II
–
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
World War II
–
Clockwise from top left: Chinese forces in the
Battle of Wanjialing, Australian
25-pounder guns during the
First Battle of El Alamein, German
Stuka dive bombers on the
Eastern Front in December 1943, a U.S. naval force in the
Lingayen Gulf,
Wilhelm Keitel signing the
German Instrument of Surrender, Soviet troops in the
Battle of Stalingrad
World War II
–
The
League of Nations assembly, held in
Geneva,
Switzerland, 1930
World War II
–
Adolf Hitler at a German
National Socialist political rally in
Weimar, October 1930
World War II
–
Italian soldiers recruited in 1935, on their way to fight the
Second Italo-Abyssinian War