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
–
Bruce Alan Martin's hexadecimal notation proposal
Hexadecimal
–
Hexadecimal finger-counting scheme.
16.
Vigesimal
–
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
–
Numeral systems
Vigesimal
–
The
Maya numerals are a base-20 system.
17.
Base 36
–
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
–
Numeral systems
Base 36
–
34 senary = 22 decimal, in senary finger counting
Base 36
18.
Natural number
–
In mathematics, the natural numbers are those used for counting and ordering. In common language, words used for counting are cardinal numbers, texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers. These chains of extensions make the natural numbers canonically embedded in the number systems. Properties of the numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics, the most primitive method of representing a natural number is to put down a mark for each object. Later, a set of objects could be tested for equality, excess or shortage, by striking out a mark, the first major advance in abstraction was the use of numerals to represent numbers. This allowed systems to be developed for recording large numbers, the ancient Egyptians developed a powerful system of numerals with distinct hieroglyphs for 1,10, and all the powers of 10 up to over 1 million. A stone carving from Karnak, dating from around 1500 BC and now at the Louvre in Paris, depicts 276 as 2 hundreds,7 tens, and 6 ones, and similarly for the number 4,622. A much later advance was the development of the idea that 0 can be considered as a number, with its own numeral. The use of a 0 digit in place-value notation dates back as early as 700 BC by the Babylonians, the Olmec and Maya civilizations used 0 as a separate number as early as the 1st century BC, but this usage did not spread beyond Mesoamerica. The use of a numeral 0 in modern times originated with the Indian mathematician Brahmagupta in 628, the first systematic study of numbers as abstractions is usually credited to the Greek philosophers Pythagoras and Archimedes. Some Greek mathematicians treated the number 1 differently than larger numbers, independent studies also occurred at around the same time in India, China, and Mesoamerica. In 19th century Europe, there was mathematical and philosophical discussion about the nature of the natural numbers. A school of Naturalism stated that the numbers were a direct consequence of the human psyche. Henri Poincaré was one of its advocates, as was Leopold Kronecker who summarized God made the integers, in opposition to the Naturalists, the constructivists saw a need to improve the logical rigor in the foundations of mathematics. In the 1860s, Hermann Grassmann suggested a recursive definition for natural numbers thus stating they were not really natural, later, two classes of such formal definitions were constructed, later, they were shown to be equivalent in most practical applications. The second class of definitions was introduced by Giuseppe Peano and is now called Peano arithmetic and it is based on an axiomatization of the properties of ordinal numbers, each natural number has a successor and every non-zero natural number has a unique predecessor. Peano arithmetic is equiconsistent with several systems of set theory
Natural number
–
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
–
Natural numbers can be used for counting (one
apple, two apples, three apples, …)
19.
Odd number
–
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
Odd number
–
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
–
Overview
21.
Deficient number
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In number theory, a deficient or deficient number is a number n for which the sum of divisors σ<2n, or, equivalently, the sum of proper divisors s<n. The value 2n − σ is called the numbers deficiency, as an example, consider the number 21. Its proper divisors are 1,3 and 7, and their sum is 11, because 11 is less than 21, the number 21 is deficient. Its deficiency is 2 ×21 −32 =10, since the aliquot sums of prime numbers equal 1, all prime numbers are deficient. An infinite number of even and odd deficient numbers exist. All odd numbers with one or two prime factors are deficient. All proper divisors of deficient or perfect numbers are deficient, there exists at least one deficient number in the interval for all sufficiently large n. Closely related to deficient numbers are perfect numbers with σ = 2n, the natural numbers were first classified as either deficient, perfect or abundant by Nicomachus in his Introductio Arithmetica. Almost perfect number Amicable number Sociable number Sándor, József, Mitrinović, Dragoslav S. Crstici, Borislav, the Prime Glossary, Deficient number Weisstein, Eric W. Deficient Number
Deficient number
–
Overview
22.
Triangular number
–
A triangular number or triangle number counts the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangular number is the number of dots composing a triangle with n dots on a side and it represents the number of distinct pairs that can be selected from n +1 objects, and it is read aloud as n plus one choose two. Carl Friedrich Gauss is said to have found this relationship in his early youth, however, regardless of the truth of this story, Gauss was not the first to discover this formula, and some find it likely that its origin goes back to the Pythagoreans 5th century BC. The two formulae were described by the Irish monk Dicuil in about 816 in his Computus, the triangular number Tn solves the handshake problem of counting the number of handshakes if each person in a room with n +1 people shakes hands once with each person. In other words, the solution to the problem of n people is Tn−1. The function T is the analog of the factorial function. In the limit, the ratio between the two numbers, dots and line segments is lim n → ∞ T n L n =13, Triangular numbers have a wide variety of relations to other figurate numbers. Most simply, the sum of two triangular numbers is a square number, with the sum being the square of the difference between the two. Algebraically, T n + T n −1 = + = + = n 2 =2, alternatively, the same fact can be demonstrated graphically, There are infinitely many triangular numbers that are also square numbers, e. g.1,36,1225. Some of them can be generated by a recursive formula. All square triangular numbers are found from the recursion S n =34 S n −1 − S n −2 +2 with S0 =0 and S1 =1. Also, the square of the nth triangular number is the same as the sum of the cubes of the integers 1 to n and this can also be expressed as ∑ k =1 n k 3 =2. The sum of the all triangular numbers up to the nth triangular number is the nth tetrahedral number, more generally, the difference between the nth m-gonal number and the nth -gonal number is the th triangular number. For example, the sixth heptagonal number minus the sixth hexagonal number equals the triangular number,15. Every other triangular number is a hexagonal number, knowing the triangular numbers, one can reckon any centered polygonal number, the nth centered k-gonal number is obtained by the formula C k n = k T n −1 +1 where T is a triangular number. The positive difference of two numbers is a trapezoidal number. Triangular numbers correspond to the case of Faulhabers formula. Alternating triangular numbers are also hexagonal numbers, every even perfect number is triangular, given by the formula M p 2 p −1 = M p 2 = T M p where Mp is a Mersenne prime
Triangular number
–
The first six triangular numbers
23.
Base 7
–
This is a list of numeral systems, that is, writing systems for expressing numbers. Numeral systems are classified here as to whether they use positional notation, the common names are derived somewhat arbitrarily from a mix of Latin and Greek, in some cases including roots from both languages within a single name. In this Youtube video, Matt Parker jokingly invented a base-1082 system and this turns out to be 1925. Radix Radix economy Table of bases List of numbers in various languages Numeral prefix
Base 7
–
Numeral systems
24.
Comet
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Community of Metros is a system of international railway benchmarking. CoMET consists of metro systems from around the world. Each metro has a volume of at least 500 million passengers annually, the four main objectives of CoMET are, To build measures to establish metro best practice. To provide comparative information both for the board and the government. To introduce a system of measures for management and these objectives were discussed in detail at the CoMET Annual Meeting 2016, hosted by SMRT Trains of SMRT Corporation. The meeting was held at Singapore in November 2016, in the UITP conference of 1982, London Underground and Hamburger Hochbahn decided to create a benchmarking exercise to compare their two railways with additional data for other 24 metro systems. The project was successful despite the fact that metros were very different in sizes, structures, however, CoMET used the Key Performance Indicator innovatively to solve the problem. In 1994, the Mass Transit Railway of Hong Kong proposed to London Underground, Berlin U-Bahn, New York City Subway, thus, the metros can exchange performance data and investigate best practice amongst similar heavy metros. These five metros are later known as the Group of Five, over time, other large transit systems joined the group. For example, Mexico City Metro, São Paulo Metro and Tokyo Metro joined in 1996, with eight members in total, the group became known as the Community of Metros. Following the success of the CoMET, the Nova group was created in 1998 as another benchmarking association, the Nova is currently consisted of 14 metro systems from around the world. Later, Moscow Metro joined the CoMET in 1999, madrid Metro transferred from Nova to CoMET in 2004. Santiago Metro and Beijing Subway joined in 2008, taipei Metro was the last member to join the CoMET which also joined in 2010
Comet
–
"CoMET" redirects here. For the geoprofession, see
Geoprofessions § Construction-materials engineering and testing (CoMET).
Comet
25.
Solar system
–
The Solar System is the gravitationally bound system comprising the Sun and the objects that orbit it, either directly or indirectly. Of those objects that orbit the Sun directly, the largest eight are the planets, with the remainder being significantly smaller objects, such as dwarf planets, of the objects that orbit the Sun indirectly, the moons, two are larger than the smallest planet, Mercury. The Solar System formed 4.6 billion years ago from the collapse of a giant interstellar molecular cloud. The vast majority of the mass is in the Sun. The four smaller inner planets, Mercury, Venus, Earth and Mars, are terrestrial planets, being composed of rock. The four outer planets are giant planets, being more massive than the terrestrials. All planets have almost circular orbits that lie within a flat disc called the ecliptic. The Solar System also contains smaller objects, the asteroid belt, which lies between the orbits of Mars and Jupiter, mostly contains objects composed, like the terrestrial planets, of rock and metal. Beyond Neptunes orbit lie the Kuiper belt and scattered disc, which are populations of trans-Neptunian objects composed mostly of ices, within these populations are several dozen to possibly tens of thousands of objects large enough that they have been rounded by their own gravity. Such objects are categorized as dwarf planets, identified dwarf planets include the asteroid Ceres and the trans-Neptunian objects Pluto and Eris. In addition to two regions, various other small-body populations, including comets, centaurs and interplanetary dust clouds. Six of the planets, at least four of the dwarf planets, each of the outer planets is encircled by planetary rings of dust and other small objects. The solar wind, a stream of charged particles flowing outwards from the Sun, the heliopause is the point at which pressure from the solar wind is equal to the opposing pressure of the interstellar medium, it extends out to the edge of the scattered disc. The Oort cloud, which is thought to be the source for long-period comets, the Solar System is located in the Orion Arm,26,000 light-years from the center of the Milky Way. For most of history, humanity did not recognize or understand the concept of the Solar System, the invention of the telescope led to the discovery of further planets and moons. The principal component of the Solar System is the Sun, a G2 main-sequence star that contains 99. 86% of the known mass. The Suns four largest orbiting bodies, the giant planets, account for 99% of the mass, with Jupiter. The remaining objects of the Solar System together comprise less than 0. 002% of the Solar Systems total mass, most large objects in orbit around the Sun lie near the plane of Earths orbit, known as the ecliptic
Solar system
–
The
Sun and
planets of the Solar System (distances not to scale)
Solar system
–
Solar System
Solar system
–
Andreas Cellarius 's illustration of the Copernican system, from the Harmonia Macrocosmica (1660)
Solar system
–
The eight planets of the Solar System (by decreasing size) are
Jupiter,
Saturn,
Uranus,
Neptune,
Earth,
Venus,
Mars and
Mercury.
26.
Asteroid belt
–
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
–
Sun Jupiter trojans Orbits of
planets
Asteroid belt
–
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
–
951 Gaspra, the first asteroid imaged by a spacecraft, as viewed during
Galileo ' s 1991 flyby; colors are exaggerated
27.
Asteroid
–
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
–
2013 EC, shown here in radar images, has a provisional designation
Asteroid
–
⚵
Asteroid
–
243 Ida and its moon Dactyl. Dactyl is the first satellite of an asteroid to be discovered.
28.
171st Air Refueling Squadron
–
The 171st Air Refueling Squadron is a unit of the Michigan Air National Guards 127th Wing located at Selfridge Air National Guard Base, Michigan. The 171st is equipped with the KC-135T Stratotanker, established in early-1943 as a P-47 Thunderbolt fighter squadron, the 374th Fighter Squadron trained under I Fighter Command in the mid-Atlantic states. Also flew air-defense missions as part of the Philadelphia Fighter Wing, deployed to the European Theater of Operations as part of the 361st Fighter Group, being assigned to VIII Fighter Command in England, November 1943. The unit served primarily as an organization, covering the penetration, attack. The squadron also engaged in patrols, fighter sweeps. Attacked such targets as airdromes, marshalling yards, missile sites, industrial areas, ordnance depots, oil refineries, trains, the unit returned to Little Walden and flew its last combat mission on April 20,1945. Demobilized during the summer of 1945 in England, inactivated in the United States as a unit in October. The wartime 374th Fighter Squadron was re-designated as the 171st Fighter Squadron and it was organized at Wayne County Airport, Michigan, and was extended federal recognition on 25 April 1948. The 171st Fighter Squadron was entitled to the history, honors, the squadron was equipped with F-47D Thunderbolts and was assigned to the Michigan ANG 127th Fighter Group. The unit was ordered into service on February 1,1951, as a result of the Korean War. In March 1951 being assigned F-51 Mustangs, F-80 Shooting Stars, the unit was relieved from active duty in November 1952, was redesignated as a Fighter-Bomber squadron. Mission aircraft were F-51H, F-86E and F-89C, redesignated at Tactical Reconnaissance Squadron in 1958. Moving to Selfridge Air National Guard Base in 1971 and upgrading to the newer RF-101 Voodoo, became an Aerospace Defense Command Fighter-Interceptor squadron in 1973, equipped with F-106 Delta Dart interceptors. Performed air defense duties of the Great Lakes and Detroit area until 1978 when ADCOM was merged into Tactical Air Command, continued air defense mission for ADTAC component of TAC with F-4 Phantom IIs, transferring to First Air Force when ADTAC was replaced in 1985. Upgraded to F-16A Fighting Falcons in 1990, realigned into an airlift squadron in 1993, equipped with C-130 Hercules Tactical Airlifters. Flew the C-130 until September 2007 when it was realigned as an Air Refueling Squadron, being equipped with the KC-135T Stratotanker. afhra. af. mil/
171st Air Refueling Squadron
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KC-135T Stratotanker 60-0346 171st Air Refueling Squadron
171st Air Refueling Squadron
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171st Airlift Squadron emblem
171st Air Refueling Squadron
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171st Airlift Squadron C-130 Hercules
171st Air Refueling Squadron
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171st Fighter Squadron F-16A interceptor, 1991
29.
Michigan Air National Guard
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The Michigan Air National Guard is the air force militia of the State of Michigan, United States of America. It is, along with the Michigan Army National Guard, an element of the Michigan National Guard, the Michigan Air National Guard is also an Air Reserve Component of the United States Air Force. As a state militia, the Michigan Air National Guard are not in the United States Air Force chain of command unless it is federalized. They are under the jurisdiction of the Governor of Michigan though the office of the Michigan Adjutant General unless they are federalized by order of the President of the United States. The Michigan Air National Guard is headquartered at the Joint Forces Headquarters compound, located in Lansing, Michigan, Michigan ANG units are trained and equipped by the Air Force and are operationally 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. At the time the C-27J was the newest cargo aircraft in the Air Force inventory, the missions of the C-27 would have included direct support of Army units, homeland security, disaster response, and medical evacuation, as well as multiple other Federal and State requirements. Due to political decisions, the C-27 mission was replaced with a new Remotely Piloted Aircraft MQ-9 Reaper mission, the Wing also supports the Air Force Special Operations Command with its 107th Weather Flight. Support Unit Functions and Capabilities, Alpena Combat Readiness Training Center Houses the Combat Readiness Training Center which trains various units from National Guard, the origins of the Michigan Air National Guard can be traced back to the 107th Aero Squadron, which was organized on 27 August 1917. The squadron assembled, serviced, and repaired aircraft during World War I and it was re-designated 801st Aero Squadron on 1 February 1918 and inactivated after the end of the war on 18 March 1919. The Militia Act of 1903 established the present National Guard system, units raised by the states but paid for by the Federal Government, if federalized by Presidential order, they fall under the regular military chain of command. On 1 June 1920, the Militia Bureau issued Circular No.1 on organization of National Guard air units and it was reformed on 7 May 1926, as the 107th Observation Squadron and is oldest unit of the Michigan Air National Guard. It is one of the 29 original National Guard Observation Squadrons of the United States Army National Guard formed before World War II. The 116th Observation Squadron was ordered into service on 15 October 1940 as part of the buildup of the Army Air Corps prior to the United States entry into World War II. The unit was activated again on 15 October 1940, being redesignated 107th Observation Squadron with Douglas O-38 and it was sent to the airfield at Camp Beauregard, Louisiana for unit training on 28 October 1940. In 1941, the 107th was joined by two other National Guard observation units to form the 67th Observation Group, the 67th Group did anti-submarine patrolling off the East Coast of the US from mid-December 1941 to March 1942, when it returned to Louisiana for training in fighter aircraft. Under War Department policy, many of Michigans National Guard units were detached from their former organizations, such was the case for the 107th Observation Squadron, which entered service with the 32nd Division. The squadron was attached to the 67th Fighter Reconnaissance Group
Michigan Air National Guard
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107th Fighter Squadron - A-10 Thunderbolt II taking off from Selfridge AGB, Detroit. The 107th FS is the oldest unit in the Michigan Air National Guard, having over 80 years of service to the state and nation
Michigan Air National Guard
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Michigan Air National Guard North American P-51D Mustang 44-73227, 1946, prior to the formal establishment of the Air National Guard in September 1947.
30.
KC-135T Stratotanker
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The Boeing KC-135 Stratotanker is a military aerial refueling aircraft. It and the Boeing 707 airliner were developed from the Boeing 367-80 prototype and it is the predominant variant of the C-135 Stratolifter family of transport aircraft. The KC-135 was the US Air Forces first jet-powered refueling tanker, the KC-135 entered service with the United States Air Force in 1957, it is one of six military fixed-wing aircraft with over 50 years of continuous service with its original operator. The KC-135 is supplemented by the larger KC-10, studies have concluded that many of the aircraft could be flown until 2040, although maintenance costs have greatly increased. The aircraft will eventually be replaced by the Boeing KC-46 Pegasus, like its sibling, the commercial Boeing 707 jet airliner, the KC-135 was derived from the Boeing 367-80 jet transport proof of concept demonstrator, which was commonly called the Dash-80. The KC-135 is similar in appearance to the 707, but has a fuselage and is shorter than the 707. The KC-135 predates the 707, and is quite different from the civilian airliner. Boeing gave the future KC-135 tanker the initial designation Model 717, in 1954 USAFs Strategic Air Command held a competition for a jet-powered aerial refueling tanker. Lockheeds tanker version of the proposed Lockheed L-193 airliner with rear fuselage-mounted engines was declared the winner in 1955, in the end, orders for the Lockheed tanker were dropped rather than supporting two tanker designs. Lockheed never produced its jet airliner, while Boeing would eventually dominate the market with a family of airliners based on the 707. In 1954, the Air Force placed an order for 29 KC-135As. The first aircraft flew in August 1956 and the initial production Stratotanker was delivered to Castle Air Force Base, California, the last KC-135 was delivered to the Air Force in 1965. These basic features make it resemble the commercial Boeing 707 and 720 aircraft. The USAF EC-135 Looking Glass was subsequently replaced in its role by the U. S. Navy E-6 Mercury aircraft, the KC-135Q variant was modified to carry JP-7 fuel necessary for the Lockheed SR-71 Blackbird, segregating the JP-7 from the KC-135s own fuel supply. The tanker also had special fuel systems for moving the different fuels between different tanks, the only external difference between a KC-135R and a KC-135T is the presence of a clear window on the underside of the empennage of the KC-135T where a remote controlled searchlight is mounted. It also has two ground refueling ports, located in rear wheel well so ground crews can fuel both the body tanks and wing tanks separately. Eight KC-135R aircraft are receiver-capable tankers, commonly referred to as KC-135R, All eight aircraft were with the 22d Air Refueling Wing at McConnell AFB, Kansas, in 1994. They are primarily used for extension and Special Operations missions
KC-135T Stratotanker
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KC-135 Stratotanker
KC-135T Stratotanker
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USAF KC-135R boom operator view
KC-135T Stratotanker
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A
Cold War -era image of B-52D refueling from a KC-135A
KC-135T Stratotanker
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A nose-on view of several reworked KC-135R aircraft
taxiing prior to takeoff. The new engines are CFM56-2 high-bypass turbofans.
31.
United States Air Force
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The United States Air Force is the aerial warfare service branch of the United States Armed Forces and one of the seven American uniformed services. Initially part of the United States Army, the USAF was formed as a branch of the military on 18 September 1947 under the National Security Act of 1947. It is the most recent branch of the U. S. military to be formed, the U. S. Air Force is a military service organized within the Department of the Air Force, one of the three military departments of the Department of Defense. The Air Force is headed by the civilian Secretary of the Air Force, who reports to the Secretary of Defense, the U. S. Air Force provides air support for surface forces and aids in the recovery of troops in the field. As of 2015, the service more than 5,137 military aircraft,406 ICBMs and 63 military satellites. It has a $161 billion budget with 313,242 active duty personnel,141,197 civilian employees,69,200 Air Force Reserve personnel, and 105,500 Air National Guard personnel. According to the National Security Act of 1947, which created the USAF and it shall be organized, trained, and equipped primarily for prompt and sustained offensive and defensive air operations. The stated mission of the USAF today is to fly, fight, and win in air, space and we will provide compelling air, space, and cyber capabilities for use by the combatant commanders. We will excel as stewards of all Air Force resources in service to the American people, while providing precise and reliable Global Vigilance, Reach and it should be emphasized that the core functions, by themselves, are not doctrinal constructs. The purpose of Nuclear Deterrence Operations is to operate, maintain, in the event deterrence fails, the US should be able to appropriately respond with nuclear options. Dissuading others from acquiring or proliferating WMD, and the means to deliver them, moreover, different deterrence strategies are required to deter various adversaries, whether they are a nation state, or non-state/transnational actor. Nuclear strike is the ability of forces to rapidly and accurately strike targets which the enemy holds dear in a devastating manner. Should deterrence fail, the President may authorize a precise, tailored response to terminate the conflict at the lowest possible level, post-conflict, regeneration of a credible nuclear deterrent capability will deter further aggression. Finally, the Air Force regularly exercises and evaluates all aspects of operations to ensure high levels of performance. Nuclear surety ensures the safety, security and effectiveness of nuclear operations, the Air Force, in conjunction with other entities within the Departments of Defense or Energy, achieves a high standard of protection through a stringent nuclear surety program. The Air Force continues to pursue safe, secure and effective nuclear weapons consistent with operational requirements, adversaries, allies, and the American people must be highly confident of the Air Forces ability to secure nuclear weapons from accidents, theft, loss, and accidental or unauthorized use. This day-to-day commitment to precise and reliable nuclear operations is the cornerstone of the credibility of the NDO mission, positive nuclear command, control, communications, effective nuclear weapons security, and robust combat support are essential to the overall NDO function. OCA is the method of countering air and missile threats, since it attempts to defeat the enemy closer to its source
United States Air Force
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First
F-35 Lightning II of the
33rd Fighter Wing arrives at
Eglin AFB
United States Air Force
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Seal of the Department of the Air Force (
United States Air Force portal)
United States Air Force
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U.S. Air Force airmen from the 720th STG jumping out of a
C-130J Hercules aircraft during water rescue training in the
Florida panhandle
United States Air Force
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Combat Controllers participating in
Operation Enduring Freedom provide air traffic control to a
C-130 taking off from a remote airfield.
32.
171st Air Refueling Wing
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The 171st Air Refueling Wing is a unit of the Pennsylvania Air National Guard, stationed at Pittsburgh IAP Air Reserve Station, Pennsylvania. If activated to service, the Wing is gained by the United States Air Force Air Mobility Command. The 171 ARW presently has 16 aircraft assigned making it the ONLY Super Tanker Wing the Air National Guard, murtha Cambria County Airport in Johnstown Pennsylvania. The 147th being transferred from the 112th Fighter-Interceptor Group and re-designated as the 147th Aeromedical Transport Squadron, the 147th ATS became the 171st ATGs flying squadron. The 147th ATS was converted to twin engine C-119J Flying Boxcar aircraft, other squadrons assigned into the group were the 171st Headquarters, 171st Material Squadron, 171st Combat Support Squadron, and the 171st USAF Dispensary. After two years with the C-119J, the 147th converted to the C-121G Super Constellation, with the Super Constellation the primary mission of the 147th was to perform military airlift, with a secondary mission of aeromedical evacuation. In 1968, the unit was re-designated as the 171st Aeromedical Airlift Group, later that year, the 171st was called to active duty to augment the airlift capability of the 375th Aeromedical Airlift Wing, Scott AFB, Illinois. The Group flew 35% of these missions, flying 510 sorties, the unit was finally released from active duty in December 1968 and returned to Pennsylvania Commonwealth control. Conforming to the new policy of the Department of Defense, the Air National Guard began to play a greater role in fulfilling total U. S. force requirements. An extensive reorganization of the National Guard system was accomplished, as a result of these actions, the 171st Aeromedical Airlift Group was re-designated as the 171st Air Refueling Wing in October 1972, transitioning from the C-121G to the KC-97L Stratotanker. On 1 July 1976, the Wing received notice of reassignment to the Strategic Air Command, a year later, the Wing transitioned to the KC-135A Stratotanker, a four-engine jet aircraft. This was a significant upgrade, increasing the Wings air refueling capacity, in 1982, the ANG increased its mission capability through an interim program by retrofitting commercial Boeing 707 engines to their tankers re-designating the aircraft to the KC-135E. Members of the 171 ARW volunteered for duty in Saudi Arabia in order to participate in air refueling missions for Operation Desert Shield and these operations were upgraded to a full federal activation in December 1990 through May 1991. During this period over 300 members of the unit were deployed throughout the world in numerous functions supporting both Desert Shield and combat operations during Operation Desert Storm. During this period the 171st ARW refueled nearly 3,000 allied aircraft while stationed near the Iraqi border in support of air missions against Iraqi forces. Maintaining a remarkable 100% mission effectiveness rate, the 171st flew 556 combat missions, Strategic Air Command was inactivated in June 1992 and the 112th ARG became a part of the Air Combat Command. The 112th Air Refueling Group was inactivated, with the consolidation, The 171st ARW consisted of 16 aircraft assigned to two squadrons, making it one of only three Super Tanker Wings within the Air National Guard. In May 1999, the 171st activated over 500 members and fourteen aircraft to Budapest, Hungary and Frankfurt, Germany, the 147th became part of the 171st Expeditionary Operations Group that flew 411 sorties and refueled 2,157 receivers
171st Air Refueling Wing
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171st Air Refueling Wing Boeing KC-135T Stratotanker landing at Pittsburgh AGB
33.
Air Mobility Command
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Air Mobility Command is a Major Command of the U. S. Air Force. AMC is headquartered at Scott Air Force Base, Illinois, east of St. Louis, the Commander of AMC is Gen Carlton D. Everhart II, with Lt Gen Wayne Schatz Jr as Vice Commander and CMSgt Shelina Frey as Command Chief Master Sergeant. Air Mobility Command was established on June 1,1992 and it was formed from elements of the inactivated Military Airlift Command and Strategic Air Command. AMC melded a worldwide system with a tanker force that had been freed from its strategic nuclear strike commitments by the dissolution of the Soviet Union. Air Mobility Commands mission is to provide global air mobility, the command also plays a crucial role in providing humanitarian support at home and around the world. Many special duty and operational aircraft and stateside aeromedical evacuation missions are also assigned to AMC. U. S. forces must be able to provide a rapid, tailored response with a capability to intervene against a foe, hit hard. Rapid global mobility lies at the heart of U. S. strategy in this environment, without the capability to project forces, there is no conventional deterrent. As the number of U. S. forces stationed overseas continue to decline, global interests remain, Air Mobility Command also has the mission of establishing bare air bases in contingencies. To accomplish this mission, AMC established two Contingency Response Wings, and operates the Eagle Flag exercise, in addition to its status as a MAJCOM of the Air Force, AMC is also the Air Force component command of the United States Transportation Command. It provides airlift, special missions, aerial refueling, and aeromedical evacuation for the United States armed forces]], AMC also operates VIP flights such as Air Force One, Air Force Two, and other Special Assignment Airlift Missions. Finally, AMC acts as the manager, on behalf of United States Transportation Command. Principal aircraft assets of the include, C-17 Globemaster III, C-5 Galaxy, C-130 Hercules, KC-135 Stratotanker, KC-10 Extender, C-40 Clipper, C-37 Gulfstream V. As of 2015, the command is preparing for the addition of the KC-46 Pegasus. Additional aircraft in support of high-profile VIP airlift include, VC-25, C-32, C-20 and these units train and exercise frequently and routinely provide augmentative operational support to AMCs active duty forces. Instead, they report to AMC via the National Guard Bureau, civil Reserve Air Fleet AMC has undergone considerable change since its establishment. Focusing on the mission of strategic air mobility, the command divested itself of infrastructure. The Air Rescue Service, intratheater aeromedical airlift forces based overseas, as a result of the Global War on Terrorism, on October 1,2003, AMC underwent a major restructuring, bringing a war fighting role to its numbered air force
Air Mobility Command
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Air Mobility Command Headquarters building, Scott Air Force Base, Illinois
Air Mobility Command
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Air Mobility Command emblem
Air Mobility Command
Air Mobility Command
34.
Pennsylvania Air National Guard
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The Pennsylvania Air National Guard is the air force militia of the Commonwealth of Pennsylvania, United States of America. It is, along with the Pennsylvania Army National Guard, an element of the Pennsylvania National Guard, as commonwealth militia units, the units in the Pennsylvania Air National Guard are not in the normal United States Air Force chain of command. They are under the jurisdiction of the Governor of Pennsylvania through the office of the Pennsylvania Adjutant General unless they are federalized by order of the President of the United States. The Pennsylvania Air National Guard is headquartered at Fort Indiantown Gap, Pennsylvania, under the Total Force concept, Pennsylvania Air National Guard units are considered to be Air Reserve Components of the United States Air Force. Pennsylvania ANG units are trained and equipped by the Air Force and are gained by a Major Command of the USAF if federalized. Commonwealth missions include disaster relief in times of earthquakes, hurricanes, floods and forest fires, search and rescue, protection of public services. 201st Red Horse Civil Engineering Flight, located at Fort Indiantown Gap, regional Equipment Operators Training Site, located at Fort Indiantown Gap. 203d Weather Flight, located at Fort Indiantown Gap, 211th Engineering Installation Squadron, located at Fort Indiantown Gap. 258th Air Traffic Control Squadron, located at Johnstown-Cambria County Airport 270th Engineering Installation Squadron, 271st Combat Communications Squadron, located at Fort Indiantown Gap. 553d Air Force Band, located at Fort Indiantown Gap, lightning Force Academy, affiliated with the Community College of the Air Force and is located at Fort Indiantown Gap. Bollen Air-to-Ground Weapons Range, located at Fort Indiantown Gap, the Militia Act of 1903 established the present National Guard system, units raised by the states but paid for by the Federal Government, liable for immediate state service. If federalized by Presidential order, they fall under the military chain of command. On 1 June 1920, the Militia Bureau issued Circular No.1 on organization of National Guard air units, the Pennsylvania Air National Guard was formed on 27 June 1924 as the 103d Squadron, Pennsylvania National Guard, received federal recognition as a Corps Aviation unit. The 103d was founded and eventually commanded by Major Charles Biddle and this new National Guard squadron was based on the sod fields of Philadelphia Airport as a unit in the Army 28th Division. It is one of the 29 original National Guard Observation Squadrons of the United States Army National Guard formed before World War II, the pilots of the 103d flew a wide variety of observation aircraft for the next 18 years. The most well-known of these aircraft was the JN-4 Jenny, the Jenny was an open-cockpit bi-plane, but was replaced in the 1930s and early 1940s with metal-skinned, prop-driven observation monoplanes. The list is long but shows the improvement in aircraft, PT-1, BT-1, O-1, O-2H, O-11, O-38, O-46, -47A, O-47B, O-49, O-52, O-57. The squadron also flew liaison type aircraft such as the L-4, the 103d Observation Squadron was ordered into active service on 125 November 1940 as part of the buildup of the Army Air Corps prior to the United States entry into World War II
Pennsylvania Air National Guard
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Pennsylvania ANG 193d Special Operations Wing Commando Solo EC-130J.
Pennsylvania Air National Guard
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103d Fighter Bomber Squadron North American F-51D Mustang 44-73551 at Philadelphia International Airport
35.
Canadian Expeditionary Force
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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.
36.
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
37.
171st Infantry Brigade (United States)
–
The 171st Infantry Brigade is an infantry brigade of the United States Army based in Fort Jackson, South Carolina. With a long history of serving, the brigade saw action during both World War I and World War II before it was inactivated in 1946, during the Cold War the brigade was once again activated for a period of ten years until again inactivated in 1972. In 2007 the brigade was reactivated as a support unit. Constituted 5 August 1917 in the National Army as Headquarters, 171st Infantry Brigade, Organized 3 September 1917 at Camp Grant in Rockford, Illinois. Demobilized in January 1919 at Camp Grant, Illinois, reconstituted 24 June 1921 in the Organized Reserves as Headquarters and headquarters Company, 171st Infantry Brigade, and assigned to the 86th Division. Organized in July 1922 at Chicago, Illinois, redesignated 23 March 1925 as Headquarters and Headquarters Company, 171st Brigade. Redesignated 24 August 1936 as Headquarters and Headquarters Company, 171st Infantry Brigade, converted and redesignated 31 March 1942 as the 86th Reconnaissance Troop, 86th Division. Troop ordered into military service 15 December 1942 and reorganized at Camp Howze, Texas, as the 86th Cavalry Reconnaissance Troop. Reorganized and redesignated 5 August 1943 as the 86th Reconnaissance Troop, reorganized and redesignated 10 October 1945 as the 86th Mechanized Reconnaissance Troop. Inactivated 30 December 1946 in the Philippine Islands, Brigade activated 1 July 1963 at Fort Wainwright in Fairbanks, Alaska. Inactivated 13 November 1972 in Alaska, while in Alaska included elements of the 40th Armor Regiment. Brigade included A Co, 40th Armor, 4th battalion, 9th inf, 1st battalion, 47th inf. 15th field artillery, 171st transportation, the 12th aviation battalion was also located at Fort Wainwright but I dont remember if it was part of the 171st Inf. brigade. I was a repairman in D Company 171st support battalion. Captain David Braithwaite was commander of Company D, 171st Support Battalion from 20 August 1965 to 21 July 1967, in 1966 the 4th battalion, 9th infantry deployed to Vietnam. The 559th Engineer Company was also a part of the 171st Infantry Brigade, in 1968 the 559th was commanded by Major William D. Anderson, who, after being assigned to South Vietnam was succeeded by the most capable Captain Peter V. B. Although, the 171st inf is now located in Fort Jackson, SC, the patch depicts the a sword with mountains of the Alaskan range, a similar patch of the 172nd Inf Brigade depicts the sword, mountains, and the constellation Big Dipper. The 171st Infantry Brigade was assigned to Fort Wainwright AK, near Fairbanks and its primary mission was to defend Eielson AFB. The 172nd Inf Brigade was near Anchorage, AK and its mission was to defend Elmendorf AFB
171st Infantry Brigade (United States)
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Some soldiers assigned to the 187th Ordnance Battalion are training
171st Infantry Brigade (United States)
–
171st Infantry Brigade shoulder sleeve insignia
38.
Fort Jackson (South Carolina)
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Fort Jackson is a United States Army installation, which TRADOC operates on for Basic Combat Training, and is located next to Columbia, South Carolina. This installation is named for Andrew Jackson, a United States Army General, Fort Jackson was created in 1917 as the United States entered World War I. At the conclusion of World War I, Camp Jackson was shut down,33, War Department,27 July 1921. Camp Jackson was reactivated for World War II, Fort Jackson is the largest and most active Initial Entry Training Center in the U. S. Army, training 50 percent of all soldiers and 60 percent of the women entering the Army each year. Providing the Army with new soldiers is the primary mission. 35,000 potential soldiers attend basic training and 8,000 advanced individual training soldiers train at Fort Jackson annually, Soldiers who have trained or worked at Fort Jackson live by the bases motto, Victory Starts Here. The training is provided by the 165th, 171st, and 193rd Infantry Brigades Monday through Sunday for a ten-week period, the post has other missions as well. Fort Jackson encompasses more than 52,000 acres of land, including 100 ranges and field training sites, Soldiers, civilians, retirees and family members make up the Fort Jackson community that continues to grow in numbers and facilities. An additional 10,000 soldiers attend courses at the Soldier Support Institute, Chaplain Center and School,12,000 military families make Fort Jackson their home. Close to 3,500 civilians are employed at Fort Jackson and 46, 000-plus retirees, on base, visitors can visit the U. S. Army Basic Combat Training Museum, previously known as Fort Jackson Museum when opened in 1974. The museum helps visitors to learn the history of Fort Jackson since created in 1917, admission into the Combat Training Museum is open Monday through Friday, except for Federal Holidays, and admission is free. Located in the heart of the region of South Carolina. Columbia has direct access to three interstate highways, I-20, I-26 and I-77, and indirect access to two additional interstates within 100 miles, I-95 and I-85. Average temperatures in the range from a high of 90+ °F in July to a low of 34 °F in January. Annual rainfall averages around 48 inches, the fort has a significant economic impact on the local area. Annual expenditures by Fort Jackson exceed $716.9 million for salaries, utilities, contracts, in addition, over 100,000 family members visit the Midlands area each year to attend basic training graduation activities, using local hotels, restaurants and shopping areas. In the 1994 film Renaissance Man, starring Danny DeVito, Mark Wahlberg, desmond Doss, Medal of Honor recipient Leonard Nimoy, actor, writer, film director, poet, musician, and photographer was in the Special Services division and was sergeant over Corporal Ken Berry. Joe Plumeri, Chairman & CEO of Willis Group Holdings, geoff Ramsey, film producer, actor, photojournalist served in Kuwait Clayton, K. B
Fort Jackson (South Carolina)
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USATC & Fort Jackson Distinctive Unit Insignia
39.
South Carolina
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South Carolina /ˌsaʊθ kærəˈlaɪnə/ is a state in the southeastern region of the United States. The state is bordered to the north by North Carolina, to the south and west by Georgia across the Savannah River, South Carolina became the eighth state to ratify the U. S. Constitution, doing so on May 23,1788. South Carolina became the first state to vote to secede from the Union on December 20,1860, after the American Civil War, it was readmitted into the United States on June 25,1868. South Carolina is the 40th most extensive and the 23rd most populous U. S. state and its GDP as of 2013 was $183.6 billion, with an annual growth rate of 3. 13%. The capital and largest city is Columbia with a 2013 population of 133,358, South Carolina is named in honor of King Charles I of England, under whose reign the English colony was first formed, with Carolus being Latin for Charles. There is evidence of activity in the area about 12000 years ago. Along the Savannah River were the Apalachee, Yuchi, and the Yamasee, further west were the Cherokee, and along the Catawba River, the Catawba. These tribes were village-dwellers, relying on agriculture as their food source. The Cherokee lived in wattle and daub houses made with wood and clay, about a dozen separate small tribes summered on the coast harvesting oysters and fish, and cultivating corn, peas and beans. Travelling inland as much as 50 miles mostly by canoe, they wintered on the plain, hunting deer and gathering nuts. The names of these survive in place names like Edisto Island, Kiawah Island. The Spanish were the first Europeans in the area, in 1521, founding San Miguel de Gualdape, established with 500 settlers, it was abandoned within a year by 150 survivors. In 1562 French settlers established a settlement at what is now the Charlesfort-Santa Elena archaeological site on Parris Island, three years later the Spanish built a fort on the same site, but withdrew following hostilities with the English navy. In 1629, King Charles I of England established the Province of Carolina an area covering what is now South and North Carolina, Georgia, in the 1670s, English planters from the Barbados established themselves near what is now Charleston. Settlers built rice plantations in the South Carolina Lowcountry, east of the Atlantic Seaboard fall line, settlers came from all over Europe. Plantation labor was done by African slaves who formed the majority of the population by 1720, another cash crop was the Indigo plant, a plant source of blue dye, developed by Eliza Lucas. Meanwhile, in Upstate South Carolina, west of the Fall Line, was settled by farmers and traders. Colonists overthrew the rule, seeing more direct representation
South Carolina
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Released in 2000
South Carolina
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Flag
South Carolina
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Table Rock State Park in the mountains of South Carolina
South Carolina
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Francis Marion National Forest in
Berkeley County
40.
USS Burns (DD-171)
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USS Burns was a Wickes-class destroyer built for the United States Navy during World War I. The Wickes class was an improved and faster version of the preceding Caldwell-class, two different designs were prepared to the same specification that mainly differed in the turbines and boilers used. The ships displaced 1, 202–1,208 long tons at load and 1. They had a length of 314 feet 4 inches, a beam of 30 feet 11 inches. They had a crew of 6 officers and 108 enlisted men, performance differed radically between the ships of the class, often due to poor workmanship. The Wickes class was powered by two turbines, each driving one propeller shaft, using steam provided by four water-tube boilers. The turbines were designed to produce a total of 27,000 shaft horsepower intended to reach a speed of 35 knots, the ships carried 225 long tons of fuel oil which was intended gave them a range of 2,500 nautical miles at 20 knots. The ships were armed with four 4-inch guns in single mounts and were fitted with two 1-pdr guns for anti-aircraft defense and their primary weapon, though, was their torpedo battery of a dozen 21-inch torpedo tubes in four triple mounts. In many ships a shortage of 1-pounders caused them to be replaced by 3-inch anti-aircraft guns and they also carried a pair of depth charge rails. A Y-gun depth charge thrower was added to many ships, Burns was attached to Destroyer Force, Pacific, until March 1920 when she was ordered to special duty as a tender for NC Seaplane Division. On 15 March 1921 she was reclassified DM-11 and on 5 May she was assigned to the Mine Force, Pacific. She was at Mare Island Navy Yard 11 July undergoing conversion and overhaul when her home yard was changed and she departed for Naval Station Pearl Harbor, in 1925 she joined the Fleet for a tour of Australia and New Zealand. In the summers of 1926,1927, and 1928 she conducted training cruises for Naval Reservists, in 1927 Burns returned to San Diego with her squadron for inspection, training, and recreation. Returning to Pearl Harbor, she participated in mining and gunnery practice, arriving at San Diego 26 November, Burns was decommissioned 2 June 1930. On 11 June she was towed to Mare Island Navy Yard where she was used as a barracks ship and she was later scrapped and her material sold 22 April 1932. U. S. Destroyers, An Illustrated Design History, gardiner, Robert & Gray, Randal, eds. Conways All the Worlds Fighting Ships, 1906–1921 and this article incorporates text from the public domain Dictionary of American Naval Fighting Ships. The entry can be found here, photo gallery of Burns at NavSource Naval History
USS Burns (DD-171)
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History
41.
United States Navy
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The United States Navy is the naval warfare service branch of the United States Armed Forces and one of the seven uniformed services of the United States. The U. S. Navy is the largest, most capable navy in the world, the U. S. Navy has the worlds largest aircraft carrier fleet, with ten in service, two in the reserve fleet, and three new carriers under construction. The service has 323,792 personnel on duty and 108,515 in the Navy Reserve. It has 274 deployable combat vessels and more than 3,700 operational aircraft as of October 2016, the U. S. Navy traces its origins to the Continental Navy, which was established during the American Revolutionary War and was effectively disbanded as a separate entity shortly thereafter. It played a role in the American Civil War by blockading the Confederacy. It played the role in the World War II defeat of Imperial Japan. The 21st century U. S. Navy maintains a global presence, deploying in strength in such areas as the Western Pacific, the Mediterranean. The Navy is administratively managed by the Department of the Navy, the Department of the Navy is itself a division of the Department of Defense, which is headed by the Secretary of Defense. The Chief of Naval Operations is an admiral and the senior naval officer of the Department of the Navy. The CNO may not be the highest ranking officer in the armed forces if the Chairman or the Vice Chairman of the Joint Chiefs of Staff. The mission of the Navy is to maintain, train and equip combat-ready Naval forces capable of winning wars, deterring aggression, the United States Navy is a seaborne branch of the military of the United States. The Navys three primary areas of responsibility, The preparation of naval forces necessary for the prosecution of war. The development of aircraft, weapons, tactics, technique, organization, U. S. Navy training manuals state that the mission of the U. S. Armed Forces is to prepare and conduct prompt and sustained combat operations in support of the national interest, as part of that establishment, the U. S. Navys functions comprise sea control, power projection and nuclear deterrence, in addition to sealift duties. It follows then as certain as that night succeeds the day, that without a decisive naval force we can do nothing definitive, the Navy was rooted in the colonial seafaring tradition, which produced a large community of sailors, captains, and shipbuilders. In the early stages of the American Revolutionary War, Massachusetts had its own Massachusetts Naval Militia, the establishment of a national navy was an issue of debate among the members of the Second Continental Congress. Supporters argued that a navy would protect shipping, defend the coast, detractors countered that challenging the British Royal Navy, then the worlds preeminent naval power, was a foolish undertaking. Commander in Chief George Washington resolved the debate when he commissioned the ocean-going schooner USS Hannah to interdict British merchant ships, and reported the captures to the Congress
United States Navy
United States Navy
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United States Navy portal
United States Navy
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USS Constellation vs L'Insurgente during the
Quasi-War
United States Navy
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USS Constitution vs HMS Guerriere during the
War of 1812
42.
Wickes-class destroyer
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The Wickes-class destroyers were a class of 111 destroyers built by the United States Navy in 1917–19. Along with the 6 preceding Caldwell-class and 156 subsequent Clemson-class destroyers, only a few were completed in time to serve in World War I, including USS Wickes, the lead ship of the class. While some were scrapped in the 1930s, the rest served through World War II, most of these were converted to other uses, nearly all in U. S. service had half their boilers and one or more stacks removed to increase fuel and range or accommodate troops. Others were transferred to the British Royal Navy and the Royal Canadian Navy, All were scrapped within a few years after World War II. The destroyer type was at time a relatively new class of fighting ship for the U. S. Navy. The type arose in response to torpedo boats that had been developing from 1865, a series of destroyers had been built over the preceding years, designed for high smooth water speed, with indifferent results, especially poor performance in heavy seas and poor fuel economy. The lesson of these destroyers was the appreciation of the need for true seakeeping and seagoing abilities. There were few cruisers in the Navy, which was a fleet of battleships and destroyers so destroyers performed scouting missions. A report of October 1915 by Captain W. S. Sims noted that the smaller destroyers used fuel far too quickly, and that war games showed the need for fast vessels with a larger radius of action. As a result, the size of U. S. destroyer classes increased steadily, starting at 450 tons and rising to over 1,000 tons between 1905 and 1916. The increase in size has never stopped, with some US Arleigh Burke-class destroyers now up to 10,800 tons full load. With World War I then in its year and tensions between the U. S. and Germany increasing, the U. S. needed to expand its navy. The Naval Appropriation Act of 1916 called for a second to none. The Act authorized 10 battleships,6 Lexington-class battlecruisers,10 Omaha-class scout cruisers, a subsequent General Board recommendation for further destroyers to combat the submarine threat resulted in a total of 267 Wickes- and Clemson-class destroyers completed. However, the design of the ships remained optimized for operation with the battleship fleet, the requirements of the new design were high speed and mass production. The development of warfare during World War I created a requirement for destroyers in numbers that had not been contemplated before the war. A top speed of 35 knots was needed for operation with the Lexington battlecruisers, the final design had a flush deck and four smokestacks. It was a fairly straightforward evolution of the preceding Caldwell class, General dissatisfaction with the earlier 1,000 ton designs led to the fuller hull form of the flush deck type
Wickes-class destroyer
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USS Wickes (DD-75)
Wickes-class destroyer
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8 ships of Wickes class destroyer, New York Shipbuilding Corporation, Camden, New Jersey, 1919.
43.
Destroyer
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Before World War II, destroyers were light vessels with little endurance for unattended ocean operations, typically a number of destroyers and a single destroyer tender operated together. After the war, the advent of the missile allowed destroyers to take on the surface combatant roles previously filled by battleships. This resulted in larger and more powerful guided missile destroyers more capable of independent operation, the emergence and development of the destroyer was related to the invention of the self-propelled torpedo in the 1860s. A navy now had the potential to destroy an enemy battle fleet using steam launches to launch torpedoes. Fast boats armed with torpedoes were built and called torpedo boats, the first seagoing vessel designed to fire the self-propelled Whitehead torpedo was the 33-ton HMS Lightning in 1876. She was armed with two drop collars to launch these weapons, these were replaced in 1879 by a torpedo tube in the bow. By the 1880s, the type had evolved into small ships of 50–100 tons, in response to this new threat, more heavily gunned picket boats called catchers were built which were used to escort the battle fleet at sea. The anti-torpedo boat origin of this type of ship is retained in its name in other languages, including French, Italian, Portuguese, Czech, Greek, Dutch and, up until the Second World War, Polish. At that time, and even into World War I, the function of destroyers was to protect their own battle fleet from enemy torpedo attacks. The task of escorting merchant convoys was still in the future, an important development came with the construction of HMS Swift in 1884, later redesignated TB81. This was a torpedo boat with four 47 mm quick-firing guns. At 23.75 knots, while still not fast enough to engage torpedo boats reliably. Another forerunner of the torpedo boat destroyer was the Japanese torpedo boat Kotaka, designed to Japanese specifications and ordered from the London Yarrow shipyards in 1885, she was transported in parts to Japan, where she was assembled and launched in 1887. The 165-foot long vessel was armed with four 1-pounder quick-firing guns and six torpedo tubes, reached 19 knots, in her trials in 1889, Kotaka demonstrated that she could exceed the role of coastal defense, and was capable of accompanying larger warships on the high seas. The Yarrow shipyards, builder of the parts for the Kotaka, the first vessel designed for the explicit purpose of hunting and destroying torpedo boats was the torpedo gunboat. Essentially very small cruisers, torpedo gunboats were equipped with torpedo tubes, by the end of the 1890s torpedo gunboats were made obsolete by their more successful contemporaries, the torpedo boat destroyers, which were much faster. The first example of this was HMS Rattlesnake, designed by Nathaniel Barnaby in 1885, the gunboat was armed with torpedoes and designed for hunting and destroying smaller torpedo boats. Exactly 200 feet long and 23 feet in beam, she displaced 550 tons, built of steel, Rattlesnake was un-armoured with the exception of a 3⁄4-inch protective deck
Destroyer
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USS Winston S. Churchill, an
Arleigh Burke-class guided missile destroyer of the
United States Navy
Destroyer
Destroyer
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The
Imperial Japanese Navy 's Kotaka (1887)
Destroyer
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HMS Havock the first modern destroyer, commissioned in 1894
44.
Cannon-class destroyer escort
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The Cannon class was a class of destroyer escorts were built by the United States primarily for ocean anti-submarine warfare escort service during World War II. The lead ship, USS Cannon, was commissioned on 26 September 1943 at Wilmington, of the 116 ships ordered 44 were canceled and six commissioned directly into the Free French Forces. Destroyer escorts were regular companions escorting the cargo ships. BRP Rajah Humabon of the Philippine Navy, formerly USS Atherton, the class was also known as the DET type from their Diesel Electric Tandem drive. The DETs substitution for a propulsion plant was the primary difference with the predecessor Buckley class. The DET was in turn replaced with a direct drive diesel plant to yield the design of the successor Edsall class, a total of 72 ships of the Cannon class were built. Evans as Berbère, served 1952-1960 USS Riddle as Kabyle, served 1950-1959 USS Samuel S
Cannon-class destroyer escort
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USS Cannon (DE-99)
Cannon-class destroyer escort
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BRP Rajah Humabon (PF-11) of the Philippine Navy
45.
Destroyer escort
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Destroyer escort was the United States Navy mid-20th century classification for a 20-knot warship designed with endurance to escort mid-ocean convoys of merchant marine ships. Kaibōkan were designed for a role in the Imperial Japanese Navy. The Royal Navy and Commonwealth forces identified such warships as frigates, Destroyer escorts, frigates and kaibōkan were mass-produced for World War II as a less expensive anti-submarine warfare alternative to fleet destroyers. Post-war destroyer escorts and frigates were larger than those produced during wartime, with increased anti-aircraft capability, as Cold War destroyer escorts became as large as wartime destroyers, the United States Navy converted some of their World War II destroyers to escort destroyers. Full-size destroyers must be able to steam as fast or faster than the fast capital ships such as carriers and cruisers. This typically requires a speed of 25–35 knots and they must carry torpedoes and a smaller caliber of cannon to use against enemy ships, as well as anti-submarine detection equipment and weapons. A destroyer escort needed only to be able to maneuver relative to a slow convoy and these lower requirements greatly reduce the size, cost, and crew required for the destroyer escort. Destroyer escorts were optimized for anti-submarine warfare, having a turning radius. Their much slower speed was not a liability in this context, Destroyer escorts were also considerably more sea-kindly than corvettes. Electric drive was selected because it does not need gearboxes to adjust engine speed to the much lower optimum speed for the propellers, Destroyer escorts were also useful for coastal anti-submarine and radar picket ship duty. During World War II, seven destroyer escorts were converted to radar picket destroyer escorts, although these were relegated to secondary roles after the war, in the mid-1950s twelve more DEs were converted to DERs, serving as such until 1960-1965. Their mission was to extend the Distant Early Warning line on coasts, in conjunction with sixteen Guardian-class radar picket ships, which were converted Liberty ships. In World War II, some 95 destroyer escorts were converted by the US to high-speed transports and this involved adding an extra deck which allowed space for about 10 officers and 150 men. Two large davits were installed, one on either side of the ship. This enabled the UK to commission the US to design, build and supply an escort vessel that was suitable for anti-submarine warfare in deep open ocean situations, cochrane of the American Bureau of Shipping came up with a design which was known as the British Destroyer Escort. S. Navy and one to the Royal Navy, after World War II United States Navy destroyer escorts were referred to as ocean escorts, but retained the hull classification symbol DE. However other navies, most notably those of NATO countries and the USSR, in order to remedy this problem the 1975 ship reclassification reclassified ocean escorts as frigates. This brought the USNs nomenclature more in line with NATO, as of 2006 there are no plans for future frigates for the US Navy
Destroyer escort
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USS Evarts (DE-5), an example of the Evarts subclass.
Destroyer escort
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USS Dealey (DE-1006)
Destroyer escort
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HMS Dacres, converted to act as a headquarters ship during
Operation Neptune
46.
Cargo ship
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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
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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
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Loading of a general cargo vessel in 1959
Cargo ship
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A Delmas container ship unloading at the Zanzibar port in Tanzania
47.
USS Cuttlefish (SS-171)
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USS Cuttlefish, a Cachalot-class submarine and one of the V-boats, was the second ship of the United States Navy to be named for the cuttlefish. Her keel was laid down by Electric Boat Company in Groton and she was launched on 21 November 1933 sponsored by Mrs. B. S. Bullard, and commissioned on 8 June 1934, Lieutenant Commander Charles W. Gin Styer in command. Four Peruvian R-class submarines had previously finished in Groton, using material from cancelled S-boats salvaged from Fore River. Cuttlefish differed from her sister Cachalot mainly in her innovative welded construction, wartime experience would later prove that welding was a sound technique. Both were medium-sized submarines built under the limits of the London Naval Treaty of 1930. Despite the calculation process, size reduction had gone too far with the Cachalots, after three Pacific war patrols, Cuttlefish was relegated to training duties in September 1942, once numerous Gato-class boats became available. The auxiliary engine was for charging batteries or for increased surface speed via a system providing power to the main electric motors. As with most V-boats, the engines proved troublesome, and were replaced in 1937-38 by two Winton GM 16-278 16-cylinder four-cycle diesels,1,600 hp each. Departing New London, Connecticut on 15 May 1935, Cuttlefish arrived at San Diego, arriving at New London on 28 July, she conducted experimental torpedo firing, sound training, and other operations for the Submarine School. At this time her troublesome MAN engines were replaced with Winton GM engines at the New York Navy Yard in 1937-38, Cuttlefish arrived at Pearl Harbor on 16 June and was based there on patrol duty, as well as joining in battle problems and exercises in the Hawaiian area. That autumn, she cruised to the Samoan Islands, and in 1940 to the West Coast, on 5 October 1941, she cleared Pearl Harbor for an overhaul at the Mare Island Navy Yard. After returning to Pearl Harbor, Cuttlefish put to sea on her first war patrol on 29 January 1942, on 13 February, she performed a reconnaissance of Marcus Island, gaining valuable information, and after patrolling in the Bonin Islands, returned to Midway Island on 24 March. She refitted there and at Pearl Harbor, and on 2 May cleared Midway for her war patrol. From 18–24 May, she reconnoitered Saipan and the part of the Mariana Islands. On 19 May, she attacked a ship, and while maneuvering for a second attack, was detected. She was forced deep to endure four hours of depth charging. The next day an enemy plane caught her on the surface. She returned to Pearl Harbor on 15 June, and there and at Midway prepared for her war patrol
USS Cuttlefish (SS-171)
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History
48.
Cachalot-class submarine
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The Cachalot-class submarines were a pair of medium-sized submarines of the United States Navy built under the tonnage limits of the London Naval Treaty of 1930. They were originally named V-8 and V-9, and so were known as V-boats even though they were unrelated to the seven submarines constructed between World War I and World War II. The previous V-boats were all built in naval shipyards, although externally much like the later fleet submarines, internally the Cachalots were quite different. EB relied on electric welding for the hull, while Portsmouth clung to riveting, during the war, the auxiliary engine was for charging batteries or for increased surface speed via a diesel-electric system providing power to the main electric motors. Despite the calculation process, size reduction had gone too far with the Cachalots, the subsequent Porpoise class were about 300 tons larger, and each succeeding class was incrementally larger than its predecessors through the Gato-class submarines of 1941. After three Pacific war patrols each, the Cachalots were relegated to training duties in September 1942, register of Ships of the U. S. Navy, 1775–1990, Major Combatants, ISBN 0-313-26202-0 Lenton, H. T. American Submarines, ISBN 0-38504-761-4 Silverstone, Paul H, warships of World War II, ISBN 0-87021-773-9 Campbell, John Naval Weapons of World War Two, ISBN 0-87021-459-4 Whitman, Edward C. The Navys Variegated V-Class, Out of One, Many, undersea Warfare, Fall 2003, Issue 20 http, //www. fleetsubmarine. com/sublist. html Gardiner, Robert, Conways all the worlds fighting ships 1922-1946, Conway Maritime Press,1980. Friedman, Norman US Submarines through 1945, An Illustrated Design History, Naval Institute Press, Annapolis,1995, ISBN 1-55750-263-3
Cachalot-class submarine
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USS Cachalot (SS-170) the lead boat of the class
49.
Submarine
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A submarine is a watercraft capable of independent operation underwater. It differs from a submersible, which has more limited underwater capability, the term most commonly refers to a large, crewed vessel. It is also used historically or colloquially to refer to remotely operated vehicles and robots, as well as medium-sized or smaller vessels, such as the midget submarine. The noun submarine evolved as a form of submarine boat, by naval tradition, submarines are usually referred to as boats rather than as ships. Although experimental submarines had been built before, submarine design took off during the 19th century, Submarines were first widely used during World War I, and now figure in many navies large and small. Civilian uses for submarines include marine science, salvage, exploration and facility inspection, Submarines can also be modified to perform more specialized functions such as search-and-rescue missions or undersea cable repair. Submarines are also used in tourism, and for undersea archaeology, most large submarines consist of a cylindrical body with hemispherical ends and a vertical structure, usually located amidships, which houses communications and sensing devices as well as periscopes. In modern submarines, this structure is the sail in American usage, a conning tower was a feature of earlier designs, a separate pressure hull above the main body of the boat that allowed the use of shorter periscopes. There is a propeller at the rear, and various hydrodynamic control fins, smaller, deep-diving and specialty submarines may deviate significantly from this traditional layout. Submarines use diving planes and also change the amount of water, Submarines have one of the widest ranges of types and capabilities of any vessel. Submarines can work at greater depths than are survivable or practical for human divers, modern deep-diving submarines derive from the bathyscaphe, which in turn evolved from the diving bell. In 1578, the English mathematician William Bourne recorded in his book Inventions or Devises one of the first plans for an underwater navigation vehicle and its unclear whether he ever carried out his idea. The first submersible of whose construction there exists reliable information was designed and built in 1620 by Cornelis Drebbel and it was propelled by means of oars. By the mid-18th century, over a dozen patents for submarines/submersible boats had been granted in England, in 1747, Nathaniel Symons patented and built the first known working example of the use of a ballast tank for submersion. His design used leather bags that could fill with water to submerge the craft, a mechanism was used to twist the water out of the bags and cause the boat to resurface. In 1749, the Gentlemens Magazine reported that a design had initially been proposed by Giovanni Borelli in 1680. By this point of development, further improvement in design stagnated for over a century, until new industrial technologies for propulsion. The first military submarine was the Turtle, a hand-powered acorn-shaped device designed by the American David Bushnell to accommodate a single person and it was the first verified submarine capable of independent underwater operation and movement, and the first to use screws for propulsion
Submarine
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A
Russian Navy Typhoon-class submarine underway. Also known as "Project 941".
Submarine
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Drebbel, the first navigable submarine
Submarine
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The French submarine Plongeur
Submarine
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The
Nordenfelt -designed,
Ottoman submarine
Abdül Hamid