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
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In mathematics and computing, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, Hexadecimal numerals are widely used by computer system designers and programmers. As each hexadecimal digit represents four binary digits, it allows a more human-friendly representation of binary-coded values, one hexadecimal digit represents a nibble, which is half of an octet or byte. For example, a byte can have values ranging from 00000000 to 11111111 in binary form. In a non-programming context, a subscript is typically used to give the radix, several notations are used to support hexadecimal representation of constants in programming languages, usually involving a prefix or suffix. The prefix 0x is used in C and related languages, where this value might be denoted as 0x2AF3, in contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers expressed in other bases. There are several conventions for expressing values unambiguously, a numerical subscript can give the base explicitly,15910 is decimal 159,15916 is hexadecimal 159, which is equal to 34510. Some authors prefer a text subscript, such as 159decimal and 159hex, or 159d and 159h. example. com/name%20with%20spaces where %20 is the space character, thus ’, represents the right single quotation mark, Unicode code point number 2019 in hex,8217. In the Unicode standard, a value is represented with U+ followed by the hex value. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #, white, CSS allows 3-hexdigit abbreviations with one hexdigit per component, #FA3 abbreviates #FFAA33. *nix shells, AT&T assembly language and likewise the C programming language, to output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h, some assembly languages use the notation HABCD. Ada and VHDL enclose hexadecimal numerals in based numeric quotes, 16#5A3#, for bit vector constants VHDL uses the notation x5A3. Verilog represents hexadecimal constants in the form 8hFF, where 8 is the number of bits in the value, the Smalltalk language uses the prefix 16r, 16r5A3 PostScript and the Bourne shell and its derivatives denote hex with prefix 16#, 16#5A3. For PostScript, binary data can be expressed as unprefixed consecutive hexadecimal pairs, in early systems when a Macintosh crashed, one or two lines of hexadecimal code would be displayed under the Sad Mac to tell the user what went wrong. Common Lisp uses the prefixes #x and #16r, setting the variables *read-base* and *print-base* to 16 can also used to switch the reader and printer of a Common Lisp system to Hexadecimal number representation for reading and printing numbers. Thus Hexadecimal numbers can be represented without the #x or #16r prefix code, MSX BASIC, QuickBASIC, FreeBASIC and Visual Basic prefix hexadecimal numbers with &H, &H5A3 BBC BASIC and Locomotive BASIC use & for hex. TI-89 and 92 series uses a 0h prefix, 0h5A3 ALGOL68 uses the prefix 16r to denote hexadecimal numbers, binary, quaternary and octal numbers can be specified similarly
Hexadecimal
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Numeral systems
Hexadecimal
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Bruce Alan Martin's hexadecimal notation proposal
Hexadecimal
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Hexadecimal finger-counting scheme.
16.
Vigesimal
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The vigesimal or base 20 numeral system is based on twenty. In a vigesimal system, twenty individual numerals are used. One modern method of finding the extra needed symbols is to write ten as the letter A20, to write nineteen as J20, and this is similar to the common computer-science practice of writing hexadecimal numerals over 9 with the letters A–F. Another method skips over the letter I, in order to avoid confusion between I20 as eighteen and one, so that the number eighteen is written as J20, the number twenty is written as 1020. According to this notation,2020 means forty in decimal = + D020 means two hundred and sixty in decimal = +10020 means four hundred in decimal = + +, in the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example,10 means ten,20 means twenty, in decimal, dividing by three twice only gives one digit periods because 9 is the number below ten. 21, however, the adjacent to 20 that is divisible by 3, is not divisible by 9. Ninths in vigesimal have six-digit periods, the prime factorization of twenty is 22 ×5, so it is not a perfect power. However, its part,5, is congruent to 1. Thus, according to Artins conjecture on primitive roots, vigesimal has infinitely many cyclic primes, but the fraction of primes that are cyclic is not necessarily ~37. 395%. An UnrealScript program that computes the lengths of recurring periods of various fractions in a set of bases found that, of the first 15,456 primes. In many European languages,20 is used as a base, vigesimal systems are common in Africa, for example in Yoruba. Ogún,20, is the basic numeric block, ogójì,40, =20 multiplied by 2. Ogota,60, =20 multiplied by 3, ogorin,80, =20 multiplied by 4. Ogorun,100, =20 multiplied by 5, twenty was a base in the Maya and Aztec number systems. The Maya used the names for the powers of twenty, kal, bak, pic, calab, kinchil. See also Maya numerals and Maya calendar, Mayan languages, Yucatec, the Aztec called them, cempoalli, centzontli, cenxiquipilli, cempoalxiquipilli, centzonxiquipilli and cempoaltzonxiquipilli. Note that the ce prefix at the beginning means one and is replaced with the number to get the names of other multiples of the power
Vigesimal
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Numeral systems
Vigesimal
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The
Maya numerals are a base-20 system.
17.
Base 36
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
Base 36
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Numeral systems
Base 36
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34 senary = 22 decimal, in senary finger counting
Base 36
18.
Natural number
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In mathematics, the natural numbers are those used for counting and ordering. In common language, words used for counting are cardinal numbers, texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers. These chains of extensions make the natural numbers canonically embedded in the number systems. Properties of the numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics, the most primitive method of representing a natural number is to put down a mark for each object. Later, a set of objects could be tested for equality, excess or shortage, by striking out a mark, the first major advance in abstraction was the use of numerals to represent numbers. This allowed systems to be developed for recording large numbers, the ancient Egyptians developed a powerful system of numerals with distinct hieroglyphs for 1,10, and all the powers of 10 up to over 1 million. A stone carving from Karnak, dating from around 1500 BC and now at the Louvre in Paris, depicts 276 as 2 hundreds,7 tens, and 6 ones, and similarly for the number 4,622. A much later advance was the development of the idea that 0 can be considered as a number, with its own numeral. The use of a 0 digit in place-value notation dates back as early as 700 BC by the Babylonians, the Olmec and Maya civilizations used 0 as a separate number as early as the 1st century BC, but this usage did not spread beyond Mesoamerica. The use of a numeral 0 in modern times originated with the Indian mathematician Brahmagupta in 628, the first systematic study of numbers as abstractions is usually credited to the Greek philosophers Pythagoras and Archimedes. Some Greek mathematicians treated the number 1 differently than larger numbers, independent studies also occurred at around the same time in India, China, and Mesoamerica. In 19th century Europe, there was mathematical and philosophical discussion about the nature of the natural numbers. A school of Naturalism stated that the numbers were a direct consequence of the human psyche. Henri Poincaré was one of its advocates, as was Leopold Kronecker who summarized God made the integers, in opposition to the Naturalists, the constructivists saw a need to improve the logical rigor in the foundations of mathematics. In the 1860s, Hermann Grassmann suggested a recursive definition for natural numbers thus stating they were not really natural, later, two classes of such formal definitions were constructed, later, they were shown to be equivalent in most practical applications. The second class of definitions was introduced by Giuseppe Peano and is now called Peano arithmetic and it is based on an axiomatization of the properties of ordinal numbers, each natural number has a successor and every non-zero natural number has a unique predecessor. Peano arithmetic is equiconsistent with several systems of set theory
Natural number
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The
Ishango bone (on exhibition at the
Royal Belgian Institute of Natural Sciences) is believed to have been used 20,000 years ago for natural number arithmetic.
Natural number
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Natural numbers can be used for counting (one
apple, two apples, three apples, …)
19.
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
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Overview
20.
Semiprime
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In mathematics, a semiprime is a natural number that is the product of two prime numbers. The semiprimes less than 100 are 4,6,9,10,14,15,21,22,25,26,33,34,35,38,39,46,49,51,55,57,58,62,65,69,74,77,82,85,86,87,91,93,94, and 95. Semiprimes that are not perfect squares are called discrete, or distinct, by definition, semiprime numbers have no composite factors other than themselves. For example, the number 26 is semiprime and its factors are 1,2,13. The total number of prime factors Ω for a n is two, by definition. A semiprime is either a square of a prime or square-free, the square of any prime number is a semiprime, so the largest known semiprime will always be the square of the largest known prime, unless the factors of the semiprime are not known. It is conceivable, but unlikely, that a way could be found to prove a number is a semiprime without knowing the two factors. A composite n non-divisible by primes ≤ n 3 is semiprime, various methods, such as elliptic pseudo-curves and the Goldwasser-Kilian ECPP theorem have been used to create provable, unfactored semiprimes with hundreds of digits. These are considered novelties, since their construction method might prove vulnerable to factorization, for a semiprime n = pq the value of Eulers totient function is particularly simple when p and q are distinct, φ = = p q − +1 = n − +1. If otherwise p and q are the same, φ = φ = p = p2 − p = n − p and these methods rely on the fact that finding two large primes and multiplying them together is computationally simple, whereas finding the original factors appears to be difficult. In the RSA Factoring Challenge, RSA Security offered prizes for the factoring of specific large semiprimes, the most recent such challenge closed in 2007. In practical cryptography, it is not sufficient to choose just any semiprime, the factors p and q of n should both be very large, around the same order of magnitude as the square root of n, this makes trial division and Pollards rho algorithm impractical. At the same time they should not be too close together, or else the number can be quickly factored by Fermats factorization method. The number may also be chosen so that none of p −1, p +1, q −1, or q +1 are smooth numbers, protecting against Pollards p −1 algorithm or Williams p +1 algorithm. However, these checks cannot take future algorithms or secret algorithms into account, in 1974 the Arecibo message was sent with a radio signal aimed at a star cluster. It consisted of 1679 binary digits intended to be interpreted as a 23×73 bitmap image, the number 1679 = 23×73 was chosen because it is a semiprime and therefore can only be broken down into 23 rows and 73 columns, or 73 rows and 23 columns. Chens theorem Weisstein, Eric W. Semiprime
Semiprime
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Overview
21.
2 (number)
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2 is a number, numeral, and glyph. It is the number following 1 and preceding 3. The number two has many properties in mathematics, an integer is called even if it is divisible by 2. For integers written in a system based on an even number, such as decimal and hexadecimal. If it is even, then the number is even. In particular, when written in the system, all multiples of 2 will end in 0,2,4,6. In numeral systems based on an odd number, divisibility by 2 can be tested by having a root that is even. Two is the smallest and first prime number, and the only prime number. Two and three are the two consecutive prime numbers. 2 is the first Sophie Germain prime, the first factorial prime, the first Lucas prime, the first Ramanujan prime, and it is an Eisenstein prime with no imaginary part and real part of the form 3n −1. It is also a Stern prime, a Pell number, the first Fibonacci prime, and it is the third Fibonacci number, and the second and fourth Perrin numbers. Despite being prime, two is also a highly composite number, because it is a natural number which has more divisors than any other number scaled relative to the number itself. The next superior highly composite number is six, vulgar fractions with only 2 or 5 in the denominator do not yield infinite decimal expansions, as is the case with all other primes, because 2 and 5 are factors of ten, the decimal base. Two is the number x such that the sum of the reciprocals of the powers of x equals itself. In symbols ∑ k =0 ∞12 k =1 +12 +14 +18 +116 + ⋯ =2. This comes from the fact that, ∑ k =0 ∞1 n k =1 +1 n −1 for all n ∈ R >1, powers of two are central to the concept of Mersenne primes, and important to computer science. Two is the first Mersenne prime exponent, the square root of 2 was the first known irrational number. The smallest field has two elements, in the set-theoretical construction of the natural numbers,2 is identified with the set
2 (number)
–
The twos of all four suits in
playing cards
22.
89 (number)
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89 is the natural number following 88 and preceding 90. 89 is, the 24th prime number, following 83 and preceding 97, the smallest Sophie Germain prime to start a Cunningham chain of the first kind of six terms. An Eisenstein prime with no part and real part of the form 3n −1. A Fibonacci number and thus a Fibonacci prime as well, the first few digits of its reciprocal coincide with the Fibonacci sequence due to the identity 189 = ∑ n =1 ∞ F ×10 − =0.011235955 …. A Markov number, appearing in solutions to the Markov Diophantine equation with other odd-indexed Fibonacci numbers, M89 is the 10th Mersenne prime. Although 89 is not a Lychrel number in base 10, it is unusual that it takes 24 iterations of the reverse, among the known non-Lychrel numbers in the first 10000 integers, no other number requires that many or more iterations. The palindrome reached is also unusually large, eighty-nine is, The atomic number of actinium. Messier object M89, a magnitude 11.5 elliptical galaxy in the constellation Virgo, the New General Catalogue object NGC89, a magnitude 13.5 peculiar spiral galaxy in the constellation Phoenix and a member of Roberts Quartet. The Oklahoma Redhawks, an American minor league team, were formerly known as the Oklahoma 89ers. The number alludes to the Land Run of 1889, when the Unassigned Lands of Oklahoma were opened to white settlement, the teams home of Oklahoma City was founded during this event. In Rugby, an 89 or eight-nine move is a following a scrum, in which the number 8 catches the ball. The Elite 89 Award is presented by the U. S. NCAA to the participant in each of the NCAAs 89 championship finals with the highest grade point average. The jersey number 89 has been retired by three National Football League teams in honor of past playing greats, The Baltimore Colts, for Hall of Famer Gino Marchetti, the franchise continues to honor the number in its current identity as the Indianapolis Colts. The Boston Patriots, for Bob Dee, the franchise, now the New England Patriots, continues to honor the number. The Chicago Bears, for Mike Ditka, eighty-nine is also, The designation of Interstate 89, a freeway that runs from New Hampshire to Vermont The designation of U. S. The number of units of each colour in the board game Blokus The number of the French department Yonne Information Is Beautiful cites eighty-nine as one of the words censored on the Chinese internet
89 (number)
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TI-89
23.
Square-free integer
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In mathematics, a square-free, or quadratfrei integer, is an integer which is divisible by no other perfect square than 1. For example,10 is square-free but 18 is not, as 18 is divisible by 9 =32. The smallest positive square-free numbers are 1,2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,30,31,33,34,35,37,38,39. The radical of an integer is its largest square-free factor, an integer is square-free if and only if it is equal to its radical. Any arbitrary positive integer n can be represented in a way as the product of a powerful number and a square-free integer. The square-free factor is the largest square-free divisor k of n that is coprime with n/k, a positive integer n is square-free if and only if in the prime factorization of n, no prime factor occurs with an exponent larger than one. Another way of stating the same is that for every prime factor p of n, also n is square-free if and only if in every factorization n = ab, the factors a and b are coprime. An immediate result of this definition is that all numbers are square-free. A positive integer n is square-free if and only if all abelian groups of n are isomorphic. This follows from the classification of finitely generated abelian groups, a integer n is square-free if and only if the factor ring Z / nZ is a product of fields. This follows from the Chinese remainder theorem and the fact that a ring of the form Z / kZ is a field if, for every positive integer n, the set of all positive divisors of n becomes a partially ordered set if we use divisibility as the order relation. This partially ordered set is always a distributive lattice and it is a Boolean algebra if and only if n is square-free. A positive integer n is square-free if and only if μ ≠0, a positive integer n is squarefree if and only if ∑ d 2 ∣ n μ =1. This results from the properties of Möbius function, and the fact that this sum is equal to ∑ d ∣ m μ, where m is the largest divisor of n such that m2 divides n. The Dirichlet generating function for the numbers is ζ ζ = ∑ n =1 ∞ | μ | n s where ζ is the Riemann zeta function. This is easily seen from the Euler product ζ ζ = ∏ p = ∏ p, let Q denote the number of square-free integers between 1 and x. For large n, 3/4 of the positive integers less than n are not divisible by 4, 8/9 of these numbers are not divisible by 9, and so on. Under the Riemann hypothesis, the term can be further reduced to yield Q = x ζ + O =6 x π2 + O
Square-free integer
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Overview
24.
Square number
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In mathematics, a square number or perfect square is an integer that is the square of an integer, in other words, it is the product of some integer with itself. For example,9 is a number, since it can be written as 3 × 3. The usual notation for the square of a n is not the product n × n. The name square number comes from the name of the shape, another way of saying that a integer is a square number, is that its square root is again an integer. For example, √9 =3, so 9 is a square number, a positive integer that has no perfect square divisors except 1 is called square-free. For a non-negative integer n, the nth square number is n2, the concept of square can be extended to some other number systems. If rational numbers are included, then a square is the ratio of two integers, and, conversely, the ratio of two square integers is a square, e. g.49 =2. Starting with 1, there are ⌊√m⌋ square numbers up to and including m, the squares smaller than 602 =3600 are, The difference between any perfect square and its predecessor is given by the identity n2 −2 = 2n −1. Equivalently, it is possible to count up square numbers by adding together the last square, the last squares root, and the current root, that is, n2 =2 + + n. The number m is a number if and only if one can compose a square of m equal squares. Hence, a square with side length n has area n2, the expression for the nth square number is n2. This is also equal to the sum of the first n odd numbers as can be seen in the above pictures, the formula follows, n 2 = ∑ k =1 n. So for example,52 =25 =1 +3 +5 +7 +9, there are several recursive methods for computing square numbers. For example, the nth square number can be computed from the square by n2 =2 + + n =2 +. Alternatively, the nth square number can be calculated from the two by doubling the th square, subtracting the th square number, and adding 2. For example, 2 × 52 −42 +2 = 2 × 25 −16 +2 =50 −16 +2 =36 =62, a square number is also the sum of two consecutive triangular numbers. The sum of two square numbers is a centered square number. Every odd square is also an octagonal number
Square number
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m = 1 2 = 1
25.
Binary numeral system
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The base-2 system is a positional notation with a radix of 2. Because of its implementation in digital electronic circuitry using logic gates. Each digit is referred to as a bit, the modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de lArithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions, the method used for ancient Egyptian multiplication is also closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, the I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique and it is based on taoistic duality of yin and yang. Eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, the Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, Pingalas Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingalas system increases towards the right, the residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Africa, sets of binary combinations similar to the I Ching have also been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been applied in sub-Saharan Africa. Leibnizs system uses 0 and 1, like the modern binary numeral system, Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own beliefs as a Christian. Binary numerals were central to Leibnizs theology and he believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. Is not easy to impart to the pagans, is the ex nihilo through Gods almighty power. In 1854, British mathematician George Boole published a paper detailing an algebraic system of logic that would become known as Boolean algebra
Binary numeral system
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Numeral systems
Binary numeral system
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Gottfried Leibniz
Binary numeral system
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George Boole
26.
0 (number)
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0 is both a number and the numerical digit used to represent that number in numerals. The number 0 fulfills a role in mathematics as the additive identity of the integers, real numbers. As a digit,0 is used as a placeholder in place value systems, names for the number 0 in English include zero, nought or naught, nil, or—in contexts where at least one adjacent digit distinguishes it from the letter O—oh or o. Informal or slang terms for zero include zilch and zip, ought and aught, as well as cipher, have also been used historically. The word zero came into the English language via French zéro from Italian zero, in pre-Islamic time the word ṣifr had the meaning empty. Sifr evolved to mean zero when it was used to translate śūnya from India, the first known English use of zero was in 1598. The Italian mathematician Fibonacci, who grew up in North Africa and is credited with introducing the system to Europe. This became zefiro in Italian, and was contracted to zero in Venetian. The Italian word zefiro was already in existence and may have influenced the spelling when transcribing Arabic ṣifr, modern usage There are different words used for the number or concept of zero depending on the context. For the simple notion of lacking, the words nothing and none are often used, sometimes the words nought, naught and aught are used. Several sports have specific words for zero, such as nil in football, love in tennis and it is often called oh in the context of telephone numbers. Slang words for zero include zip, zilch, nada, duck egg and goose egg are also slang for zero. Ancient Egyptian numerals were base 10 and they used hieroglyphs for the digits and were not positional. By 1740 BC, the Egyptians had a symbol for zero in accounting texts. The symbol nfr, meaning beautiful, was used to indicate the base level in drawings of tombs and pyramids. By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system, the lack of a positional value was indicated by a space between sexagesimal numerals. By 300 BC, a symbol was co-opted as a placeholder in the same Babylonian system. In a tablet unearthed at Kish, the scribe Bêl-bân-aplu wrote his zeros with three hooks, rather than two slanted wedges, the Babylonian placeholder was not a true zero because it was not used alone
0 (number)
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Example of the early Greek symbol for zero (lower right corner) from a 2nd-century papyrus
0 (number)
0 (number)
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The number 605 in Khmer numerals, from the Sambor inscription (
Saka era 605 corresponds to AD 683). The earliest known material use of zero as a decimal figure.
0 (number)
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The back of Olmec stela C from
Tres Zapotes, the second oldest
Long Count date discovered. The numerals 7.16.6.16.18 translate to September, 32 BC (Julian). The glyphs surrounding the date are thought to be one of the few surviving examples of
Epi-Olmec script.
27.
1 (number)
–
1, is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement, for example, a line segment of unit length is a line segment of length 1. It is also the first of the series of natural numbers. The word one can be used as a noun, an adjective and it comes from the English word an, which comes from the Proto-Germanic root *ainaz. The Proto-Germanic root *ainaz comes from the Proto-Indo-European root *oi-no-, compare the Proto-Germanic root *ainaz to Old Frisian an, Gothic ains, Danish een, Dutch een, German eins and Old Norse einn. Compare the Proto-Indo-European root *oi-no- to Greek oinos, Latin unus, Old Persian aivam, Old Church Slavonic -inu and ino-, Lithuanian vienas, Old Irish oin, One, sometimes referred to as unity, is the first non-zero natural number. It is thus the integer before two and after zero, and the first positive odd number, any number multiplied by one is that number, as one is the identity for multiplication. As a result,1 is its own factorial, its own square, its own cube, One is also the result of the empty product, as any number multiplied by one is itself. It is also the natural number that is neither composite nor prime with respect to division. The Gupta wrote it as a line, and the Nagari sometimes added a small circle on the left. The Nepali also rotated it to the right but kept the circle small and this eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the Roman numeral I. Where the 1 is written with an upstroke, the number 7 has a horizontal stroke through the vertical line. While the shape of the 1 character has an ascender in most modern typefaces, in typefaces with text figures, many older typewriters do not have a separate symbol for 1 and use the lowercase letter l instead. It is possible to find cases when the uppercase J is used,1 cannot be used as the base of a positional numeral system, as the only digit that would be permitted in such a system would be 0. Since the base 1 exponential function always equals 1, its inverse does not exist, there are two ways to write the real number 1 as a recurring decimal, as 1.000. and as 0.999. There is only one way to represent the real number 1 as a Dedekind cut, in a multiplicative group or monoid, the identity element is sometimes denoted 1, but e is also traditional. However,1 is especially common for the identity of a ring. When such a ring has characteristic n not equal to 0,1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few
1 (number)
–
The 24-hour tower clock in
Venice, using J as a symbol for 1.
28.
178 Belisana
–
178 Belisana is a rocky main belt asteroid that was discovered by Austrian astronomer Johann Palisa on November 6,1877. It is named after the Celtic goddess Belisana, photometric observations of this asteroid from multiple observatories during 2007 gave a light curve with a period of 12.321 ±0.002 hours and a brightness variation of 0.10 ±0.03 in magnitude. This is in agreement with a performed in 1992. However, it is possible that the curve may have a period of 24.6510 ±0.0003 hours. 178 Belisana at the JPL Small-Body Database Discovery · Orbit diagram · Orbital elements · Physical parameters
178 Belisana
–
A three-dimensional model of 178 Belisana based on its light curve.
29.
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
30.
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.
31.
178P/Hug-Bell
–
178P/Hug–Bell is a periodic comet in the Solar System. It was discovered by Northeast Kansas Amateur Astronomers League members Gary Hug and it was declared a comet less than two days after its initial discovery, after having its course confirmed on previous images. Hug-Bells orbital period is seven years, its orbit is eccentric. Hug-Bells orbit lies entirely outside the orbit of Mars, but at its aphelion overlaps in solar distance with the orbit of Jupiter. Because it never comes closer to the Sun than about 2 AU, it is never expected to be a bright comet. Orbital simulation from JPL / Horizons Ephemeris 178P/Hug-Bell – Seiichi Yoshida @ aerith. net 178P/Hug-Bell @ JPL Small-Body Database Browser
178P/Hug-Bell
–
Features
178P/Hug-Bell
32.
Comet
–
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
33.
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.
34.
Galaxy
–
A galaxy is a gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter. The word galaxy is derived from the Greek galaxias, literally milky, Galaxies range in size from dwarfs with just a few billion stars to giants with one hundred trillion stars, each orbiting its galaxys center of mass. Galaxies are categorized according to their morphology as elliptical, spiral. Many galaxies are thought to have holes at their active centers. The Milky Ways central black hole, known as Sagittarius A*, has a four million times greater than the Sun. Recent estimates of the number of galaxies in the observable universe range from 200 billion to 2 trillion or more, most of the galaxies are 1,000 to 100,000 parsecs in diameter and separated by distances on the order of millions of parsecs. The space between galaxies is filled with a gas having an average density of less than one atom per cubic meter. The majority of galaxies are organized into groups, clusters. At the largest scale, these associations are generally arranged into sheets and filaments surrounded by immense voids. In Greek mythology, Zeus places his son born by a mortal woman, the infant Heracles, on Heras breast while she is asleep so that the baby will drink her divine milk and will thus become immortal. Hera wakes up while breastfeeding and then realizes she is nursing a baby, she pushes the baby away, some of her milk spills and. In the astronomical literature, the capitalized word Galaxy is often used to refer to our galaxy, the Milky Way, to distinguish it from the other galaxies in our universe. The English term Milky Way can be traced back to a story by Chaucer c. 1380, See yonder, lo, the Galaxyë Which men clepeth the Milky Wey, For hit is whyt. However, the word Universe was later understood to mean the entirety of existence, so this expression fell into disuse and the objects instead became known as galaxies. Tens of thousands of galaxies have been catalogued, but only a few have well-established names, such as the Andromeda Galaxy, the Magellanic Clouds, the Whirlpool Galaxy, and the Sombrero Galaxy. Astronomers work with numbers from certain catalogues, such as the Messier catalogue, the NGC, the IC, the CGCG, all of the well-known galaxies appear in one or more of these catalogues but each time under a different number. For example, Messier 109 is a galaxy having the number 109 in the catalogue of Messier, but also codes NGC3992, UGC6937, CGCG 269-023, MCG +09-20-044. One of the arguments to do so is that these impressive objects deserve better than uninspired codes, for instance, Bodifee and Berger propose the informal, descriptive name Callimorphus Ursae Majoris for the well-formed barred galaxy Messier 109 in Ursa Major
Galaxy
–
NGC 4414, a typical spiral galaxy in the
constellation Coma Berenices, is about 55,000
light-years in diameter and approximately 60 million light-years away from Earth
Galaxy
–
A
fish-eye mosaic of the Milky Way arching at a high inclination across the night sky, shot from a dark-sky location in Chile
Galaxy
–
Photograph of the "Great Andromeda Nebula" from 1899, later identified as the
Andromeda Galaxy
Galaxy
–
NGC 3923 Elliptical Shell Galaxy-Hubble Space Telescope photograph
35.
Canadian Expeditionary Force
–
The Canadian Expeditionary Force was the designation of the field force created by Canada for service overseas in the First World War. The force fielded several combat formations on the Western Front in France and Belgium, the Canadian Cavalry Brigade and the Canadian Independent Force, which were independent of the Canadian Corps, also fought on the Western Front. The CEF also had a reserve and training organization in England. The Germans went so far as to call them storm troopers for their combat efficiency. In August 1918, the CEFs Canadian Siberian Expeditionary Force travelled to revolution-torn Russia and it reinforced an anti-Bolshevik garrison in Vladivostok during the winter of 1918–19. At this time, another force of Canadian soldiers were placed in Archangel, the Canadian Expeditionary Force was mostly volunteers, as conscription was not enforced until the end of the war when call-ups began in January 1918. Ultimately, only 24,132 conscripts arrived in France before the end of the war, Canada was the senior Dominion in the British Empire and automatically at war with Germany upon the British declaration. According to Canadian historian Dr. Serge Durflinger at the Canadian War Museum, of the first contingent formed at Valcartier, Quebec in 1914, fully two-thirds were men born in the United Kingdom. By the end of the war in 1918, at least fifty per cent of the CEF consisted of British-born men, many British nationals from the United Kingdom or other territories who were resident in Canada also joined the CEF. As several CEF battalions were posted to the Bermuda Garrison before proceeding to France, although the Bermuda Militia Artillery and Bermuda Volunteer Rifle Corps both sent contingents to the Western Front, the first would not arrive there til June 1915. By then, many Bermudians had already been serving on the Western Front in the CEF for months, Bermudians in the CEF enlisted under the same terms as Canadians, and all male British Nationals resident in Canada became liable for conscription under the Military Service Act,1917. Two tank battalions were raised in 1918 but did not see service, most of the infantry battalions were broken up and used as reinforcements, with a total of fifty being used in the field, including the mounted rifle units, which were re-organized as infantry. The artillery and engineering units underwent significant re-organization as the war progressed, a distinct entity within the Canadian Expeditionary Force was the Canadian Machine Gun Corps. It consisted of several machine gun battalions, the Eatons, Yukon, and Borden Motor Machine Gun Batteries. During the summer of 1918, these units were consolidated into four machine gun battalions, the Canadian Corps with its four infantry divisions comprised the main fighting force of the CEF. The Canadian Cavalry Brigade also served in France, the 1915 Battle of Ypres, the first engagement of Canadian forces in the Great War, changed the Canadian perspective on war. Ypres exposed Canadian soldiers and their commanders to modern war and they had already experienced the effects of shellfire and developed a reputation for aggressive trench raiding despite their lack of formal training and generally inferior equipment. In April 1915, they were introduced to yet another facet of modern war, the Germans employed chlorine gas to create a hole in the French lines adjacent to the Canadian force and poured troops into the gap
Canadian Expeditionary Force
–
26th Battalion of the Second Canadian Expeditionary Force, 1915
Canadian Expeditionary Force
Canadian Expeditionary Force
–
Private Joseph Pappin, 130 Battalion, Canadian Expeditionary Force.
36.
178th Airlift Squadron
–
The 178th Reconnaissance Squadron is a unit of the North Dakota Air National Guard 119th Wing located at Fargo Air National Guard Base, North Dakota. The 178th is equipped with the MQ-1A Predator, the 178th Reconnaissance Squadron includes operations of the MQ-1 Predator, a medium-altitude, long-endurance, remotely piloted aircraft. The MQ-1s primary mission is interdiction and conducting armed reconnaissance against critical, the squadron was first organized as the 392d Fighter Squadron at Hamilton Field, California on 15 July 1943, as one of the original squadrons of the 367th Fighter Group. Several members of its cadre were former Flying Tigers with prior combat experience. It was not until late August, however, that the received its first Bell P-39 Airacobra. After building up its strength, the squadron moved in October to Santa Rosa Army Air Field, in December group headquarters moved to Oakland Municipal Airport, while the 392d was at Sacramento Municipal Airport. The squadron moved temporarily Tonopah Army Air Field, Nevada, where they performed dive bombing, training accidents with the Bell P-39 Airacobra cost several pilots their lives. In January 1944, as it prepared for movement, the 392d was beefed up with personnel from the 328th and 368th Fighter Groups. The squadron staged through Camp Shanks, and sailed for England aboard the SS Duchess of Bedford, the Drunken Duchess docked at Greenock, Scotland on 3 April and the group was transported by train to its airfield at RAF Stoney Cross, England. Having trained on single engine aircraft, the pilots were surprised to find Lockheed P-38 Lightnings sitting on Stoney Crosss dispersal pads. Only members of the party had any experience flying the Lightning. These pilots had flown combat sorties with the 55th Fighter Group, the change from single engine to twin engine aircraft required considerable retraining for both pilots and ground crew. However, the lack of instrument training in the P-38 took its toll on the 392d as weather, not enemy action, caused the loss of pilots, on 9 May, the squadron flew its first combat mission, a fighter sweep over Alençon. For the remainer of the month, the unit flew fighter sweeps, bomber escort and dive bombing, missions, on D-Day and the next three days the squadron flew missions maintaining air cover over shipping carrying invasion troops. These missions continued for the three days. Shortly after the Normandy invasion, on 12 June, the 367th Group was selected to test the ability of the P-38 to carry a 2,000 lb bomb under each wing, the selected target was a railroad yard, and results were mixed. An attack by VII Corps on 22 June was to be preceded by low level bombing and strafing attack by IX Fighter Command, briefed by intelligence to expect a milk run The 394th flew at low altitude through what turned out to be a heavily defended area. Seven group pilots were killed in action, nearly all surviving aircraft received battle damage and the entire 367th Group was out of action for several days
178th Airlift Squadron
–
178th Reconnaissance Squadron MQ-1B Predator
178th Airlift Squadron
–
P-39D as used by the group for training
178th Airlift Squadron
–
392d Fighter Squadron P-38
178th Airlift Squadron
–
367th Fighter Group commander's P-47D
37.
North Dakota Air National Guard
–
The North Dakota Air National Guard is the air force militia of the State of North Dakota, United States of America. It is, along with the North Dakota Army National Guard, as state militia units, the units in the North Dakota Air National Guard are not in the normal United States Air Force chain of command. They are under the jurisdiction of the Governor of North Dakota though the office of the North Dakota Adjutant General unless they are federalized by order of the President of the United States. The North Dakota Air National Guard is headquartered in Fargo, under the Total Force concept, North Dakota Air National Guard units are considered to be Air Reserve Components of the United States Air Force. North Dakota ANG units are trained and equipped by the Air Force and are gained by a Major Command of the USAF if federalized. State missions include disaster relief in times of earthquakes, hurricanes, floods and forest fires, search and rescue, protection of public services. The 178th Reconnaissance Squadron includes operations of the General Atomics MQ-1 Predator, truman, allocated inactive unit designations to the National Guard Bureau for the formation of an Air Force National Guard. These unit designations were allotted and transferred to various State National Guard bureaus to provide them unit designations to re-establish them as Air National Guard units, the North Dakota Air National Guard received federal recognition on 1 February 1947 as the 1178th Fighter Squadron at Hector Field, Fargo. It was equipped with F-51D Mustangs and its mission was the air defense of the state, the North Dakota Air National Guard has been tasked to perform its state mission on many occasions. Federalization of the North Dakota Air National Guard occurred during the Korean War, with the unit mobilized and ordered to duty in 1951, returning to Fargo. Air Defense alert has been a part of the North Dakota Air National Guards tasking since September 1953. The unit provided alert coverage at Fargo, with two or four aircraft continuously on status, until March 1990 when home station alert was discontinued. Other alert sites include March Air Reserve Base, California, and Kingsley Field, near Klamath Falls, the detachment closed in October 2006 due to the change from the F-16C fighter to the Learjet C-21A transport. The first overseas deployment of the North Dakota Air Guard occurred in 1983, with six F-4D Phantom II fighters and 120 support personnel deploying to Naval Air Station Keflavik, eight Soviet Tupolev Tu-95 reconnaissance aircraft were intercepted by the Happy Hooligan pilots during the deployment. In 1986, the 119th Fighter Group became the first core unit to assume the USAF Zulu alert mission at Ramstein Air Base, referred to as Creek Klaxon, the 119th and other air defense units stood continuous alert for one year providing air sovereignty in Europe for NATO. During Operation Desert Storm,107 North Dakota ANG members were mobilized and deployed in support of operations at numerous locations in the United States. The Lockheed C-130 Hercules support aircraft assigned to the North Dakota Air National Guard and aircrew also provided airlift of personnel. The Services Flight also prepared over 210,000 meals over a 60-day period for the relief workers, in its 2005 Base Realignment and Closure recommendations, the United States Department of Defense recommended to realign the 119th Fighter Wing and retire the wing’s 15 F-16s
North Dakota Air National Guard
–
178th Reconnaissance Squadron - General Atomics MQ-1B-10 Predator 08-024. The 178th RS is the oldest unit in the North Dakota Air National Guard, having over 60 years of service to the state and nation
North Dakota Air National Guard
–
North Dakota F-51D Mustang, about 1947, note the "ND" (National Guard) fuselage designation, dating the photo prior to the official establishment of the Air National Guard in September.
38.
Dive bomber
–
A dive bomber is a bomber aircraft that dives directly at its targets in order to provide greater accuracy for the bomb it drops. Diving towards the target simplifies the bombs trajectory and allows the pilot to keep visual contact throughout the bomb run and this allows attacks on point targets and ships, which were difficult to attack with conventional level bombers, even en-masse. A dive bomber dives at an angle, normally between 45 and 90 degrees, and thus requires an abrupt pull-up after dropping its bombs. This puts great strains on both pilot and aircraft and it demands an aircraft of strong construction, with some means to slow its dive. This limited the class to light bomber designs with ordnance loads in the range of 1,000 lb although there were larger examples. The SBD Dauntless helped win the Battle of Midway, was instrumental in the victory at the Battle of the Coral Sea, a second and simpler technique is to bomb from a shallow dive angle, sometimes referred to as glide bombing. This reduces the accuracy, but still allows line of sight to the target during the bomb run, the Junkers Ju 88 and Petlyakov Pe-2 were widely used in this role. The Heinkel He 177 is often mentioned as having its development upset by the demand that it be able to dive bomb, the phrase glide bombing should not be confused with the term glide bomb, where the bomb glides towards its target while the aircraft remains in level flight. Attachments for this type of bombing were fitted to the Norden bombsight, Dive bombing was most widely used before and during World War II, its use declined during the war, when its vulnerability to enemy fighters became apparent. Most tactical aircraft today allow bombing in shallow dives to keep the target visible, when released from an aircraft, a bomb carries with it the aircrafts velocity. In the case of a bomber flying horizontally, the bomb will only be travelling forward. This forward motion is opposed by the drag of the air, additionally, gravity accelerates the bomb downward. The combination of two forces, drag and gravity, results in a complex pseudo-parabolic trajectory. The distance that the bomb moves forward while it falls is known as its range, if the range for a given set of conditions is calculated, simple trigonometry can be used to find the angle between the aircraft and the target. By setting the bombsight to this angle, the aircraft can time the drop of its bombs at the instant when the target is lined up in the sight. This was only effective for area bombing, however, since the path of the bomb is only roughly estimated. Large formations could drop bombs on an area hoping to hit a target, but there was no guarantee of success. The advantage to this approach, however, was that it is easy to build such an aircraft and fly it at high altitude, the horizontal bomber was thus ill-suited for tactical bombing, particularly in close support
Dive bomber
–
An
SBD Dauntless drops its
bomb. The dive brakes are extended and are visible behind the wings.
Dive bomber
–
Final assembly view of
SBD Dauntless dive bombers in 1943 at the
Douglas Aircraft Company plant in
El Segundo, California. The
dive brakes are visible behind the wings.
Dive bomber
–
The
Aichi D1A 2, a
carrier-borne dive bomber.
Dive bomber
–
Ju87D Stukas over the Eastern Front, winter 1943-44
39.
Panhard 178
–
The Panhard 178 or Pan-Pan was an advanced French reconnaissance 4x4 armoured car that was designed for the French Cavalry before World War II. It had a crew of four and was equipped with an effective 25 mm main armament, after the war a derived version, the Panhard 178B, was again taken into production by France. In December 1931, the French Cavalry conceived a plan for the production of armoured fighting vehicles. One of the classes foreseen was that of an Automitrailleuse de Découverte or AMD, the specifications were formulated on 22 December 1931, changed on 18 November 1932 and approved on 9 December 1932. In 1933, one of the competing companies — the others being Renault, Berliet and Latil — that had put forward proposals, the Panhard vehicle was ready in October 1933 and presented to the Commission de Vincennes in January 1934 under the name Panhard voiture spéciale type 178. It carried a Vincennes workshop 13.2 mm machine gun turret, of all the competing projects it was considered the best, the Berliet VUB e. g. was reliable but too heavy and traditional, the Latil version had no all-terrain capacity. In the autumn the improved prototype, now lacking the bottom tracks of the type, was tested by the Cavalry. In late 1934 the type was accepted under the name AMD Panhard Modèle 1935, the type was now fitted with the APX3B turret. The ultimate design was advanced for its day and still appeared modern in the 1970s. It was the first 4x4 armoured car mass-produced for a major country, the final assembly and painting of the armoured cars took place in the Panhard & Levassor factory at the Avenue dIvry in the 13th arrondissement of Paris. There however, only the parts and lesser fittings were built in. At first the main supplying company was Batignolles-Châtillon at Nantes, that could supply a maximum of twenty per month. Likewise the turret, fitted with its armament by the Atelier de construction de Rueil was as such made by subcontractors. The actual orders were made on 1 January and 29 April 1935 respectively, due to strikes, the first vehicles of these orders were only delivered from 2 February 1937 onwards, nineteen had been produced by April, the last delivered in November. The two first orders together can be seen as a separate preseries of thirty, that slightly in many details from later produced vehicles. A third order for eighty vehicles was made on 15 September 1935 and they were scheduled to be delivered between January and July 1938, but due to strikes and delays in the production of the turrets, the actual dates were 24 June 1938 and 10 February 1939. On 1 September 1939,219 vehicles had been delivered including prototypes,71 behind schedule, however, production increases soon allowed Panhard to reduce the backlog — at least for the hulls. The total production of completed vehicles of the version of the AMD35 for France was thus 339
Panhard 178
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Preserved AMD Panhard 35 at the
Musée des Blindés
Panhard 178
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The rear of the same vehicle, showing the position of the second driver; the hull, despite having been repainted with a number belonging to the third production batch, is in fact that of a Panhard 178B. The APX3B turret is of the latest type with a rear episcope
Panhard 178
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The old Panhard factory where the AMD 35s were assembled
Panhard 178
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The Panhard 178 from the right side
40.
Armored car (military)
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A military armored car is a lightweight wheeled armored fighting vehicle, historically employed for reconnaissance, internal security, armed escort, and other subordinate battlefield tasks. With the gradual decline of mounted cavalry, armored cars were developed for carrying out duties formerly assigned to horsemen, following the invention of the tank, the armored car remained popular due to its comparatively simplified maintenance and low production cost. It also found favor with several colonial armies as a weapon for use in underdeveloped regions. During World War II, most armored cars were engineered for reconnaissance and passive observation, some equipped with heavier armament could even substitute for tracked combat vehicles in favorable conditions—such as pursuit or flanking maneuvers during the North African Campaign. The Motor Scout was designed and built by British inventor F. R. Simms in 1898 and it was the first armed petrol engine-powered vehicle ever built. The vehicle was a De Dion-Bouton quadricycle with a mounted Maxim machine gun on the front bar, an iron shield in front of the car protected the driver. However, these were not armored cars as the term is understood today and they were also, by virtue of their small capacity engines, less efficient than the cavalry and horse-drawn guns that they were intended to complement. At the beginning of the 20th century, the first military armored vehicles were manufactured, by adding armor and weapons to existing vehicles. The vehicle had Vickers armour 6 mm thick and was powered by a four-cylinder 3. 3-litre 16-hp Cannstatt Daimler engine, the armament, consisting of two Maxim guns, was carried in two turrets with 360° traverse. Simms Motor War Car was presented at the Crystal Palace, London, another early armored car of the period was the French Charron, Girardot et Voigt 1902, presented at the Salon de lAutomobile et du cycle in Brussels, on 8 March 1902. The vehicle was equipped with a Hotchkiss machine gun, and with 7 mm armour for the gunner, one of the first operational armoured cars with four wheel drive and fully enclosed rotating turret, was the Austro-Daimler Panzerwagen built by Austro-Daimler in 1904. It was armoured with 3-3.5 mm thick curved plates over the body and had a 4mm thick dome-shaped rotating turret that housed one or two machine-guns and it had a 4-cylinder 35 hp 4.4 litre engine giving it average cross country performance. Of note, both the driver and co-driver had adjustable seats enabling them to them to see out of the roof of the drive compartment as needed. The Italians used armored cars during the Italo-Turkish War, a great variety of armored cars appeared on both sides during World War I and these were used in various ways. Generally, the cars were used by more or less independent car commanders. However, sometimes they were used in units up to squadron size. The cars were armed with light machine guns, but larger units usually employed a few cars with heavier guns. As air power became a factor, armored cars offered a platform for antiaircraft guns
Armored car (military)
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F.R. Simms '
Motor Scout, built in 1898 as an armed car.
Armored car (military)
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Eland Mk7 light armoured car at the South African Armour Museum,
Bloemfontein.
Armored car (military)
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F.R. Simms ' 1902
Motor War Car, the first armored car to be built.
Armored car (military)
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The earliest French armored car - the
Charron-Girardot-Voigt 1902.
41.
U.S. 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
U.S. Navy
U.S. Navy
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United States Navy portal
U.S. Navy
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USS Constellation vs L'Insurgente during the
Quasi-War
U.S. Navy
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USS Constitution vs HMS Guerriere during the
War of 1812
42.
USNS Frederick Funston (T-AP-178)
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USS Frederick Funston was a Frederick Funston-class attack transport that served with the US Navy during World War II. Before serving as a Navy APA, she had been the US Army transport USAT Frederick Funston, after World War II, she was returned to the Army and operated as USAT Frederick Funston. Funston was among the seventy-two ships transferred to the Navys Military Sea Transportation Service in the 1 March 1950 group and placed in service as USNS Frederick Funston. She was acquired from the Army by the US Navy on 8 April 1943, reclassified an APA, the ship’s construction was based on a special design prepared by the firm of Gibbs and Cox to meet requirements of the War Department and the U. S. Army. The Funston went from Seattle to San Francisco, from where she sailed in mid-December, via Honolulu and she also visited Espiritu Santo before returning home. From San Francisco again in February 1943, she went to Brisbane, from Brisbane the ship sailed, via the Panama Canal, to New York arriving there in early April. At New York, following renovations, the Funston was transferred to. She went to Norfolk for training and was in operation in the Atlantic until she returned to New York on 30 December 1943, from then until the end of the war, she was locally operated by the Navy. The Funston left Honolulu on 9 July 1945 and went to Eniwetok and she sailed from the latter port for Manila in September and returned to Los Angeles on 31 October and then made a trip to Manus Island and returned to San Francisco in December. Her next voyage took her to Guam, the Marianna’s and Saipan, the Frederick Funston returned to Los Angeles, and from there went to San Francisco, where she was redelivered to the Army in Early April 1946. In June 1946 crew quarters on the vessel were altered for accommodating War Department peacetime civilian crew and guns, three days later she sailed to train at Oran for the assault on Salerno, off which she lay from 8 to 10 September landing soldiers. On 30 November, she cleared Oran for Northern Ireland with paratroopers on board, after loading men of naval construction battalions at Davisville, Rhode Island, Frederick Funston sailed for the Pacific, arriving at Honolulu 16 March 1944. Here she landed the Seabees and embarked Marines for the invasion of Saipan, after a week off the beaches offloading cargo and taking casualties on board, she returned to Honolulu. Here the casualties were transferred to hospitals, and soldiers taken on board with whom she reinforced Guam on 24 July. During August, the transport joined in training operations in the Hawaiian Islands, then crossed to Manus and she landed her troops and cargo on 21 October, the day after the initial assault, and the following day cleared for Aitape, New Guinea, to embark reinforcements. These were put ashore at Leyte 14 November, training off New Guinea and in Huon Gulf prepared Frederick Funston for the initial landings on Luzon of 9 January 1945. That night a watchful lookout spotted and shot a suicide swimmer only 50 yards from the ship, completing her unloading the next day, Frederick Funston sailed by way of Leyte and Ulithi to Guam to embark Marines for the assault on Iwo Jima. With her troops held in reserve, she did not land them until 27 February and she returned to Guam with casualties 8 March, then replaced her landing craft at Guadalcanal and exercised at Nouméa through April
USNS Frederick Funston (T-AP-178)
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USS Frederick Funston (APA-89)
43.
Frederick Funston class attack transport
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The Frederick Funston-class attack transport was a class of US Navy attack transports. They saw service in World War II and later in the Korean War, like all attack transports, the Frederick Funston class was generously armed with antiaircraft weaponry to protect itself and its vulnerable cargo of troops from air attack in the battle zone. The class derives its name from US Army General Frederick Funston, the two ships of the Frederick Funston class were based on the Maritime Commissions ubiquitous Type C3 hull. They began their lives as transport ships for the US Army. It is not known whether they underwent any modifications for their new role, there is no mention of cargo space in the DANFS entries, so it is not known how much cargo the vessels carried. The class carried a number of troops than most attack transports—2,200 as opposed to the 1,200 to 1,500 of most other APAs. The Frederick Funstons participated in the Mediterranean Theatre, taking part in the invasions of Salerno and Italy, after the war, they were decommissioned and returned to the US Army, when they were redesignated USAT. In the 1950s the ships were reacquired by the Navy and reclassified T-AP, both of them then went on to serve in the Korean War - mostly it appears on transport missions. James OHara was struck from the Naval Register in 1961, both vessels were scrapped in 1968-69. See the DANFS entries for the ships, USS Frederick Funston
Frederick Funston class attack transport
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USS James O'Hara (APA-90), a ship of the Frederick Funston class, at Hampton Roads, 23 August 1943
44.
Attack transport
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Attack transport is a United States Navy ship classification for a variant of ocean-going troopship adapted to transporting invasion forces ashore. Unlike standard troopships – often drafted from commercial shipping fleets – that rely on either a quay or tenders and they are not to be confused with landing ships, which beach themselves to bring their troops directly ashore, or their general British equivalent, the Landing ship, infantry. A total of 388 APA and AKA attack transports were built for service in World War II in at least fifteen classes, depending on class they were armed with one or two 5-inch guns and a variety of 40 mm and 20 mm anti-aircraft weapons. Some of these were outfitted with heavy boat davits and other arrangements to enable them to handle landing craft] for amphibious assault operations. In 1942, when the AP number series had extended beyond 100. Therefore, the new classification of attack transport was created and numbers assigned to fifty-eight APs then in commission or under construction, the actual reclassification of these ships was not implemented until February 1943, by which time two ships that had APA numbers assigned had been lost. Another two transports sunk in 1942, USS George F. Elliott and USS Leedstown, were configured as attack transports. In addition, as part of the 1950s modernization of the Navys amphibious force with faster ships, as a result, only attack transport ships were assigned for the assault, without support from any companion attack cargo ships. This created extreme logistics burdens for the force because it resulted in considerable overloading of the transports with both men and equipment. To compound problems, these forces were not able to assemble or train together before executing the Aleutian invasion on 11 May 1943, lack of equipment and training subsequently resulted in confusion during the landings on Attu. By the end of the 1950s, it was clear that boats would soon be superseded by amphibious tractors and helicopters for landing assault troops. These could not be supported by attack transports in the numbers required, by 1969, when the surviving attack transports were redesignated LPA, only a few remained in commissioned service. The last of these were decommissioned in 1980 and sold abroad, the APA/LPA designation may, therefore, now be safely considered extinct. Nearly identical ships used to transport vehicles, supplies and landing craft, Landing Ship Infantry This article incorporates text from the public domain Dictionary of American Naval Fighting Ships. APA/LPA -- Attack Transports by the US Naval Historical Center
Attack transport
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The
USS American Legion was a
Harris-class attack transport launched in 1919 that saw extensive service in World War II
Attack transport
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Soldiers climb down netting on the sides of the attack transport
USS McCawley (APA-4) on 14 June 1943, rehearsing for landings on
New Georgia
Attack transport
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A loaded
Bayfield-class attack transport underway, the
USS Hamblen (APA-114)
45.
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
46.
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
47.
USS Hogan (DD-178)
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USS Hogan was a Wickes-class destroyer in the United States Navy during World War II. She was the first ship named for Seaman Daniel Hogan, after shakedown, Hogan arrived at San Diego on 21 November to join the Pacific Destroyer Force. From 23 November to 6 February 1920 she sailed in company with her division and engaged in maneuvers, patrol duty, torpedo exercises. On 25 March she departed for Hawaii, where she operated for the next month, the destroyer rejoined her squadron at San Diego in late April for five months of gunnery exercises and trial runs in that area. She returned to San Diego in early 1921 and engaged in important experimental torpedo practice, during that time, in October, Hogan became the first US Navy ship to be refuelled while underway, towed astern by the oiler Cuyama. For the remainder of her service Hogan assisted U. S. battleships in conducting torpedo firing exercises in the Pacific and she decommissioned at San Diego on 27 May 1922. Recommissioned 7 August 1940, Hogan underwent conversion to a high speed minesweeper at Mare Island, the first major operation in which she took part was the invasion of North Africa in late 1942. For this important amphibious assault, mounted over an ocean, Hogan departed Norfolk 24 October. As the landings began next day, the minesweeper continued to patrol the vital transport area. Just after 05,00, she was sent to investigate strange running lights and came upon a French steamer, Hogan ordered both ships to reverse course, and when the order was not obeyed fired a burst of machine gun fire across the escorts bow. The ship, Victoria, replied with fire of her own and attempted to ram the minesweeper, in the days that followed, the minesweeper continued to conduct antisubmarine patrol off Fedhala, searching for submarines that attacked the transports on 11 November. The ship entered Casablanca harbor on 18 November, the invasion a success, Hogan next returned to coastal convoy duties until November 1943. She sailed on 13 November from Norfolk to join the Pacific Fleet, transited the Panama Canal, the minesweeper was needed for the first phase of the long island campaign toward Japan, the invasion of the Marshalls, and sailed for Pearl Harbor and Kwajalein on 16 January 1944. Hogan carried out anti-submarine patrol off Roi Island before departing on 4 February for Espiritu Santo, after another period of convoy duty, Hogan arrived at Milne Bay on 7 April to prepare for the Hollandia operation. The attack group sailed on 18 April and arrived at Humboldt Bay four days later, Hogan and other minesweepers cleared enemy mines for Admiral Daniel Barbeys invasion force, after which the ship carried out shore bombardment and screening duties. She arrived at Cape Sudest with HMAS Westralia on 25 April, Hogan sailed from Eniwetok on 10 June to make preliminary sweeps of Saipan for the invasion to come. She remained off Saipan during the assault on 15 June, coming under shore fire. As the Japanese fleet moved toward the Marianas for a naval battle
USS Hogan (DD-178)
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History