1.
2000
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According to the Gregorian Calendar, these distinctions fall to the year 2001 because the 1st century was retroactively said to start with year AD1. Since the calendar does not have zero, its first millennium spanned from years 1 to 1000 inclusively. The year 2000 is sometimes abbreviated as Y2K, the year 2000 was the subject of Y2K concerns, which are fears that computers would not shift from 1999 to 2000 correctly. However, by the end of 1999, many companies had already converted to new, or upgraded, as a result of massive effort, relatively few problems occurred. January 1 – The piece Longplayer begins and it lasts 1,000 years, finishing on December 31,2999. January 3–10 – Israel and Syria hold inconclusive peace talks, january 5–8 – The 2000 al-Qaeda Summit of several high-level al-Qaeda members is held in Kuala Lumpur, Malaysia. January 6 – The last natural Pyrenean ibex is found dead, january 10 – America Online announces an agreement to purchase Time Warner for $162 billion. January 11 – The armed wing of the Islamic Salvation Front concludes its negotiations with the government for an amnesty, january 14 A United Nations tribunal sentences 5 Bosnian Croats to up to 25 years in prison for the 1993 killing of over 100 Bosnian Muslims in a Bosnian village. The Dow Jones Industrial Average closes at 11,722.98, january 18 – The Tagish Lake meteorite impacts the Earth. January 24 – Gods Army, a Karen militia group led by twins Johnny and Luther Htoo, january 30 – Kenya Airways Flight 431 crashes off the coast of Ivory Coast into the Atlantic Ocean, killing 169. January 31 Alaska Airlines Flight 261 crashes off the California coast into the Pacific Ocean, dr. Harold Shipman is found guilty of murdering 15 patients between 1995 and 1998 at Hyde, Greater Manchester, and sentenced to life imprisonment. February 4 – German extortionist Klaus-Peter Sabotta is jailed for life for attempted murder and extortion, February 6 – Tarja Halonen is elected the first female president of Finland. February 7 – Stipe Mesić is elected president of Croatia, February 8 – Radio broadcaster Bob Collins plane collides with that of a student pilot over Zion, Illinois. February 9 – Torrential rains in Africa lead to the worst flooding in Mozambique in 50 years, February 13 – The final original Peanuts comic strip is published, following the death of its creator, Charles M. Schulz. February 21 – UNESCO holds the inaugural celebration of International Mother Language Day, February 29 – a rare century leap year date occurs. Usually, century years are common due to not being exactly divisible by 400. 2000 is the first such year to have a February 29 since the year 1600, the next such leap year will not occur until 2400. March 1 The Constitution of Finland is rewritten, jorge Batlle, a son, grandnephew and great-grandson of former presidents, is sworn in as President of Uruguay
2.
Year 2000 problem
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The Year 2000 problem, also known as the Y2K problem, the Millennium bug, the Y2K bug, or Y2K, was a computer bug related to the formatting and storage of calendar data. Problems were anticipated, and arose, because twentieth-century software often represented the year with only the final two digits—making the year 2000 indistinguishable from 1900. The assumption of a date in such programs caused various errors, such as the incorrect display of dates. It identifies two problems that may exist in computer programs. First, the practice of representing the year with two digits became problematic with logical error arising upon rollover from x99 to x00. This had caused some date-related processing to operate incorrectly for dates and times on and after 1 January 2000, without corrective action, long-working systems would break down when the. Ascending numbering assumption suddenly became invalid, years divisible by 100 are not leap years, except for years that are divisible by 400. Thus the year 2000 was a leap year, companies and organisations worldwide checked, fixed, and upgraded their computer systems to address the anticipated problem. Very few computer failures were reported when the clocks rolled over into 2000 and it is not known how many problems went unrecorded. Y2K is a numeronym and was the abbreviation for the year 2000 software problem. The abbreviation combines the letter Y for year, and k for the SI unit prefix kilo meaning 1000, hence, 2K signifies 2000. It was also named the Millennium Bug because it was associated with the popular roll-over of the millennium, the Year 2000 problem was the subject of the early book, Computers in Crisis by Jerome and Marilyn Murray. The first recorded mention of the Year 2000 Problem on a Usenet newsgroup occurred on Friday,18 January 1985, the acronym Y2K has been attributed to David Eddy, a Massachusetts programmer, in an e-mail sent on 12 June 1995. He later said, People were calling it CDC, FADL, Y2K just came off my fingertips. It was therefore important for programmers to reduce usage. As space on disc and tape was also expensive, this also saved money by reducing the size of stored data files, many computer programs stored years with only two decimal digits, for example,1980 was stored as 80. Some such programs could not distinguish between the year 2000 and the year 1900, other programs tried to represent the year 2000 as 19100. This could cause a failure and cause date comparisons to produce incorrect results
3.
Integer
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An integer is a number that can be written without a fractional component. For example,21,4,0, and −2048 are integers, while 9.75, 5 1⁄2, the set of integers consists of zero, the positive natural numbers, also called whole numbers or counting numbers, and their additive inverses. This is often denoted by a boldface Z or blackboard bold Z standing for the German word Zahlen, ℤ is a subset of the sets of rational and real numbers and, like the natural numbers, is countably infinite. The integers form the smallest group and the smallest ring containing the natural numbers, in algebraic number theory, the integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, the integers are the integers that are also rational numbers. Like the natural numbers, Z is closed under the operations of addition and multiplication, that is, however, with the inclusion of the negative natural numbers, and, importantly,0, Z is also closed under subtraction. The integers form a ring which is the most basic one, in the following sense, for any unital ring. This universal property, namely to be an object in the category of rings. Z is not closed under division, since the quotient of two integers, need not be an integer, although the natural numbers are closed under exponentiation, the integers are not. The following lists some of the properties of addition and multiplication for any integers a, b and c. In the language of algebra, the first five properties listed above for addition say that Z under addition is an abelian group. As a group under addition, Z is a cyclic group, in fact, Z under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to Z. The first four properties listed above for multiplication say that Z under multiplication is a commutative monoid. However, not every integer has an inverse, e. g. there is no integer x such that 2x =1, because the left hand side is even. This means that Z under multiplication is not a group, all the rules from the above property table, except for the last, taken together say that Z together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of algebraic structure. Only those equalities of expressions are true in Z for all values of variables, note that certain non-zero integers map to zero in certain rings. The lack of zero-divisors in the means that the commutative ring Z is an integral domain
4.
Negative number
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In mathematics, a negative number is a real number that is less than zero. If positive represents movement to the right, negative represents movement to the left, if positive represents above sea level, then negative represents below level. If positive represents a deposit, negative represents a withdrawal and they are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, if a quantity may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. In the medical context of fighting a tumor, an expansion could be thought of as a negative shrinkage, negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common idea of an opposite is reflected in arithmetic. For example, − −3 =3 because the opposite of an opposite is the original thing, negative numbers are usually written with a minus sign in front. For example, −3 represents a quantity with a magnitude of three, and is pronounced minus three or negative three. To help tell the difference between a subtraction operation and a number, occasionally the negative sign is placed slightly higher than the minus sign. Conversely, a number that is greater than zero is called positive, the positivity of a number may be emphasized by placing a plus sign before it, e. g. +3. In general, the negativity or positivity of a number is referred to as its sign, every real number other than zero is either positive or negative. The positive whole numbers are referred to as natural numbers, while the positive and negative numbers are referred to as integers. In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, Liu Hui established rules for adding and subtracting negative numbers. By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers, islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients. Western mathematicians accepted the idea of numbers by the 17th century. Prior to the concept of numbers, mathematicians such as Diophantus considered negative solutions to problems false. Negative numbers can be thought of as resulting from the subtraction of a number from a smaller. For example, negative three is the result of subtracting three from zero,0 −3 = −3, in general, the subtraction of a larger number from a smaller yields a negative result, with the magnitude of the result being the difference between the two numbers
5.
Factorization
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In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 ×5, in all cases, a product of simpler objects is obtained. The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viètes formulas relate the coefficients of a polynomial to its roots, the opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms. Integer factorization for large integers appears to be a difficult problem, there is no known method to carry it out quickly. Its complexity is the basis of the security of some public key cryptography algorithms. A matrix can also be factorized into a product of matrices of special types, One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types, QR decomposition, LQ, QL, RQ and this situation is generalized by factorization systems. By the fundamental theorem of arithmetic, every integer greater than 1 has a unique prime factorization. Given an algorithm for integer factorization, one can factor any integer down to its constituent primes by repeated application of this algorithm, for very large numbers, no efficient classical algorithm is known. Modern techniques for factoring polynomials are fast and efficient, but use sophisticated mathematical ideas and these techniques are used in the construction of computer routines for carrying out polynomial factorization in Computer algebra systems. This article is concerned with classical techniques. While the general notion of factoring just means writing an expression as a product of simpler expressions, when factoring polynomials this means that the factors are to be polynomials of smaller degree. Thus, while x 2 − y = is a factorization of the expression, another issue concerns the coefficients of the factors. It is not always possible to do this, and a polynomial that can not be factored in this way is said to be irreducible over this type of coefficient, thus, x2 -2 is irreducible over the integers and x2 +4 is irreducible over the reals. In the first example, the integers 1 and -2 can also be thought of as real numbers, and if they are, then x 2 −2 = shows that this polynomial factors over the reals. Similarly, since the integers 1 and 4 can be thought of as real and hence complex numbers, x2 +4 splits over the complex numbers, i. e. x 2 +4 =. The fundamental theorem of algebra can be stated as, Every polynomial of n with complex number coefficients splits completely into n linear factors
6.
Greek numerals
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Greek numerals are a system of writing numbers using the letters of the Greek alphabet. These alphabetic numerals are known as Ionic or Ionian numerals, Milesian numerals. In modern Greece, they are used for ordinal numbers. For ordinary cardinal numbers, however, Greece uses Arabic numerals, attic numerals, which were later adopted as the basis for Roman numerals, were the first alphabetic set. They were acrophonic, derived from the first letters of the names of the numbers represented and they ran =1, =5, =10, =100, =1000, and =10000. 50,500,5000, and 50000 were represented by the letter with minuscule powers of ten written in the top right corner, the same system was used outside of Attica, but the symbols varied with the local alphabets, in Boeotia, was 1000. The present system probably developed around Miletus in Ionia, 19th-century classicists placed its development in the 3rd century BC, the occasion of its first widespread use. The present system uses the 24 letters adopted by Euclid as well as three Phoenician and Ionic ones that were not carried over, digamma, koppa, and sampi. The position of characters within the numbering system imply that the first two were still in use while the third was not. Greek numerals are decimal, based on powers of 10, the units from 1 to 9 are assigned to the first nine letters of the old Ionic alphabet from alpha to theta. Each multiple of one hundred from 100 to 900 was then assigned its own separate letter as well and this alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total. For example,241 was represented as, in ancient and medieval manuscripts, these numerals were eventually distinguished from letters using overbars, α, β, γ, etc. In medieval manuscripts of the Book of Revelation, the number of the Beast 666 is written as χξϛ, although the Greek alphabet began with only majuscule forms, surviving papyrus manuscripts from Egypt show that uncial and cursive minuscule forms began early. These new letter forms sometimes replaced the ones, especially in the case of the obscure numerals. The old Q-shaped koppa began to be broken up and simplified, the numeral for 6 changed several times. During antiquity, the letter form of digamma came to be avoided in favor of a special numerical one. By the Byzantine era, the letter was known as episemon and this eventually merged with the sigma-tau ligature stigma. In modern Greek, a number of changes have been made
7.
Roman numerals
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The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet, Roman numerals, as used today, are based on seven symbols, The use of Roman numerals continued long after the decline of the Roman Empire. The numbers 1 to 10 are usually expressed in Roman numerals as follows, I, II, III, IV, V, VI, VII, VIII, IX, Numbers are formed by combining symbols and adding the values, so II is two and XIII is thirteen. Symbols are placed left to right in order of value. Named after the year of its release,2014 as MMXIV, the year of the games of the XXII Olympic Winter Games The standard forms described above reflect typical modern usage rather than a universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval, Roman inscriptions, especially in official contexts, seem to show a preference for additive forms such as IIII and VIIII instead of subtractive forms such as IV and IX. Both methods appear in documents from the Roman era, even within the same document, double subtractives also occur, such as XIIX or even IIXX instead of XVIII. Sometimes V and L are not used, with such as IIIIII. Such variation and inconsistency continued through the period and into modern times. Clock faces that use Roman numerals normally show IIII for four o’clock but IX for nine o’clock, however, this is far from universal, for example, the clock on the Palace of Westminster in London uses IV. Similarly, at the beginning of the 20th century, different representations of 900 appeared in several inscribed dates. For instance,1910 is shown on Admiralty Arch, London, as MDCCCCX rather than MCMX, although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used
8.
Unicode
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Unicode is a computing industry standard for the consistent encoding, representation, and handling of text expressed in most of the worlds writing systems. As of June 2016, the most recent version is Unicode 9.0, the standard is maintained by the Unicode Consortium. Unicodes success at unifying character sets has led to its widespread, the standard has been implemented in many recent technologies, including modern operating systems, XML, Java, and the. NET Framework. Unicode can be implemented by different character encodings, the most commonly used encodings are UTF-8, UTF-16 and the now-obsolete UCS-2. UTF-8 uses one byte for any ASCII character, all of which have the same values in both UTF-8 and ASCII encoding, and up to four bytes for other characters. UCS-2 uses a 16-bit code unit for each character but cannot encode every character in the current Unicode standard, UTF-16 extends UCS-2, using one 16-bit unit for the characters that were representable in UCS-2 and two 16-bit units to handle each of the additional characters. Many traditional character encodings share a common problem in that they allow bilingual computer processing, Unicode, in intent, encodes the underlying characters—graphemes and grapheme-like units—rather than the variant glyphs for such characters. In the case of Chinese characters, this leads to controversies over distinguishing the underlying character from its variant glyphs. In text processing, Unicode takes the role of providing a unique code point—a number, in other words, Unicode represents a character in an abstract way and leaves the visual rendering to other software, such as a web browser or word processor. This simple aim becomes complicated, however, because of concessions made by Unicodes designers in the hope of encouraging a more rapid adoption of Unicode, the first 256 code points were made identical to the content of ISO-8859-1 so as to make it trivial to convert existing western text. For other examples, see duplicate characters in Unicode and he explained that he name Unicode is intended to suggest a unique, unified, universal encoding. In this document, entitled Unicode 88, Becker outlined a 16-bit character model, Unicode could be roughly described as wide-body ASCII that has been stretched to 16 bits to encompass the characters of all the worlds living languages. In a properly engineered design,16 bits per character are more than sufficient for this purpose, Unicode aims in the first instance at the characters published in modern text, whose number is undoubtedly far below 214 =16,384. By the end of 1990, most of the work on mapping existing character encoding standards had been completed, the Unicode Consortium was incorporated in California on January 3,1991, and in October 1991, the first volume of the Unicode standard was published. The second volume, covering Han ideographs, was published in June 1992, in 1996, a surrogate character mechanism was implemented in Unicode 2.0, so that Unicode was no longer restricted to 16 bits. The Microsoft TrueType specification version 1.0 from 1992 used the name Apple Unicode instead of Unicode for the Platform ID in the naming table, Unicode defines a codespace of 1,114,112 code points in the range 0hex to 10FFFFhex. Normally a Unicode code point is referred to by writing U+ followed by its hexadecimal number, for code points in the Basic Multilingual Plane, four digits are used, for code points outside the BMP, five or six digits are used, as required. Code points in Planes 1 through 16 are accessed as surrogate pairs in UTF-16, within each plane, characters are allocated within named blocks of related characters
9.
Binary number
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The base-2 system is a positional notation with a radix of 2. Because of its implementation in digital electronic circuitry using logic gates. Each digit is referred to as a bit, the modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de lArithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions, the method used for ancient Egyptian multiplication is also closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, the I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique and it is based on taoistic duality of yin and yang. Eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, the Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, Pingalas Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingalas system increases towards the right, the residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Africa, sets of binary combinations similar to the I Ching have also been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been applied in sub-Saharan Africa. Leibnizs system uses 0 and 1, like the modern binary numeral system, Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own beliefs as a Christian. Binary numerals were central to Leibnizs theology and he believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. Is not easy to impart to the pagans, is the ex nihilo through Gods almighty power. In 1854, British mathematician George Boole published a paper detailing an algebraic system of logic that would become known as Boolean algebra
10.
Ternary numeral system
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The ternary numeral system has three as its base. Analogous to a bit, a digit is a trit. One trit is equivalent to bits of information. Representations of integer numbers in ternary do not get uncomfortably lengthy as quickly as in binary, for example, decimal 365 corresponds to binary 101101101 and to ternary 111112. However, they are far less compact than the corresponding representations in bases such as decimal – see below for a compact way to codify ternary using nonary. The value of a number with n bits that are all 1 is 2n −1. Then N = M, N = /, and N = bd −1, for a three-digit ternary number, N =33 −1 =26 =2 ×32 +2 ×31 +2 ×30 =18 +6 +2. Nonary or septemvigesimal can be used for representation of ternary. A base-three system is used in Islam to keep track of counting Tasbih to 99 or to 100 on a hand for counting prayers. In certain analog logic, the state of the circuit is often expressed ternary and this is most commonly seen in Transistor–transistor logic using 7406 open collector logic. The output is said to either be low, high, or open, in this configuration the output of the circuit is actually not connected to any voltage reference at all. Where the signal is usually grounded to a reference, or at a certain voltage level. Thus, the voltage level is sometimes unpredictable. A rare ternary point is used to denote fractional parts of an inning in baseball, since each inning consists of three outs, each out is considered one third of an inning and is denoted as.1. For example, if a player pitched all of the 4th, 5th and 6th innings, plus 2 outs of the 7th inning, his Innings pitched column for that game would be listed as 3.2, meaning 3⅔. In this usage, only the part of the number is written in ternary form. Ternary numbers can be used to convey self-similar structures like the Sierpinski triangle or the Cantor set conveniently, additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed. The Cantor set consists of the points from 0 to 1 that have an expression that does not contain any instance of the digit 1
11.
Quaternary numeral system
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Quaternary is the base-4 numeral system. It uses the digits 0,1,2 and 3 to represent any real number. Four is the largest number within the range and one of two numbers that is both a square and a highly composite number, making quaternary a convenient choice for a base at this scale. Despite being twice as large, its economy is equal to that of binary. However, it no better in the localization of prime numbers. See decimal and binary for a discussion of these properties, as with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system. Each radix 4,8 and 16 is a power of 2, so the conversion to and from binary is implemented by matching each digit with 2,3 or 4 binary digits, for example, in base 4,302104 =11001001002. Although octal and hexadecimal are widely used in computing and computer programming in the discussion and analysis of binary arithmetic and logic, by analogy with byte and nybble, a quaternary digit is sometimes called a crumb. There is a surviving list of Ventureño language number words up to 32 written down by a Spanish priest ca, the Kharosthi numerals have a partial base 4 counting system from 1 to decimal 10. Quaternary numbers are used in the representation of 2D Hilbert curves, here a real number between 0 and 1 is converted into the quaternary system. Every single digit now indicates in which of the respective 4 sub-quadrants the number will be projected, parallels can be drawn between quaternary numerals and the way genetic code is represented by DNA. The four DNA nucleotides in order, abbreviated A, C, G and T, can be taken to represent the quaternary digits in numerical order 0,1,2. With this encoding, the complementary digit pairs 0↔3, and 1↔2 match the complementation of the pairs, A↔T and C↔G. For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010, quaternary line codes have been used for transmission, from the invention of the telegraph to the 2B1Q code used in modern ISDN circuits
12.
Quinary
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Quinary is a numeral system with five as the base. A possible origination of a system is that there are five fingers on either hand. The base five is stated from 0–4, in the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100, today, the main usage of base 5 is as a biquinary system, which is decimal using five as a sub-base. Another example of a system, is sexagesimal, base 60. Each quinary digit has log25 bits of information, many languages use quinary number systems, including Gumatj, Nunggubuyu, Kuurn Kopan Noot, Luiseño and Saraveca. Gumatj is a true 5–25 language, in which 25 is the group of 5. The Gumatj numerals are shown below, In the video game Riven and subsequent games of the Myst franchise, a decimal system with 2 and 5 as a sub-bases is called biquinary, and is found in Wolof and Khmer. Roman numerals are a biquinary system, the numbers 1,5,10, and 50 are written as I, V, X, and L respectively. Eight is VIII and seventy is LXX, most versions of the abacus use a biquinary system to simulate a decimal system for ease of calculation. Urnfield culture numerals and some tally mark systems are also biquinary, units of currencies are commonly partially or wholly biquinary. A vigesimal system with 4 and 5 as a sub-bases is found in Nahuatl, pentimal system Quibinary Yan Tan Tethera References, Quinary Base Conversion, includes fractional part, from Math Is Fun Media related to Quinary numeral system at Wikimedia Commons
13.
Senary
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
14.
Octal
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The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping binary digits into groups of three. For example, the representation for decimal 74 is 1001010. Two zeroes can be added at the left,1001010, corresponding the octal digits 112, in the decimal system each decimal place is a power of ten. For example,7410 =7 ×101 +4 ×100 In the octal system each place is a power of eight. The Yuki language in California and the Pamean languages in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves and it has been suggested that the reconstructed Proto-Indo-European word for nine might be related to the PIE word for new. Based on this, some have speculated that proto-Indo-Europeans used a number system. In 1716 King Charles XII of Sweden asked Emanuel Swedenborg to elaborate a number based on 64 instead of 10. Swedenborg however argued that for people with less intelligence than the king such a big base would be too difficult, in 1718 Swedenborg wrote a manuscript, En ny rekenkonst som om vexlas wid Thalet 8 i stelle then wanliga wid Thalet 10. The numbers 1-7 are there denoted by the l, s, n, m, t, f, u. Thus 8 = lo,16 = so,24 = no,64 = loo,512 = looo etc, numbers with consecutive consonants are pronounced with vowel sounds between in accordance with a special rule. Writing under the pseudonym Hirossa Ap-Iccim in The Gentlemans Magazine, July 1745, Hugh Jones proposed a system for British coins, weights. In 1801, James Anderson criticized the French for basing the Metric system on decimal arithmetic and he suggested base 8 for which he coined the term octal. In the mid 19th century, Alfred B. Taylor concluded that Our octonary radix is, therefore, so, for example, the number 65 would be spoken in octonary as under-un. Taylor also republished some of Swedenborgs work on octonary as an appendix to the above-cited publications, in the 2009 film Avatar, the language of the extraterrestrial Navi race employs an octal numeral system, probably due to the fact that they have four fingers on each hand. In the TV series Stargate SG-1, the Ancients, a race of beings responsible for the invention of the Stargates, in the tabletop game series Warhammer 40,000, the Tau race use an octal number system. Octal became widely used in computing systems such as the PDP-8, ICL1900. Octal was an abbreviation of binary for these machines because their word size is divisible by three
15.
Duodecimal
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The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written by a rotated 2 and this notation was introduced by Sir Isaac Pitman. These digit forms are available as Unicode characters on computerized systems since June 2015 as ↊ and ↋, other notations use A, T, or X for ten and B or E for eleven. The number twelve is written as 10 in duodecimal, whereas the digit string 12 means 1 dozen and 2 units. Similarly, in duodecimal 100 means 1 gross,1000 means 1 great gross, the number twelve, a superior highly composite number, is the smallest number with four non-trivial factors, and the smallest to include as factors all four numbers within the subitizing range. As a result, duodecimal has been described as the number system. Of its factors,2 and 3 are prime, which means the reciprocals of all 3-smooth numbers have a representation in duodecimal. In particular, the five most elementary fractions all have a terminating representation in duodecimal. This all makes it a convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary. Although the trigesimal and sexagesimal systems do even better in respect, this is at the cost of unwieldy multiplication tables. In this section, numerals are based on decimal places, for example,10 means ten,12 means twelve. Languages using duodecimal number systems are uncommon, germanic languages have special words for 11 and 12, such as eleven and twelve in English. However, they are considered to come from Proto-Germanic *ainlif and *twalif, historically, units of time in many civilizations are duodecimal. There are twelve signs of the zodiac, twelve months in a year, traditional Chinese calendars, clocks, and compasses are based on the twelve Earthly Branches. There are 12 inches in a foot,12 troy ounces in a troy pound,12 old British pence in a shilling,24 hours in a day. The Romans used a system based on 12, including the uncia which became both the English words ounce and inch. The importance of 12 has been attributed to the number of cycles in a year. It is possible to count to 12 with the acting as a pointer
16.
Hexadecimal
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In mathematics and computing, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, Hexadecimal numerals are widely used by computer system designers and programmers. As each hexadecimal digit represents four binary digits, it allows a more human-friendly representation of binary-coded values, one hexadecimal digit represents a nibble, which is half of an octet or byte. For example, a byte can have values ranging from 00000000 to 11111111 in binary form. In a non-programming context, a subscript is typically used to give the radix, several notations are used to support hexadecimal representation of constants in programming languages, usually involving a prefix or suffix. The prefix 0x is used in C and related languages, where this value might be denoted as 0x2AF3, in contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers expressed in other bases. There are several conventions for expressing values unambiguously, a numerical subscript can give the base explicitly,15910 is decimal 159,15916 is hexadecimal 159, which is equal to 34510. Some authors prefer a text subscript, such as 159decimal and 159hex, or 159d and 159h. example. com/name%20with%20spaces where %20 is the space character, thus ’, represents the right single quotation mark, Unicode code point number 2019 in hex,8217. In the Unicode standard, a value is represented with U+ followed by the hex value. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #, white, CSS allows 3-hexdigit abbreviations with one hexdigit per component, #FA3 abbreviates #FFAA33. *nix shells, AT&T assembly language and likewise the C programming language, to output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h, some assembly languages use the notation HABCD. Ada and VHDL enclose hexadecimal numerals in based numeric quotes, 16#5A3#, for bit vector constants VHDL uses the notation x5A3. Verilog represents hexadecimal constants in the form 8hFF, where 8 is the number of bits in the value, the Smalltalk language uses the prefix 16r, 16r5A3 PostScript and the Bourne shell and its derivatives denote hex with prefix 16#, 16#5A3. For PostScript, binary data can be expressed as unprefixed consecutive hexadecimal pairs, in early systems when a Macintosh crashed, one or two lines of hexadecimal code would be displayed under the Sad Mac to tell the user what went wrong. Common Lisp uses the prefixes #x and #16r, setting the variables *read-base* and *print-base* to 16 can also used to switch the reader and printer of a Common Lisp system to Hexadecimal number representation for reading and printing numbers. Thus Hexadecimal numbers can be represented without the #x or #16r prefix code, MSX BASIC, QuickBASIC, FreeBASIC and Visual Basic prefix hexadecimal numbers with &H, &H5A3 BBC BASIC and Locomotive BASIC use & for hex. TI-89 and 92 series uses a 0h prefix, 0h5A3 ALGOL68 uses the prefix 16r to denote hexadecimal numbers, binary, quaternary and octal numbers can be specified similarly
17.
Vigesimal
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The vigesimal or base 20 numeral system is based on twenty. In a vigesimal system, twenty individual numerals are used. One modern method of finding the extra needed symbols is to write ten as the letter A20, to write nineteen as J20, and this is similar to the common computer-science practice of writing hexadecimal numerals over 9 with the letters A–F. Another method skips over the letter I, in order to avoid confusion between I20 as eighteen and one, so that the number eighteen is written as J20, the number twenty is written as 1020. According to this notation,2020 means forty in decimal = + D020 means two hundred and sixty in decimal = +10020 means four hundred in decimal = + +, in the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example,10 means ten,20 means twenty, in decimal, dividing by three twice only gives one digit periods because 9 is the number below ten. 21, however, the adjacent to 20 that is divisible by 3, is not divisible by 9. Ninths in vigesimal have six-digit periods, the prime factorization of twenty is 22 ×5, so it is not a perfect power. However, its part,5, is congruent to 1. Thus, according to Artins conjecture on primitive roots, vigesimal has infinitely many cyclic primes, but the fraction of primes that are cyclic is not necessarily ~37. 395%. An UnrealScript program that computes the lengths of recurring periods of various fractions in a set of bases found that, of the first 15,456 primes. In many European languages,20 is used as a base, vigesimal systems are common in Africa, for example in Yoruba. Ogún,20, is the basic numeric block, ogójì,40, =20 multiplied by 2. Ogota,60, =20 multiplied by 3, ogorin,80, =20 multiplied by 4. Ogorun,100, =20 multiplied by 5, twenty was a base in the Maya and Aztec number systems. The Maya used the names for the powers of twenty, kal, bak, pic, calab, kinchil. See also Maya numerals and Maya calendar, Mayan languages, Yucatec, the Aztec called them, cempoalli, centzontli, cenxiquipilli, cempoalxiquipilli, centzonxiquipilli and cempoaltzonxiquipilli. Note that the ce prefix at the beginning means one and is replaced with the number to get the names of other multiples of the power
18.
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
19.
Lever 2000
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This is a list of Unilever brands. These brands have annual sales of one billion euros or more, Unilever is the worlds biggest ice cream manufacturer, with the exception of its U. S. The Heartbrand was launched in 1998 as an effort to increase brand awareness. It is present in more than 40 countries, under terms of the agreement, Strauss ice cream and krembo may be sold only in kosher supermarkets and import shops. It is distributed in North America by Dairy Delight, a subsidiary of Normans Dairy, Unilever generally manufactures the same ice cream with the same names, with rare occasions of regional availability, under different brands. Some of these ice creams include Carte DOr, Cornetto, Magnum, Solero, Twister, Choc Ice, Super Split, Fat Frog, Feast, Brunch and Viennetta
20.
Windows 2000
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Windows 2000 is an operating system for use on both client and server computers. It was produced by Microsoft and released to manufacturing on December 15,1999 and it is the successor to Windows NT4.0, and is the last version of Microsoft Windows to display the Windows NT designation. It is succeeded by Windows XP and Windows Server 2003, during development, Windows 2000 was known as Windows NT5.0. Four editions of Windows 2000 were released, Professional, Server, Advanced Server, and Datacenter Server, Windows 2000 introduces NTFS3.0, Encrypting File System, as well as basic and dynamic disk storage. Support for people with disabilities was improved over Windows NT4.0 with a number of new assistive technologies, the Windows 2000 Server family has additional features including the ability to provide Active Directory services. Windows 2000 can be installed either a manual or unattended installation. Microsoft marketed Windows 2000 as the most secure Windows version ever at the time, however, it became the target of a number of high-profile virus attacks such as Code Red and Nimda. For ten years after its release, it continued to receive patches for security vulnerabilities nearly every month until reaching the end of its lifecycle on July 13,2010. Windows 2000 is a continuation of the Microsoft Windows NT family of operating systems, the original name for the operating system was Windows NT5.0 and its Beta 1 was released in September 1997, followed by Beta 2 in August 1998. On October 27,1998, Microsoft announced that the name of the version of the operating system would be Windows 2000. Windows 2000 Beta 3 was released in January 1999, NT5.0 Beta 1 was similar to NT4.0, including a very similar themed logo. NT5.0 Beta 2 introduced a new boot screen. The new login prompt from the version made its first appearance in Beta 3 build 1946. The new, updated icons first appeared in Beta 3 build 1976, the Windows 2000 boot screen in the final version first appeared in Beta 3 build 1994. Windows 2000 did not have a codename because, according to Dave Thompson of Windows NT team, Windows 2000 Service Pack 1 was codenamed Asteroid and Windows 2000 64-bit was codenamed Janus. During development, there was a build for the Alpha which was abandoned some time after RC1 after Compaq announced they had dropped support for Windows NT on Alpha. From here, Microsoft issued three release candidates between July and November 1999, and finally released the system to partners on December 12,1999. The public could buy the version of Windows 2000 on February 17,2000
21.
Star Trek
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Star Trek is an American science fiction media franchise based on the television series created by Gene Roddenberry. The first television series, simply called Star Trek and now referred to as The Original Series, debuted in 1966 and it followed the interstellar adventures of Captain James T. Kirk and his crew aboard the starship USS Enterprise, an exploration vessel. The Star Trek canon of the franchise include The Original Series, a series, four spin-off television series, its film franchise. In creating Star Trek, Roddenberry was inspired by the Horatio Hornblower novels, the satirical book Gullivers Travels and these adventures continued in the short-lived Star Trek, The Animated Series and six feature films. The adventures of The Next Generation crew continued in four feature films. In 2009, the franchise underwent a reboot set in an alternate timeline, or Kelvin Timeline. This film featured a new cast portraying younger versions of the crew from the show, their adventures were continued in the sequel film. The thirteenth film feature and sequel, Star Trek Beyond, was released to coincide with the franchises 50th anniversary, a new Star Trek TV series, titled Star Trek, Discovery, will premiere in May 2017 on the digital platform CBS All Access. Star Trek has been a phenomenon for decades. Fans of the franchise are called Trekkies or Trekkers, the franchise spans a wide range of spin-offs including games, figurines, novels, toys, and comics. Star Trek had an attraction in Las Vegas that opened in 1998. At least two museum exhibits of props travel the world, the series has its own full-fledged constructed language, Klingon. Several parodies have been made of Star Trek, in addition, viewers have produced several fan productions. As of July 2016, the franchise had generated $10 billion in revenue, Star Trek is noted for its cultural influence beyond works of science fiction. The franchise is also noted for its civil rights stances. The Original Series included one of televisions first multiracial casts, Star Trek references can be found throughout popular culture from movies such as the submarine thriller Crimson Tide to the animated series South Park. As early as 1964, Gene Roddenberry drafted a proposal for the series that would become Star Trek
22.
Star Trek III: The Search for Spock
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Star Trek III, The Search for Spock is a 1984 American science fiction film released by Paramount Pictures. After the death of Spock, the crew of the USS Enterprise returns to Earth, Kirk learns that Spocks spirit, or katra, is held in the mind of Dr. Leonard Bones McCoy, Kirk and company steal the Enterprise to return Spocks body to his home planet. The crew must also contend with hostile Klingons, led by Kruge, Paramount commissioned the film after positive critical and commercial reaction to The Wrath of Khan. Nimoy directed, the first Star Trek cast member to do so, producer Harve Bennett wrote the script starting from the end and working back, and intended the destruction of the Enterprise to be a shocking development. Bennett and Nimoy collaborated with effects house Industrial Light & Magic to develop storyboards and new ship designs, aside from a single day of location shooting, all of the films scenes were shot on Paramount and ILM soundstages. Composer James Horner returned to expand his themes from the previous film, the Search for Spock opened June 1,1984. In its first week of release, the film grossed over $16 million from almost 2,000 theaters across North America and it went on to gross $76 million at the domestic box office, toward a total of $87 million worldwide. Critical reaction to The Search for Spock was positive, but notably less so than the previous film, reviewers generally praised the cast and characters, while criticism tended to focus on the plot, the special effects were conflictingly received. Roger Ebert called the film a compromise between the tones of the first and second Star Trek films, the Search for Spock was released on multiple home video formats, including VHS, DVD, and Blu-ray high definition discs. Nimoy went on to direct The Search for Spocks sequel, Star Trek IV, the casualties of the fight include Admiral James T. Kirks Vulcan friend, Spock, whose casket was launched into space and eventually landed on the planet created by the Genesis Device. On arriving at Earth Spacedock, Doctor Leonard McCoy begins to act strangely and is detained, David Marcus —Kirks son, a key scientist in Genesiss development—and Lieutenant Saavik are investigating the Genesis planet on board the science vessel Grissom. Discovering an unexpected life form on the surface, Marcus and Saavik transport to the planet and they find that the Genesis Device has resurrected Spock in the form of a child, although his mind is not present. Marcus admits that he used unstable protomatter in the development of the Genesis Device, causing Spock to age rapidly, meanwhile, Kruge, the commander of a Klingon vessel, intercepts information about Genesis. Believing the device to be useful as a weapon, he takes his cloaked ship to the Genesis planet, destroys the Grissom. Spocks father, Sarek, confronts Kirk about his sons death, the pair learn that before he died, Spock transferred his katra, or living spirit, to McCoy. Spocks katra and body are needed to lay him to rest on his homeworld, Vulcan, disobeying orders, Kirk and his officers spring McCoy from detention, disable the USS Excelsior, and steal the Enterprise from Spacedock to return to the Genesis planet to retrieve Spocks body. In orbit, the undermanned Enterprise is attacked and disabled by Kruge, in the standoff that follows, Kruge orders that one of the hostages on the surface be executed. Marcus is killed defending Saavik and Spock, Kirk and company feign surrender and activate the Enterprises self-destruct sequence, killing the Klingon boarding party while the Enterprise crew transports to the planets surface
23.
Hikaru Sulu
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Hikaru Kato Sulu is a fictional character in the Star Trek media franchise. Originally known simply as Sulu, he was portrayed by George Takei in the original Star Trek series. Sulu also appears in the animated Star Trek series, the first six Star Trek movies, one episode of Star Trek, Voyager, and in books, comics. Sulus first name, Hikaru, appeared in a 1981 novel well over a decade after the series had ended. John Cho assumed the role of the character in both the 2009 film Star Trek and its sequels, Star Trek Into Darkness and Star Trek Beyond. Takei recalled Gene Roddenberry wanted the character to represent all of Asia, Roddenberry did not want a nationally specific surname, so he looked at a map and saw the Sulu Sea. He thought, Ah, the waters of that sea touch all shores, the actor recalled, historically, Sulu was a Muslim sultanate founded in 1405 until March 1915 when the Sultan abdicated when it had become part of the United States. The island province of Sulu continued to be a US territory until 1946, in the book Inside Star Trek, The Real Story, the characters name is noted as a pun on the name of vice president of Desilu Studios, Herb Solow. Novelist Vonda McIntyre first presents Hikaru as the characters first name in the novel The Entropy Effect, McIntyre derived the characters first name from The Tale of Genji. In some Japanese dubs, Commander Sulus family name is changed to Kato and this is because there is no lu syllable in Japanese, so to Japanese speakers Sulu does not sound like a Japanese name. However, in recent movies, it is slightly changed. The name スールー, is used as opposed to スル, which would be a closer transliteration, suru with short vowels in Japanese is the verb to do, and as such might also come across as odd to Japanese audiences. The fictional character Hikaru Sulu was born in San Francisco, and is of Japanese heritage and he was shown as the USS Enterprises staff physicist in the pilot episode, Where No Man Has Gone Before. An early Paramount press release described this initial conception of his character as follows, Physicist Sulu is the trim, frequently it is his assessment of the conditions on unexplored planets that finally determines when and how they will be approached, or if they can be explored at all. However, throughout the rest of the series, he served as officer and senior helmsman. Throughout the series, Sulu is shown having many interests and hobbies, including gymnastics, botany, fencing, in the episode The Naked Time, Spock observes that Sulu is at heart a swashbuckler out of the 18th century. The character is promoted to lieutenant commander some time before Star Trek, The Motion Picture, during the first five Star Trek movies, he serves as helmsman aboard both the USS Enterprise and USS Enterprise-A. He is promoted to captain and given command of the USS Excelsior three years before the events of Star Trek VI, The Undiscovered Country, Star Trek Generations introduces Hikarus daughter, Demora Sulu, whose origins are also depicted in Peter Davids non-canon novel The Captains Daughter
24.
Star Trek VI: The Undiscovered Country
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Star Trek VI, The Undiscovered Country is a 1991 American science fiction film released by Paramount Pictures. It is the feature film based on Star Trek. Taking place after the events of Star Trek V, The Final Frontier, principal photography took place between April and September 1991. The production budget was smaller than anticipated because of the critical and commercial disappointment of The Final Frontier, because of a lack of sound stage space on the Paramount lot, many scenes were filmed around Hollywood. Meyer and cinematographer Hiro Narita aimed for a darker and more dramatic mood, subtly altering sets originally used for the television series Star Trek, producer Steven-Charles Jaffe led a second unit that filmed on an Alaskan glacier that stood in for a Klingon gulag. Cliff Eidelman produced the score, which is intentionally darker than previous Star Trek offerings. The film was released in North America on December 6,1991, the Undiscovered Country garnered positive reviews, with publications praising the lighthearted acting and facetious references. The film performed strongly at the box office and it posted the largest opening weekend gross of the series before going on to earn $96,888,996 worldwide. The film earned two Academy Award nominations, for Best Makeup and Best Sound Effects, and is the only Star Trek movie to win the Saturn Award for Best Science Fiction Film. A special collectors edition DVD version of the film was released in 2004, Star Trek creator Gene Roddenberry died shortly before the movies premiere, just days after viewing the film. The film marked the final appearance together of the series cast. The loss of their key energy production facility and the destruction of the Klingon homeworlds ozone layer throws the Klingon Empire into turmoil, no longer able to maintain a hostile footing, the Klingons sue for peace with their longstanding enemy, the United Federation of Planets. Enterprises captain, James T. Kirk, whose son David was murdered by Klingons years earlier, opposes the negotiations, after a rendezvous between Enterprise and Gorkons battlecruiser they continue towards Earth, with the crews sharing a tense meal aboard Enterprise. Later that night, Enterprise appears to fire on the Klingon ship with a pair of photon torpedoes, during the confusion, two figures wearing Starfleet suits and gravity boots beam aboard the Klingon ship and grievously wound Gorkon before beaming away. Kirk surrenders to avoid a fight, and beams aboard the Klingon ship with Doctor Leonard McCoy to attempt to save Gorkons life, the chancellor dies, and Gorkons chief of staff, General Chang, puts Kirk and McCoy on trial for his assassination. The pair are found guilty and sentenced to imprisonment on the frozen asteroid Rura Penthe. Gorkons daughter, Azetbur, becomes the new chancellor, and continues diplomatic negotiations, for reasons of security, the conference is relocated, while several senior Starfleet officers want to rescue Kirk and McCoy, the Federation president refuses to risk full-scale war. Azetbur likewise refuses to invade Federation space, stating that only Kirk, once her betrayal is revealed, Martia transforms into Kirks double and fights him, but she is killed by the prison guards to silence any witnesses
25.
Harry Potter and the Philosopher's Stone
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Harry Potter and the Philosophers Stone is the first novel in the Harry Potter series and J. K. Rowlings debut novel, first published in 1997 by Bloomsbury. It was published in the United States as Harry Potter and the Sorcerers Stone by Scholastic Corporation in 1998. The plot follows Harry Potter, a wizard who discovers his magical heritage as he makes close friends. With the help of his friends, Harry faces an attempted comeback by the dark wizard Lord Voldemort, who killed Harrys parents, the novel won most of the British book awards that were judged by children and other awards in the US. The book reached the top of the New York Times list of best-selling fiction in August 1999 and it has been translated into at least sixty-seven other languages and has been made into a feature-length film of the same name, as have all six of its sequels. Most reviews were favourable, commenting on Rowlings imagination, humour, simple, direct style and clever plot construction. The series has used as a source of object lessons in educational techniques, sociological analysis. The most evil and powerful wizard in history, Lord Voldemort, murdered James and Lily Potter but mysteriously disappeared after failing to kill their infant son. For ten years, living at number Four Privet Drive, Harry is treated by the Dursleys more like a servant than a member of the family and is forced to live in a cupboard under the stairs. Shortly before his birthday, a series of letters addressed to Harry arrive. To evade the pursuit of these letters, Vernon first takes the family to a hotel, but when the letters arrive there too, he hires a boat out to a hut on a small island. Hagrid takes Harry to a hidden London street called Diagon Alley, where he is surprised to discover how famous he is among the witches and wizards and he also finds that his parents inheritance is waiting for him at Gringotts Wizarding Bank. Guided by Hagrid, he buys the equipment he will need for his first year at Hogwarts, a month later, Harry leaves the Dursleys home to catch the Hogwarts Express from Kings Cross railway station. There he meets the Weasley family, who show him how to pass through the wall to Platform 9¾. While on the train, Harry meets two fellow first years, Ron Weasley, who becomes his friend, and Hermione Granger. Harry also makes an enemy of yet another first-year, Draco Malfoy, Draco offers to advise Harry, but Harry dislikes Draco for his arrogance and prejudice and rejects his offer of friendship. At Hogwarts, the first-years are assigned by the magical Sorting Hat to houses that best suit their personalities. While Harry is being sorted, the Hat suggests that he be placed into Slytherin which is known to house potential dark witches and wizards, but when Harry objects, Ron and Hermione are also sorted into Gryffindor
26.
Harry Potter and the Chamber of Secrets
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Harry Potter and the Chamber of Secrets is the second novel in the Harry Potter series, written by J. K. Rowling. These threats are found after attacks which leave residents of the school petrified, throughout the year, Harry and his friends Ron and Hermione investigate the attacks. The book was published in the United Kingdom on 2 July 1998 by Bloomsbury, several commentators have noted that personal identity is a strong theme in the book, and that it addresses issues of racism through the treatment of non-magical, non-human and non-living characters. Some commentators regard the diary as a warning against uncritical acceptance of information from sources whose motives, institutional authority is portrayed as self-serving and incompetent. The book is known to have some connections to the sixth novel of the series, Harry Potter. The film adaptation of the novel, released in 2002, became the seventh highest-grossing film ever, video games loosely based on Harry Potter and the Chamber of Secrets were also released for several platforms, and most obtained favourable reviews. This comes to nothing, as Draco’s father only told his son the general facts of the opening of the Chamber. Hermione provides the last set of clues that inform them of the identity, It is a basilisk, that kills with a stare. Harry, Ron, and Lockhart enter the Chamber, but the dunderheaded professor causes a rockfall upon attempt to modify the boys’ memories with Ron’s damaged wand, and Harry must enter alone. Harry, Ron, Ginny, and Lockhart return to the castle and reunite with McGonagall, Dumbledore. Lucius Malfoy bursts in after this meeting, demanding to know why and how Dumbledore has returned to the school and accompanied by Dobby, revealing the family to whom he is enslaved. The petrified students are cured, the exams are cancelled, Hagrid comes back in the middle of the final feast. Rowling found it difficult to finish Harry Potter and the Chamber of Secrets because she was afraid it would not live up to the expectations raised by Harry Potter, after delivering the manuscript to Bloomsbury on schedule, she took it back for six weeks of revision. In early drafts of the book, the ghost Nearly Headless Nick sang a song explaining his condition. This was cut as the editor did not care for the poem. Harry Potter and the Chamber of Secrets was published in the UK on 2 July 1998, in June 1999, it went straight to the top of three US best-seller lists, including The New York Times. First edition printings had several errors, which were fixed in subsequent reprints, initially Dumbledore said that Voldemort was the last remaining ancestor of Salazar Slytherin, instead of his descendant. Gilderoy Lockharts book on werewolves is entitled Weekends with Werewolves at one point, Harry Potter and the Chamber of Secrets was met with near universal acclaim
27.
Harry Potter and the Prisoner of Azkaban
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Harry Potter and the Prisoner of Azkaban is the third novel in the Harry Potter series, written by J. K. Rowling. The book follows Harry Potter, a wizard, in his third year at Hogwarts School of Witchcraft. Along with friends Ron Weasley and Hermione Granger, Harry investigates Sirius Black, the book was published in the United Kingdom on 8 July 1999 by Bloomsbury and in the United States on 8 September 1999 by Scholastic Inc. Rowling found the book easy to write, finishing it just a year after she had begun writing it, the book sold 68,000 copies in just three days after its release in the United Kingdom, and since has sold over three million in the country. The book won the 1999 Whitbread Childrens Book Award, the Bram Stoker Award, the 2000 Locus Award for Best Fantasy Novel, the film adaptation of the novel was released in 2004, grossing more than $796 million and earned notable critical acclaim. Video games loosely based on Harry Potter and the Prisoner of Azkaban were also released for several platforms, Harry is back at the Dursleys, where he sees on Muggle television that a prisoner named Sirius Black has escaped. Harry involuntarily inflates Aunt Marge when she comes to visit after she insults Harry and this leads to his running away and getting picked up by the Knight Bus. The night before he is expected to leave for Hogwarts, Harry learns that the prisoner, Sirius Black, is a convicted murderer. On the way to Hogwarts, a Dementor boards the train, causing Harry to faint, Harry, Ron, and Hermione learn that the Dementors will be patrolling the school in an attempt to protect Harry from Black. Later on, Lupins Defence Against the Dark Arts sessions prove far better than those of Gilderoy Lockharts. At Hogwarts, Harry has several problems with the Dementors, including an episode at a Quidditch match, during which he faints and his broom is smashed by the Whomping Willow. Working with Harry outside class, Lupin teaches him the Patronus Charm to repel Dementors, Ron and Hermiones friendship later suffers when Ron believes that Hermiones cat, Crookshanks, ate his rat, Scabbers. At Christmas, Harry receives a present, a late-model Firebolt broom. Fearing it might be cursed, Hermione reports the gift to Professor McGonagall, Ron, Hermione, and Harry join the effort to save Hagrids hippogriff, Buckbeak, from being executed for attacking Draco Malfoy, after Draco provoked him. Their efforts are unsuccessful, but Scabbers reappears shortly after they hear Buckbeak being executed, Ron chases Scabbers, only to be attacked by a big black dog, which Harry has seen several times before. The dog drags Ron through a tunnel under the Whomping Willow into the Shrieking Shack, Harry and Hermione follow, and there is a brief standoff when they find Ron and Sirius, who has transformed from the dog. Lupin enters, and they explain the situation to Harry and his friends, Lupin is a werewolf, which led to his friends James Potter, Sirius Black, and Peter Pettigrew becoming animagi. Lupin explains that Scabbers is Pettigrew in his form, he has been hiding from Black, whom he had framed for the murders of Harrys parents
28.
Antwerp
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Antwerp is a city in Belgium, the capital of Antwerp province in the region of Flanders. With a population of 510,610, it is the most populous city proper in Belgium and its metropolitan area houses around 1,200,000 people, which is second behind Brussels. Antwerp is on the River Scheldt, linked to the North Sea by the Westerschelde estuary, the Port of Antwerp is one of the biggest in the world, ranking second in Europe and within the top 20 globally. Antwerp has long been an important city in the Low Countries, the inhabitants of Antwerp are nicknamed Sinjoren, after the Spanish honorific señor or French seigneur, lord, referring to the Spanish noblemen who ruled the city in the 17th century. The city hosted the 1920 Summer Olympics, according to folklore, notably celebrated by a statue in front of the town hall, the city got its name from a legend about a giant called Antigoon who lived near the Scheldt river. He exacted a toll from passing boatmen, and for those who refused, he severed one of their hands, eventually the giant was killed by a young hero named Silvius Brabo, who cut off the giants own hand and flung it into the river. Hence the name Antwerpen, from Dutch hand werpen, akin to Old English hand and wearpan, a longstanding theory is that the name originated in the Gallo-Roman period and comes from the Latin antverpia. Antverpia would come from Ante Verpia, indicating land that forms by deposition in the curve of a river. Note that the river Scheldt, before a period between 600 and 750, followed a different track. This must have coincided roughly with the current ringway south of the city, however, many historians think it unlikely that there was a large settlement which would be named Antverpia, but more something like an outpost with a river crossing. However, John Lothrop Motley argues, and so do a lot of Dutch etymologists and historians, aan t werp is also possible. This warp is a hill or a river deposit, high enough to remain dry at high tide. Another word for werp is pol hence polders, historical Antwerp allegedly had its origins in a Gallo-Roman vicus. Excavations carried out in the oldest section near the Scheldt, 1952–1961, produced pottery shards, the earliest mention of Antwerp dates from the 4th century. In the 4th century, Antwerp was first named, having been settled by the Germanic Franks, the name was reputed to have been derived from anda and werpum. The Merovingian Antwerp was evangelized by Saint Amand in the 7th century, at the end of the 10th century, the Scheldt became the boundary of the Holy Roman Empire. Antwerp became a margraviate in 980, by the German emperor Otto I, in the 11th century Godfrey of Bouillon was for some years known as the marquis of Antwerp. In the 12th century, Norbert of Xanten established a community of his Premonstratensian canons at St. Michaels Abbey at Caloes
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Belgium
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Belgium, officially the Kingdom of Belgium, is a sovereign state in Western Europe bordered by France, the Netherlands, Germany, Luxembourg, and the North Sea. It is a small, densely populated country which covers an area of 30,528 square kilometres and has a population of about 11 million people. Additionally, there is a group of German-speakers who live in the East Cantons located around the High Fens area. Historically, Belgium, the Netherlands and Luxembourg were known as the Low Countries, the region was called Belgica in Latin, after the Roman province of Gallia Belgica. From the end of the Middle Ages until the 17th century, today, Belgium is a federal constitutional monarchy with a parliamentary system of governance. It is divided into three regions and three communities, that exist next to each other and its two largest regions are the Dutch-speaking region of Flanders in the north and the French-speaking southern region of Wallonia. The Brussels-Capital Region is a bilingual enclave within the Flemish Region. A German-speaking Community exists in eastern Wallonia, Belgiums linguistic diversity and related political conflicts are reflected in its political history and complex system of governance, made up of six different governments. Upon its independence, declared in 1830, Belgium participated in the Industrial Revolution and, during the course of the 20th century, possessed a number of colonies in Africa. This continuing antagonism has led to several far-reaching reforms, resulting in a transition from a unitary to a federal arrangement during the period from 1970 to 1993. Belgium is also a member of the Eurozone, NATO, OECD and WTO. Its capital, Brussels, hosts several of the EUs official seats as well as the headquarters of major international organizations such as NATO. Belgium is also a part of the Schengen Area, Belgium is a developed country, with an advanced high-income economy and is categorized as very high in the Human Development Index. A gradual immigration by Germanic Frankish tribes during the 5th century brought the area under the rule of the Merovingian kings, a gradual shift of power during the 8th century led the kingdom of the Franks to evolve into the Carolingian Empire. Many of these fiefdoms were united in the Burgundian Netherlands of the 14th and 15th centuries, the Eighty Years War divided the Low Countries into the northern United Provinces and the Southern Netherlands. The latter were ruled successively by the Spanish and the Austrian Habsburgs and this was the theatre of most Franco-Spanish and Franco-Austrian wars during the 17th and 18th centuries. The reunification of the Low Countries as the United Kingdom of the Netherlands occurred at the dissolution of the First French Empire in 1815, although the franchise was initially restricted, universal suffrage for men was introduced after the general strike of 1893 and for women in 1949. The main political parties of the 19th century were the Catholic Party, French was originally the single official language adopted by the nobility and the bourgeoisie
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Frederiksberg
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Frederiksberg is a part of the Capital Region of Denmark. It is formally an independent municipality, Frederiksberg Municipality, but is treated as a part of Copenhagen. It occupies an area of less than 9 km2 and had a population of 103,192 in 2015, Frederiksberg is an enclave surrounded by Copenhagen Municipality and there is no clear border between the two. Some sources ambiguously refer to Frederiksberg as a quarter or neighbourhood of Copenhagen, however, Frederiksberg has its own mayor and municipal council, and is fiercely independent. Frederiksberg is considered to be an affluent, or posh, area, the town is characterised by its many green spaces, such as the Frederiksberg Gardens and Søndermarken. Some institutions and locations that are considered to be part of Copenhagen are actually located in Frederiksberg. For example, Copenhagen Zoo as well as stations of the Copenhagen Metro are located in Frederiksberg. The Copenhagen S-train system also has stations in Frederiksberg, including Peter Bangs Vej station. Frederiksbergs original name was Tulehøj, indicating that a thul lived there, the term is known from the Snoldelev rune stone. In Beowulf, Unferth holds the same title, in Håvamål, Odin himself is referred to as the old thul. Thula translates as song, like in the Rigsthula poem from the Edda, by 1443 the name Tulehøj was spelled Tulleshøy. It was regarded as Copenhagens border to the west, people lived here since the Bronze Age. Farming was not very successful, and in 1697 most of the burned down. This meant that the peasants were unable to pay taxes, in 1700-1703, King Frederik IV built a palace on top of the hill known as Valby Bakke. He named the palace Frederichs Berg, and the town at the foot of the hill consequently changed its name to Frederiksberg. A number of the houses were bought by wealthy citizens of Copenhagen who did not farm the land. The town changed slowly from a community to a merchant town, with craftsmen. During the summer rooms were offered for rent, and restaurants served food to the people of Copenhagen who had left the city for the open land
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Denmark
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The term Danish Realm refers to the relationship between Denmark proper, the Faroe Islands and Greenland—three countries constituting the Kingdom of Denmark. The legal nature of the Kingdom of Denmark is fundamentally one of a sovereign state. The Faroe Islands and Greenland have been part of the Crown of Denmark since 1397 when the Kalmar Union was ratified, legal matters in The Danish Realm are subject to the Danish Constitution. Beginning in 1953, state law issues within The Danish Realm has been governed by The Unity of the Realm, a less formal name for The Unity of the Realm is the Commonwealth of the Realm. In 1978, The Unity of The Realm was for the first time referred to as rigsfællesskabet. The name caught on and since the 1990s, both The Unity of The Realm and The Danish Realm itself has increasingly been referred to as simply rigsfællesskabet in daily parlance. The Danish Constitution stipulates that the foreign and security interests for all parts of the Danish Realm are the responsibility of the Danish government, the Faroes received home rule in 1948 and Greenland did so in 1979. In 2005, the Faroes received a self-government arrangement, and in 2009 Greenland received self rule, the Danish Realms unique state of internal affairs is acted out in the principle of The Unity of the Realm. This principle is derived from Article 1 of the Danish Constitution which specifies that constitutional law applies equally to all areas of the Danish Realm, the Constitutional Act specifies that sovereignty is to continue to be exclusively with the authorities of the Realm. The language of Denmark is Danish, and the Danish state authorities are based in Denmark, the Kingdom of Denmarks parliament, with its 179 members, is located in the capital, Copenhagen. Two of the members are elected in each of Greenland and the Faroe Islands. The Government ministries are located in Copenhagen, as is the highest court, in principle, the Danish Realm constitutes a unified sovereign state, with equal status between its constituent parts. Devolution differs from federalism in that the powers of the subnational authority ultimately reside in central government. The Self-Government Arrangements devolves political competence and responsibility from the Danish political authorities to the Faroese, the Faroese and Greenlandic authorities administer the tasks taken over from the state, enact legislation in these specific fields and have the economic responsibility for solving these tasks. The Danish government provides a grant to the Faroese and the Greenlandic authorities to cover the costs of these devolved areas. The 1948 Home Rule Act of the Faroe Islands sets out the terms of Faroese home rule, the Act states. the Faroe Islands shall constitute a self-governing community within the State of Denmark. It establishes the government of the Faroe Islands and the Faroese parliament. The Faroe Islands were previously administered as a Danish county, the Home Rule Act abolished the post of Amtmand and these powers were expanded in a 2005 Act, which named the Faroese home government as an equal partner with the Danish government
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Sydney
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Sydney /ˈsɪdni/ is the state capital of New South Wales and the most populous city in Australia and Oceania. Located on Australias east coast, the metropolis surrounds the worlds largest natural harbour, residents of Sydney are known as Sydneysiders. The Sydney area has been inhabited by indigenous Australians for at least 30,000 years, the first British settlers, led by Captain Arthur Phillip, arrived in 1788 to found Sydney as a penal colony, the first European settlement in Australia. Since convict transportation ended in the century, the city has transformed from a colonial outpost into a major global cultural. As at June 2016 Sydneys estimated population was 5,005,358, in the 2011 census,34 percent of the population reported having been born overseas, representing many different nationalities and making Sydney one of the most multicultural cities in the world. There are more than 250 different languages spoken in Sydney and about one-third of residents speak a language other than English at home and it is classified as an Alpha+ World City by the Globalization and World Cities Research Network, indicating its influence in the region and throughout the world. Ranked eleventh in the world for economic opportunity, Sydney has a market economy with strengths in finance, manufacturing. Its gross regional product was $337 billion in 2013, the largest in Australia, there is a significant concentration of foreign banks and multinational corporations in Sydney and the city is promoted as one of Asia Pacifics leading financial hubs. Its natural features include Sydney Harbour, the Royal National Park, man-made attractions such as the Sydney Opera House, Sydney Tower and the Sydney Harbour Bridge are also well known to international visitors. The first people to inhabit the now known as Sydney were indigenous Australians having migrated from northern Australia. Radiocarbon dating suggests human activity first started to occur in the Sydney area from around 30,735 years ago, the earliest British settlers called them Eora people. Eora is the term the indigenous used to explain their origins upon first contact with the British. Its literal meaning is from this place, prior to the arrival of the British there were 4,000 to 8,000 native people in Sydney from as many as 29 different clans. Sydney Cove from Port Jackson to Petersham was inhabited by the Cadigal clan, the principal language groups were Darug, Guringai, and Dharawal. The earliest Europeans to visit the area noted that the people were conducting activities such as camping and fishing, using trees for bark and food, collecting shells. Development has destroyed much of the citys history including that of the first inhabitants, there continues to be examples of rock art and engravings located in the protected Ku-ring-gai Chase National Park. The first meeting between the people and the British occurred on 29 April 1770 when Lieutenant James Cook landed at Botany Bay on the Kurnell Peninsula. He noted in his journal that they were confused and somewhat hostile towards the foreign visitors, Cook was on a mission of exploration and was not commissioned to start a settlement
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United States Chess Federation
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The United States Chess Federation is the governing body for chess competition in the United States and represents the U. S. in FIDE, the World Chess Federation. USCF administers the national rating system, awards national titles, sanctions over twenty national championships annually. USCF was founded and incorporated in Illinois in 1939, from the merger of two older chess organizations and it is a 501 non-profit organization headquartered in Crossville, Tennessee. Its membership as of 2016 is over 85,000, in 1939, the United States of America Chess Federation was created in Illinois through the merger of the American Chess Federation and National Chess Federation. The American Chess Federation, formerly the Western Chess Association, had held an open championship since 1900. The National Chess Federation, founded in 1927 to organize U. S. participation in the Olympiads, had held the prestigious invitational U. S, the combined membership at the time was around 1,000. Membership experienced consistent, modest growth until 1958, when Bobby Fischer won the U. S, Championship at the age of 14. This began the Fischer era, during which USCF membership grew thirty-fold, to approximately 60,000 in 1974, the Fischer era did not last long, but the USCF has grown substantially since then, largely because of the explosive growth of scholastic chess. Annual national championship tournaments are now held at different grade and age levels, none of these tournaments, at its founding, the USCF had no employees and no headquarters, but in 1952, the USCF hired a Business Manager, headquartered in New York. In 1967, headquarters moved to Newburgh, New York, in 1976, New Windsor, New York, USCF is a federation of state affiliates. Each state has an affiliate which selects delegates to represent that state affiliate in the governance of the organization and this Board of Delegates was the board of directors until changes to the USCF Articles of Incorporation and Bylaws were approved by the Delegates in 2012. The 2012 governance changes made the seven member Executive Board the corporate board of directors while reserving specific powers to the Board of Delegates. At the same time, the Delegates made the Articles of Incorporation much more difficult to change as a way to protect the reservation of powers to the Delegates. The election of what is now called the Executive Board has evolved over time, the changes have generally been to expand the number of voters. At one time this board was elected by the Board of Delegates, a significant change in the early 2000s was to adopt changes which allow any member age 16 and over to vote for the Executive Board. Members who wish to vote are required to register with the USCF office, USCF implements rating systems for chess players. In each system, a rating is a calculated numerical estimate of his strength. Tournament organizers submit results to the USCF, which carries out the calculations, a player can have up to six ratings, for correspondence games, for over-the-board games at regular, quick, or blitz time controls, and for online games at quick or blitz time controls
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Sphenic number
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In number theory, a sphenic number is a positive integer that is the product of three distinct prime numbers. A sphenic number is a product pqr where p, q and this definition is more stringent than simply requiring the integer to have exactly three prime factors. For instance,60 =22 ×3 ×5 has exactly 3 prime factors, the smallest sphenic number is 30 =2 ×3 ×5, the product of the smallest three primes. The first few numbers are 30,42,66,70,78,102,105,110,114,130,138,154,165. As of January 2016 the largest known number is × ×. It is the product of the three largest known primes, all sphenic numbers have exactly eight divisors. If we express the number as n = p ⋅ q ⋅ r, where p, q. For example,24 is not a number, but it has exactly eight divisors. All sphenic numbers are by definition squarefree, because the factors must be distinct. The Möbius function of any number is −1. The cyclotomic polynomials Φ n, taken over all sphenic numbers n, the first case of two consecutive sphenic integers is 230 = 2×5×23 and 231 = 3×7×11. The first case of three is 1309 = 7×11×17,1310 = 2×5×131, and 1311 = 3×19×23, there is no case of more than three, because every fourth consecutive positive integer is divisible by 4 = 2×2 and therefore not squarefree. The numbers 2013,2014, and 2015 are all sphenic, the next three consecutive sphenic years will be 2665,2666 and 2667. Semiprimes, products of two prime numbers