1.
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
2.
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
3.
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
4.
Divisor
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In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some other integer to produce n. In this case one says also that n is a multiple of m, an integer n is divisible by another integer m if m is a divisor of n, this implies dividing n by m leaves no remainder. Under this definition, the statement m ∣0 holds for every m, as before, but with the additional constraint k ≠0. Under this definition, the statement m ∣0 does not hold for m ≠0, in the remainder of this article, which definition is applied is indicated where this is significant. Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4, they are 1,2,4, −1, −2, and −4,1 and −1 divide every integer. Every integer is a divisor of itself, every integer is a divisor of 0. Integers divisible by 2 are called even, and numbers not divisible by 2 are called odd,1, −1, n and −n are known as the trivial divisors of n. A divisor of n that is not a divisor is known as a non-trivial divisor. A non-zero integer with at least one divisor is known as a composite number, while the units −1 and 1. There are divisibility rules which allow one to recognize certain divisors of a number from the numbers digits, the generalization can be said to be the concept of divisibility in any integral domain. 7 is a divisor of 42 because 7 ×6 =42 and it can also be said that 42 is divisible by 7,42 is a multiple of 7,7 divides 42, or 7 is a factor of 42. The non-trivial divisors of 6 are 2, −2,3, the positive divisors of 42 are 1,2,3,6,7,14,21,42. 5 ∣0, because 5 ×0 =0, if a ∣ b and b ∣ a, then a = b or a = − b. If a ∣ b and a ∣ c, then a ∣ holds, however, if a ∣ b and c ∣ b, then ∣ b does not always hold. If a ∣ b c, and gcd =1, then a ∣ c, if p is a prime number and p ∣ a b then p ∣ a or p ∣ b. A positive divisor of n which is different from n is called a proper divisor or a part of n. A number that does not evenly divide n but leaves a remainder is called an aliquant part of n, an integer n >1 whose only proper divisor is 1 is called a prime number
5.
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
6.
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
7.
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
8.
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
9.
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
10.
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
11.
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
12.
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
13.
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
14.
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
15.
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
16.
George Lucas
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George Walton Lucas Jr. is an American filmmaker and entrepreneur. He is best known as the creator of the Star Wars and Indiana Jones franchises, as well as the founder of Lucasfilm and he was the Chairman and Chief Executive Officer of Lucasfilm, before selling it to The Walt Disney Company in 2012. Upon graduating from the University of Southern California in 1967, Lucas co-founded American Zoetrope with fellow filmmaker Francis Ford Coppola, Lucas wrote and directed THX1138, based on his earlier student short Electronic Labyrinth, THX1138 4EB, which was a critical success but a financial failure. His next work as a writer-director was the film, American Graffiti, inspired by his teen years in early 1960s Modesto, California, the film was critically and commercially successful, and received five Academy Award nominations including Best Picture. Following the first Star Wars film, Lucas produced and co-wrote the following installments in the trilogy, The Empire Strikes Back, along with Steven Spielberg, Lucas co-created and wrote the Indiana Jones films Raiders of the Lost Ark, Temple of Doom, and The Last Crusade. Lucas also produced and/or wrote a variety of films through Lucasfilm in the 1980s and 1990s, Lucas also returned to directing with the Star Wars prequel trilogy, consisting of The Phantom Menace, Attack of the Clones, and Revenge of the Sith. He later collaborated on the story for the Indiana Jones sequel Kingdom of the Crystal Skull, five of Lucass seven features are among the 100 highest-grossing movies at the North American box office, adjusted for ticket-price inflation. Lucas is one of the American film industrys most financially successful filmmakers, Lucas is considered a significant figure in the New Hollywood era. Lucas was born and raised in Modesto, California, the son of Dorothy Ellinore Lucas and George Walton Lucas and he is of German, Swiss-German, English, Scottish, and distant Dutch and French descent. Growing up, Lucas had a passion for cars and motor racing, on June 12,1962, while driving his souped-up Autobianchi Bianchina, another driver broadsided him, flipping over his car, nearly killing him, causing him to lose interest in racing as a career. He attended Modesto Junior College, where he studied anthropology, sociology and he also began shooting with an 8 mm camera, including filming car races. At this time, Lucas and his friend John Plummer became interested in Canyon Cinema, screenings of underground, avant-garde 16 mm filmmakers like Jordan Belson, Stan Brakhage, and Bruce Conner. Lucas and Plummer also saw classic European films of the time, including Jean-Luc Godards Breathless, François Truffauts Jules et Jim, thats when George really started exploring, Plummer said. Through his interest in racing, Lucas met renowned cinematographer Haskell Wexler, another race enthusiast. Wexler, later to work with Lucas on several occasions, was impressed by Lucas talent, George had a very good eye, and he thought visually, he recalled. Lucas then transferred to the University of Southern California School of Cinematic Arts, USC was one of the earliest universities to have a school devoted to motion picture film. During the years at USC, Lucas shared a room with Randal Kleiser. Along with classmates such as Walter Murch, Hal Barwood, and John Milius and he also became good friends with fellow acclaimed student filmmaker and future Indiana Jones collaborator, Steven Spielberg
17.
THX 1138
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THX1138 is a 1971 American social science fiction film directed by George Lucas in his feature film directorial debut. THX1138 was developed from Lucass student film Electronic Labyrinth, THX1138 4EB, the feature film was produced in a joint venture between Warner Bros. and Francis Ford Coppolas production company, American Zoetrope. A novelization by Ben Bova was published in 1971, emotions, coitus, and the concept of family are a taboo. Everyone is clad in uniforms and has shaven heads to emphasize equality, except the police androids. Instead of names, people have designations – reminiscent of licence plates – with three letters and four digits, shown on an identity badge worn at all times. At their jobs in central video CCTV control centers, SEN5241, LUH has a male roommate, THX1138, who works in a factory producing android police officers. On the way home, he stops at a booth in a row of many. A soothing voice greets THX, and OMM ends every confession with a salutation, You are a true believer, blessings of the State. Work hard, increase production, prevent accidents and be happy, at home, THX takes his drugs, and watches holo-broadcasts while engaging with a masturbatory device. LUH secretly substitutes pills in her possession for THXs medications, whereupon THX eventually suffers physical discomfort along with mental/emotional changes, the drug substitution also leads to LUH and THX becoming involved romantically, resulting in the two engaging in intercourse. THX later is confronted by SEN, who arranges THX as his new roommate, without drugs in his system, THX falters during a critical and hazardous phase of his job, and a control center engages a mind lock on THX which raises the level of danger. After the release of the lock, THX makes the necessary correction to that work phase. THX enjoys a reunion with LUH, disrupted shortly after she reveals her pregnancy. At THXs trial, THX is sentenced to prison, alongside SEN, most of the prisoners seem uninterested in escape, but eventually THX and SEN find an exit, they are later joined by hologram SRT5752, who starred in the holo-broadcasts. During the escape, THX and SRT are separated from SEN, SEN eventually escapes to an area reserved for the monks of OMM, where a lone monk notices that SEN has no identification badge. SEN attacks him and later wanders into an area, strikes up a conversation with children. THX and SRT steal two cars, but SRT crashes his into a concrete pillar, pursued by two police androids on motorcycles, THX flees to the limits of the city and escapes into a ventilation shaft. It is then revealed that the city is entirely underground, from the 1969 incarnation of American Zoetrope
18.
THX
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THX is an American company headquartered in San Francisco, California, and founded in 1983 by George Lucas. It develops the THX high fidelity audio/visual reproduction standards for movie theaters, screening rooms, home theaters, computer speakers, gaming consoles, car audio systems, the current THX was created in 2002 when it spun off from Lucasfilm Ltd. THX was named after Holman, with the X standing for crossover or possibly experiment as well as in homage to Lucass first film, THX1138. The distinctive glissando up from a low pitch used in the THX trailers. The THX system is not a technology and it does not specify a sound recording format, all sound formats, whether digital or analog. THX is mainly a quality assurance system, THX also provides certified theaters with a special crossover circuit whose use is part of the standard. The company has had a history with Creative, which was responsible for the creation of the first THX-certified audio card for computers. In 2016, THX was acquired by videogame hardware company Razer Inc. with Razer owning all of THX, the first theater THX was used in was the University of Southern Californias Eileen L. Norris Cinema Theatre, a part of USCs film school. THX has created a process for additional products including home audio, home theater, video. THX certification extends to home receivers, speakers, desktop systems, soundbars, acoustic materials, microphones. THXs Ultra2 certification is given for home theater components said to be enough for a large home cinema of 3,000 cubic feet or more. THXs Select2 certification is given for home theater components said to be enough for medium-sized rooms, up to 2,000 cubic feet in size. THXs I/S Plus systems include an AV Receiver + Speaker Bundle and are certified to fill a home theater or dorm room where the viewing distance from the screen is 6–8 feet. These THX certified home theater in a box systems are so far exclusively made by Onkyo, THX Certified Multimedia Products are designed and engineered for PC gaming and multimedia on the desktop. THX-certified video displays include a THX mode which allows users to see a program or movie as the creator intended, THX first appeared in theaters, in which their logo would show before the start of a film. Since THX was originally created for motion picture quality, the very first film to show THX was Return of the Jedi, in its theatrical debut on May 25,1983. From there, THX began to appear before all movies from June 1,1983, until August 31,1996, at that point, THX had certified VHS/home video releases beginning in 1995. Also, in 2000, based on the long-lasting Broadway trailer, grampa Simpson shouts, Turn it up
19.
Lucasfilm
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LLC is an American film and television production company based in the Letterman Digital Arts Center in San Francisco, California. The studio is best known for creating and producing the Star Wars and Indiana Jones franchises, as well as its leadership in developing special effects, sound and computer animation for film. Lucasfilm was founded by filmmaker George Lucas in 1971 in San Rafael, California, the Walt Disney Company acquired Lucasfilm in 2012 at a valuation of $4.06 billion. Lucasfilm was founded by filmmaker George Lucas in 1971, and incorporated as Lucasfilm Ltd. on September 12,1977, on July 8,2005, Lucasfilms marketing, online, and licensing units moved into the new Letterman Digital Arts Center located in the Presidio in San Francisco. It shares the complex with Industrial Light & Magic, Lucasfilm had planned an expansion at Skywalker Ranch in Marin County, California, but shelved the plan in 2012 due to opposition from neighbors. However, it plans to expand elsewhere. Skywalker Sound remains the only Lucasfilm division based at Skywalker Ranch, in January 2012, Lucas announced his retirement from producing large-scale blockbuster films and instead re-focusing his career on smaller, independently budgeted features. She would in June 2013 and is now chairperson of Lucasfilm, on September 5,2012, Micheline Chau, who served as president and COO of Lucasfilm for two decades, announced that she was retiring. With her departure, senior executives for each of the Lucasfilm divisions will report directly to Kathleen Kennedy, Chau was credited with keeping the Lucasfilm and Star Wars brands strong, especially through animation spin-offs and licensing initiatives. Lucas told Iger he was considering retirement and planned to sell the company, on October 30,2012, Disney announced a deal to acquire Lucasfilm for $4.05 billion, with approximately half in cash and half in shares of Disney stock. Kathleen Kennedy, co-chairman of Lucasfilm, became president of Lucasfilm, additionally she serves as the brand manager for Star Wars, working directly with Disneys global lines of business to build, further integrate, and maximize the value of this global franchise. Kennedy serves as producer on new Star Wars feature films, with George Lucas originally announced as serving as creative consultant, the company also announced the future release of new Star Wars films, starting with Star Wars, The Force Awakens in 2015. Disney also acquired Lucasfilms portfolio of entertainment technologies, the intent was for Lucasfilm employees to remain in their current locations. Star Wars merchandising would begin under Disney in the fiscal year 2014, starting with Star Wars Rebels, certain products will be co-branded with the Disney brand, akin to what Disney has done with Pixar. On December 4,2012, the Disney-Lucasfilm merger was approved by the Federal Trade Commission, on December 18,2012, Lucasfilm Ltd. was reincorporated as Lucasfilm Ltd. LLC, and on December 21,2012, the deal was announced to be completed, in April 2013, the development arm of the LucasArts division was closed down and most of its staff was laid off. However, LucasArts remained open with a staff of fewer than ten employees so it could retain its function as a video game licensor. On May 6,2013, Disney announced a deal with Electronic Arts to produce Star Wars games for the core gaming market
20.
LucasArts
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LucasArts Entertainment Company, LLC is an American video game publisher and licensor. Until 2013, it was also a game developer. LucasArts is best known for its graphic adventure games, as well as based on the Star Wars. Its headquarters are located in San Francisco, California and it was founded in May 1982 by George Lucas as Lucasfilm Games, the video game development group of his film company, Lucasfilm. Lucas initially served as the companys chairman, during a 1990 reorganization of Lucas companies, the Lucasfilm Games division was renamed LucasArts. LucasArts was acquired by The Walt Disney Company through the acquisition of its parent company Lucasfilm in 2012, on April 3,2013, Disney halted all internal development at LucasArts and laid off most of its staff. However, LucasArts remained open so that it could retain its function as a licensor, development of games based on the Star Wars license will be performed by Electronic Arts, through an exclusive license, for the core gaming market. Disney Interactive Studios retained the ability to develop, and LucasArts retained the ability to license the franchise for the gaming market. Development of video based upon other Lucasfilm properties will now be assumed by Disney Interactive Studios or licensed to third parties. The company was founded in May 1982 as the game development group of Lucasfilm Limited. Lucas wanted his company to branch out into areas of entertainment. The Lucasfilm Games Group originally cooperated with Atari, which helped fund the video game groups founding, the first results of this collaboration were unique action games like Ballblazer in 1984, and Rescue on Fractalus. In 1984, they were released for the Atari 5200 under the Lucasfilm Games label, versions for home computers were not released until 1985, by publisher Epyx. Lucasfilms next two games were Koronis Rift and The Eidolon and their first games were only developed by Lucasfilm, and a publisher would distribute the games. Atari published their games for Atari systems, Activision and Epyx would do their computer publishing, Maniac Mansion was the first game to be published and developed by Lucasfilm Games. The early charter of Lucasfilm Games was to make experimental, innovative, Habitat, an early online role-playing game, was one such title. It was only released as a beta test in 1986 by Quantum Link, Quantum Link could not provide the bandwidth at the time to support the game, so the full Habitat was never released outside of the beta test. However, Lucasfilm Games recouped the cost of development by releasing a sized down version called Club Caribe in 1988, Lucasfilm later licensed the software to Fujitsu, who released it in Japan as Fujitsu Habitat in 1990
21.
PC game
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PC games, also known as computer games or personal computer games, are video games played on a personal computer rather than a dedicated video game console or arcade machine. Home computer games became popular following the game crash of 1983 leading to the era of the bedroom coder. In the 1990s, PC games lost mass-market traction to console games before enjoying a resurgence in the mid-2000s through digital distribution. Newzoo, reports that gaming is a US$99.6 billion dollar industry, PC is considered synonymous with IBM PC compatible systems, while mobile computers – smartphones and tablets, such as those running Android or iOS – are also personal computers. The APAC region is estimated to generate $46.6 billion in 2016, or 47% of total global game revenues. China alone accounts for half of APACs revenues, reaching $24.4 billion, cementing its place as the largest games market in the world, the uncoordinated nature of the PC game market and its lack of physical media make precisely assessing its size difficult. Although personal computers became popular with the development of the microprocessor and microcomputer, computer gaming on mainframes. OXO, an adaptation of tic-tac-toe for the EDSAC, debuted in 1952, another pioneer computer game was developed in 1961, when MIT students Martin Graetz and Alan Kotok, with MIT student Steve Russell, developed Spacewar. On a PDP-1 mainframe computer used for statistical calculations, the first generation of computer games were often text adventures or interactive fiction, in which the player communicated with the computer by entering commands through a keyboard. An early text-adventure, Adventure, was developed for the PDP-11 minicomputer by Will Crowther in 1976, by the 1980s, personal computers had become powerful enough to run games like Adventure, but by this time, graphics were beginning to become an important factor in games. Later games combined textual commands with basic graphics, as seen in the SSI Gold Box games such as Pool of Radiance, or Bards Tale for example. By the late 1970s to early 1980s, games were developed and distributed through hobbyist groups and gaming magazines, such as Creative Computing and these publications provided game code that could be typed into a computer and played, encouraging readers to submit their own software to competitions. Microchess was one of the first games for microcomputers which was sold to the public, first sold in 1977, Microchess eventually sold over 50,000 copies on cassette tape. As with second-generation video game consoles at the time, early computer game companies capitalized on successful arcade games at the time with ports or clones of popular arcade games. By 1982, the games for the Atari 400 were ports of Frogger and Centipede. That same year, Pac-Man was ported to the Atari 800, grossly underperformed, the popularity of personal computers for education rose dramatically. In 1983, consumer interest in video games dwindled to historical lows. The effects of the crash were largely limited to the console market, the North American console market experienced a resurgence in the United States with the release of the Nintendo Entertainment System
22.
American Graffiti
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Suzanne Somers and Joe Spano have cameos. Set in Modesto, California in 1962, the film is a study of the cruising and rock, the film is told in a series of vignettes, telling the story of a group of teenagers and their adventures over a single evening. The genesis of American Graffiti was in Lucas own teenage years in early 1960s Modesto. filming was initially set to take place in San Rafael, California, but the production crew was denied permission to shoot beyond a second day. American Graffiti premiered on August 2,1973 at the Locarno International Film Festival in Switzerland and was released on August 11,1973 in the United States, the film received widespread critical acclaim and was nominated for the Academy Award for Best Picture. Produced on a $777,000 budget, it has one of the most profitable films of all time. Since its initial release, American Graffiti has garnered an estimated return of well over $200 million in box office gross and home video sales, not including merchandising. In 1995, the United States Library of Congress deemed the film culturally, historically, or aesthetically significant, a sequel, More American Graffiti, was released in 1979. Curt and Steve are scheduled to travel the next morning to Northeastern United States to start college, despite receiving a $2,000 scholarship from the local Moose Lodge, Curt has second thoughts about leaving Modesto. Steve gives Toad his 1958 Chevrolet Impala to watch while hes away at college until he returns at Christmas, Steves girlfriend, Laurie, who is also Curts sister, arrives in her car. Steve suggests to Laurie, who is already glum about him going to college, though not openly upset, she is displeased with his proposal which affects their interactions the rest of the evening. Curt accompanies Steve, last years high school student class president, and Laurie, after leaving the hop, Curt is coerced by a group of greasers to participate in an initiation rite that involves hooking a chain to a police car and ripping out its back axle. The Pharaohs tell Curt that The Blonde is a wife or prostitute. Determined to get a message to the girl, Curt drives to the local radio station to ask DJ Wolfman Jack. Inside the radio station, Curt encounters a man who tells him that the voice of The Wolfman is pre-taped from afar. The man still accepts the message from Curt to see what he could do, as he is leaving the station, Curt sees the man talking into the microphone and hears the voice of The Wolfman, and realizes the man is the actual DJ himself. Sure enough, The Wolfman eventually reads the message on the radio for The Blonde to meet Curt or call him at a number which happens to be a telephone booth, Curt waits by the telephone booth and early the next morning, he is awakened by the phone ringing. It turns out to be The Blonde who says she knows him, Curt replies probably not, intimating that he decided to go to college and will be leaving that morning. Meanwhile The Toad, in Steves car, and John, in his yellow 1932 Deuce Coupé hot rod, Toad, who is normally socially inept with girls, successfully picks up a flirtatious, and somewhat rebellious, girl named Debbie
23.
1932 Ford
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Ford produced three cars between 1932 and 1934, the Model B, Model 18 & Model 40. The Model B continued to offer Fords proven four cylinder and was available from 1932 to 1934, the V8 was succeeded by the Model 48. It was the first Ford fitted with the flathead V‑8, in Europe, it was built slightly longer. The same bodies were available on both 4 cylinder Model Bs and V8 Model 18/40s, the company also replaced the Model AA truck with the Model BB, available with either the four- or eight-cylinder engine. Rather than just a much updated version of the Model A, the V-8 was marketed as the Model 18 in its initial year, and commonly simply called the Ford V‑8. It had the new flathead V‑8 engine, the Model 18 was the first low-priced, mass-marketed car to have a V8 engine, an important milestone in Automotive industry in the United States. The 221 cu in V8 was rated at 65 hp when introduced and this engine choice was more popular than the four-cylinder, which was essentially a variant of the Model A engine with improvements to balancing and lubrication. Model B was derived with as few changes as possible to keep cost low. Other than the engine, and badging on headlamp support bar and hub caps and its intention was to be a price leader, and as it offered more than the popular Model A, this should have been a winning formula. In fact, the new and only slightly more expensive V-8 stole the show, the V8 engine was previously exclusive to Lincoln products, which in 1932 switched to V12 engines only. Although there is a certain relationship with the predecessor Model A. While the Model A has a frame with two straight longitudinal members, the new car got a longer wheelbase, and an outward curved. While the V-8 was developed from scratch, the B just had an improved four-cylinder Model A engine of 201 cu in displacement producing 50 horsepower. When Ford introduced the Model A in late 1927, there were several competitors also offering four cylinder cars, among them Chevrolet, Dodge, Durant, or Willys. That changed within a few years, soon leaving the new Plymouth the sole major make in the Fords price class with a four. Although sharing a platform, Model Bs and Model 18s came not only in Standard and Deluxe trim. Some of them, like the commercial cars described below, were available as Standards. The wooden panels were manufactured at the Ford Iron Mountain Plant in the Michigan Upper Peninsula from Ford owned lumber, one of the more well known and popular models was the two-door Victoria, which was largely designed by Edsel Ford
24.
Star Wars (film)
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Star Wars is a 1977 American epic space opera film written and directed by George Lucas. The first installment in the Star Wars film series, it stars Mark Hamill, Harrison Ford, Carrie Fisher, Peter Cushing, David Prowse, James Earl Jones, Anthony Daniels, Kenny Baker, and Peter Mayhew co-star in supporting roles. The plot focuses on the Rebel Alliance, led by Princess Leia, and its attempt to destroy the Galactic Empires space station and this conflict disrupts the isolated life of farmhand Luke Skywalker, who inadvertently acquires a pair of droids that possess stolen architectural plans for the Death Star. Star Wars was released theatrically in the United States on May 25,1977 and it earned $461 million in the U. S. and $314 million overseas, totaling $775 million. It surpassed Jaws to become the film of all time until the release of E. T. the Extra-Terrestrial. When adjusted for inflation, Star Wars is the film in North America. It received ten Academy Award nominations, winning seven and it was among the first films to be selected as part of the U. S. Library of Congress National Film Registry as being culturally, historically, at the time, it was the most recent film on the registry and the only one chosen from the 1970s. Its soundtrack was added to the U. S. National Recording Registry in 2004, today, it is often regarded as one of the best films of all time, as well as one of the most important films in the history of motion pictures. It launched an industry of tie-in products, including TV series spinoffs, novels, comic books, and video games, the films success led to two critically and commercially successful sequels, The Empire Strikes Back and Return of the Jedi. A prequel trilogy was released between 1999 and 2005, followed by a trilogy beginning in 2015. In 2016, Rogue One was released as a prequel to the original Star Wars film. The galaxy is in the midst of a civil war, spies for the Rebel Alliance have stolen plans to the Galactic Empires Death Star, a heavily armed space station capable of destroying an entire planet. Rebel leader Princess Leia has the plans, but her ship is captured by Imperial forces under the command of the evil Darth Vader, before she is captured, Leia hides the plans in the memory of an astromech droid, R2-D2, along with a holographic recording. R2-D2 flees to the surface of the desert planet Tatooine with C-3PO, the droids are captured by Jawa traders, who sell them to moisture farmers Owen and Beru Lars and their nephew Luke Skywalker. While cleaning R2-D2, Luke accidentally triggers part of Leias message, the next morning, Luke finds R2-D2 searching for Obi-Wan, and meets Ben Kenobi, an old hermit who lives in the hills and reveals himself to be Obi-Wan. Contrary to his uncles statements, Luke learns that his father, Anakin, Obi-Wan tells Luke that Vader was his former pupil who turned to the dark side of the Force and killed Anakin. Obi-Wan then presents to Luke his fathers weapon – a lightsaber, Obi-Wan views Leias complete message, in which she begs him to take the Death Star plans to her home planet of Alderaan and give them to her father for analysis
25.
Death Star
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The Death Star refers to any of several fictional mobile space stations and galactic superweapons appearing in the Star Wars science-fiction franchise created by George Lucas. The first Death Star was stated to be over 100 km in diameter with a volume of 7,240,000 cubic kilometers and it was crewed by an estimated 1.7 million military personnel and 400,000 droids. Its superweapon delivered enough energies on an equivalent to all the energy released by the Sun in an entire week. The second Death Star was significantly larger and technologically advanced than its predecessor. Both versions of these dwarf planet-sized fortresses were designed for power projection capabilities. George Lucas gave the task of designing a Death Star to concept artist and spaceship modeler Colin Cantwell. As it would have taken a week of work just to fill and sand and refill this depression, Lucas liked the idea, and the Death Star model was created by John Stears. The buzzing sound counting down to the Death Star firing its superlaser comes from the Flash Gordon serials, portraying an incomplete yet powerful space station posed a problem for Industrial Light & Magics modelmakers for Return of the Jedi. Only the front side of the 137-centimeter model was completed, both Death Stars were depicted by a combination of complete and sectional models and matte paintings. The Death Star explosions featured in the edition of A New Hope and in Return of the Jedi are rendered with a Praxis effect. These are depictions of the Death Star and other weapons of mass destruction within the Star Wars canon. The original Death Stars completed form appears in Star Wars, the film opens with Princess Leia transporting the stations schematics to the Rebel Alliance to aid them in destroying the Death Star. Later, Luke Skywalker, Han Solo, Chewbacca, Obi-Wan Kenobi, C-3PO, and R2-D2 are pulled aboard the station by a tractor beam, as they make their escape, Obi-Wan dies fighting Darth Vader, enabling the others to flee the station. Later, Luke returns as part of a force to attack its only weak point. The Death Star plans are a central plot-point in the 2016 film Rogue One, the anthology film Rogue One, focuses on a band of Rebels stealing the plans for the first Death Star prior to the events of A New Hope. The Death Star project was overseen by Orson Krennic, the Director of Advanced Weapons Research for the Imperial Military, Grand Moff Tarkin assumes control over the Death Star while Krennic investigates security breaches in the design project. It is subsequently revealed that Galen discreetly sabotaged the design by building a vulnerability into the reactor and this is the same vulnerability that Luke Skywalker takes advantage of during the events of A New Hope. After the Death Star plans are stolen from the Scarif vault Tarkin fires the Death Star laser on the base killing Krennic as well as Jyn Erso and Cassian Andor
26.
Luke Skywalker
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Luke Skywalker is a fictional character and the main protagonist of the original film trilogy of the Star Wars franchise created by George Lucas. The character, portrayed by Mark Hamill, is an important figure in the Rebel Alliances struggle against the Galactic Empire. The now non-canon Star Wars expanded universe depicts him as a powerful Jedi Master, husband of Mara Jade, in 2015, the character was selected by Empire magazine as the 50th greatest movie character of all time. On their list of the 100 Greatest Fictional Characters, Fandomania. com ranked the character at number 14, Luke Skywalker was initially called Anakin Starkiller, and went through multiple design changes. The character was at one point designed as a 60-year-old grizzled war hero, later as a Jedi Master, the last name Starkiller remained for the first few months of production, Hamill on-camera using the name Luke Starkiller the sole time he referred to himself during filming. Starkiller was dropped due to what Lucas called unpleasant connotations, after Hamill was involved in a car accident, the Wampa attack at the beginning of The Empire Strikes Back was written in to explain his facial injuries. An alternative ending pitched by George Lucas for Return of the Jedi was Luke assuming his fathers role as Darth Vader after the latters death, though Lawrence Kasdan favored the idea, Lucas ultimately declined, since the films were made for children. Another conclusion to the featured the character disappearing into the wilderness akin to Clint Eastwood in the spaghetti westerns. During the filming of the original Star Wars trilogy, George Lucas informed Hamill that he would be needed to reprise the role when he was middle aged, Lucas further explained that his role as Luke would be handing Excalibur to the next generation. Hamill had no reaction at the time, as he thought of making Star Wars films decades in the future as an abstract concept, Hamill learned of the sequel trilogy over the summer of 2012 at a Star Wars celebration during lunch where Lucas told him one was in development. Hamill recalled shaving his beard to portray The Trickster in The Flash, Hamill attended meetings for script readings, and helped conceal Lukes role in the film, instead of dialogue, he read stage directions. Abrams said it allowed him to remain involved and that his reading helped make an experience for everyone. In the prequel film, Star Wars, Episode III – Revenge of the Sith, Luke is born to Senator Padmé Amidala along with his twin sister, Luke Skywalker lives on a moisture farm on Tatooine with his Uncle Owen and Aunt Beru. Luke takes his first steps toward his destiny when he buys the droids C-3PO, when R2-D2 goes missing, Luke goes out to find him and encounters Obi-Wan Kenobi, an old hermit. Luke discovers that R2-D2 contains a message for Obi-Wan from Princess Leia Organa of Alderaan beseeching him to help her defeat the Galactic Empire, Obi-Wan says that he and Lukes father were once Jedi Knights, and that his father was murdered by a traitorous Jedi named Darth Vader. Obi-Wan presents Luke with his fathers lightsaber and offers to him to Alderaan and train him in the ways of the Force. Luke changes his mind when he returns home to find that Imperial stormtroopers have killed his aunt, Obi-Wan deactivates the tractor beam and he later sacrifices his life in a duel with Vader so that Luke and his friends can board the Falcon and escape. During the films battle scene, Luke joins the Rebel Alliance in attacking the Death Star
27.
Chewbacca
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Chewbacca, nicknamed Chewie, is a fictional character in the Star Wars franchise. He is a Wookiee, a tall, hirsute biped and intelligent species from the planet Kashyyyk, Chewbacca is the loyal friend and associate of Han Solo, and serves as co-pilot on Solos spaceship, the Millennium Falcon. The character has appeared on television, in books, comics. To repay this debt, Chewbacca protected Han for the rest of his life, standing at 8 feet tall, Chewbacca is covered with long hair, and wears only a bandolier. His weapon of choice is the Wookiee bowcaster, Chewbacca was named one of the greatest sidekicks in film history by Entertainment Weekly. In Italy the name of Chewbacca was changed to Chewbecca and his nickname is Chewbe, Chewbaccas creation as a gentle, hairy, non-English-speaking co-pilot was inspired by George Lucas seeing his own dog sitting up on the passenger seat of his car. It is said that Chewbaccas name is derived from собака, the Russian word for dog, in all five screen appearances, Chewbacca was played by Peter Mayhew, who was chosen for his height of 73. Five identical costumes were made for Mayhew, in the three films and a holiday special, the suits were made of yak hair and mohair. In Revenge of the Sith, the suit was made of more comfortable materials, only Mayhews blue eyes could be seen in his costume, but fans easily recognize him by his gestures, and his co-workers claimed the ability to tell when a stand-in was taking his place. Chewbaccas voice was created by the films sound designer, Ben Burtt, from recordings of walruses, lions, camels, bears, rabbits, tigers. The individual recordings were mixed at different ratios for Chewbaccas different utterances, one of the most prominent elements in the voice was a black bear named Tarik, from Happy Hollow Zoo in San Jose, California. The original costume was created by Stuart Freeborn and his wife Kay Freeborn, First appearing in Star Wars, Chewbacca and Han Solo accept a charter to take Luke Skywalker, Obi-Wan Kenobi, and droids C-3PO and R2-D2 to the planet Alderaan. When they find the destroyed by the Death Star, the two smugglers are drawn into the Rebel Alliance. As part of a plan to rescue Leia, Luke tries to put handcuffs on Chewbacca to make it look like hes a prisoner. Chewbacca almost attacks Luke believing him to be selling him and Solo out, after rescuing Leia and taking her to the rebel base on Yavin IV, the two smugglers are given reward money in the value of a payload lost by him to which he owes Jabba The Hutt. Somehow, Chewbacca is able to convince Han to put his debt to Jabba aside for the time being and they manage to save Luke from being killed, also allowing him to be the one to destroy the space station. In The Empire Strikes Back, Chewbacca finds a dismantled C-3PO in a pile in Cloud City. He later tries to him, but does a terrible job at it
28.
Stormtrooper (Star Wars)
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A stormtrooper is a fictional soldier in the Star Wars franchise created by George Lucas. In The Force Awakens, the upgraded stormtroopers serve the First Order, under the leadership of Supreme Leader Snoke and his commanders, most notably Kylo Ren, General Hux, the order of battle of the Stormtrooper Corps is unspecified in the Star Wars universe. They are shown in collective groups of varying organizational sizes ranging from squads to legions and for some, their armor and training are modified for special operations and environments. Introduced in Star Wars, the Imperial stormtroopers serve as the army of the Galactic Empire, establishing Imperial authority and putting down any revolts. In the prequel film Star Wars, Episode II – Attack of the Clones, in Star Wars, Episode III – Revenge of the Sith, Chancellor Palpatine orders them to slay their Jedi generals in the Great Jedi Purge. As established in Star Wars, The Force Awakens, after Palpatines death the stormtroopers continue to serve under the factions that broke apart from the Empire, with redesigned armor, they eventually serve under the leadership of the First Order. In this film, it is established that an undisclosed number of stormtroopers were conscripted as young children, given serial numbers for names. Stormtrooper FN-2187, later known as Finn, plans his escape when his resistance to this conditioning puts him in line to be reprogrammed, Star Wars Legends expanded universe media such as games and comics feature a number of specialized stormtrooper units. The Marvel-produced comics of the late 1970s and early 1980s featured Shadow Troopers, others, such as the Beach Troopers, are for comical effect. Appearing only briefly in Lego Star Wars II, The Original Trilogy, they are clad in a Speedo, in Lego Star Wars, The Complete Saga, they also wear life jackets. Shadowtroopers appear in Star Wars Jedi Knight II, Jedi Outcast wearing black armour made from a lightsaber-resistant metal called cortosis and this armour has a green synthetic gem set into the breastplate which gives the wearer Force powers. Their armour can also render them invisible, with only a small area of blue discoloration giving them away. They use this ability to lie in wait and ambush the enemy, most often the games protagonist and these troopers also possess the invisible feature and use this tactic to ambush their enemies, but only if stormtrooper officers call out for support. Disloyalty or failures were heavily punished and individualism was discouraged, command structure was sacred and this meant Imperial Stormtroopers lacked improvisation and were highly ineffective when cut off from command, but also allowed the best trained soldiers who prefer death over retreat. First Order Stormtroopers are regularly put through mental indoctrination and propaganda programs, to make sure that they remain fanatically loyal, being taken from their families at birth, these soldiers are not even given individual names for themselves but merely serial numbers, such as FN-2187. Based on conceptual drawings by Ralph McQuarrie, Liz Moore and Nick Pemberton sculpted designs for the helmet, Muir, who was also responsible for sculpting the Darth Vader costume, worked out of the Art Department at Elstree Studios. The suit was molded and initially cast in plaster, with Muir sharpening the detail at the plaster stage, the plaster casts were then remolded and cast in fiberglass to use as the tools for the vacuum forming process. The suits were produced in house by Tashy Baines, the resident vacuum former, as Shepperton Design Studios had already been used to vacuum form the helmets, the fiberglass molds for the armor were then sent to them for vacuum forming the suits
29.
The Empire Strikes Back
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The Empire Strikes Back is a 1980 American epic space opera film directed by Irvin Kershner. Leigh Brackett and Lawrence Kasdan wrote the screenplay, with George Lucas writing the films story, the film is set three years after Star Wars. The Galactic Empire, under the leadership of the villainous Darth Vader and the Emperor, is in pursuit of Luke Skywalker, while Vader chases a small band of Lukes friends—Han Solo, Princess Leia Organa, and others—across the galaxy, Luke studies the Force under Jedi Master Yoda. When Vader captures Lukes friends, Luke must decide whether to complete his training and become a full Jedi Knight or to confront Vader, following a difficult production, The Empire Strikes Back was released on May 21,1980. The film ranks #3 on Empires 2008 list of the 500 greatest movies of all time and it became the highest-grossing film of 1980 and, to date, has earned more than $538 million worldwide from its original run and several re-releases. When adjusted for inflation, it is the sequel of all time. The film was followed by a sequel, titled Return of the Jedi, in 2010, the film was selected for preservation in the United States National Film Registry by the Library of Congress for being culturally, historically, and aesthetically significant. Three years after the destruction of the Death Star, the Rebel Alliance has been driven from their base on Yavin IV by the Galactic Empire. The Rebels, led by Princess Leia, have set up their new base on the ice planet Hoth, the Imperial fleet, led by Darth Vader, continues to hunt for the Rebels’ new base by dispatching probe droids across the galaxy. While investigating a meteor strike, Luke Skywalker is injured and captured by a wampa. He manages to escape from its cave with his lightsaber, the ghost of his late mentor, Obi-Wan Kenobi, instructs him to go to the Dagobah system to train under Jedi Master Yoda. He is found by Han Solo, who kills his tauntaun, Han and Luke make it through the night and are rescued by a search party. On patrol, Han and Chewbacca discover the meteor Luke had planned to investigate is actually a probe droid, the Empire launches a large-scale attack, using AT-AT Walkers to capture the base. Despite heavy resistance, the Walkers destroy the shield generator. Han and Leia escape on the Millennium Falcon with C-3PO and Chewbacca and they hide in an asteroid field, where Han and Leia grow closer, and eventually, kiss. Vader summons bounty hunters, including the notorious Boba Fett, to assist in finding the Falcon, Luke, meanwhile, escapes with R2-D2 in his X-wing fighter and crash-lands on the swamp planet Dagobah. He meets a creature who is revealed to be Yoda, after conferring with Obi-Wans spirit. Yoda trains Luke as a Jedi and raises his sunken ship from the swamp with the power of the Force, after evading the Empire, Han sets a course for Cloud City, a floating colony in the skies of the gas giant planet Bespin
30.
Carlist Rieekan
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This list of characters from the Star Wars franchise contains only those which are considered part of the official Star Wars canon. C-3PO and R2-D2 are the characters to appear in all films to date
31.
Raiders of the Lost Ark
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Raiders of the Lost Ark is a 1981 American action adventure film directed by Steven Spielberg, with a screenplay written by Lawrence Kasdan, from a story by George Lucas and Philip Kaufman. It was produced by Frank Marshall for Lucasfilm Ltd. with Lucas, starring Harrison Ford, it was the first installment in the Indiana Jones film franchise to be released, though it is the second in internal chronological order. It pits Indiana Jones against a group of Nazis who are searching for the Ark of the Covenant, the film originated from Lucas desire to create a modern version of the serials of the 1930s and 1940s. Production was based at Elstree Studios, England, but filming took place in La Rochelle, France, Tunisia, Hawaii. Released on June 12,1981, Raiders of the Lost Ark became the years top-grossing film, in 1999, the film was included in the U. S. Library of Congress National Film Registry as having been deemed culturally, historically, Raiders of the Lost Ark is often ranked as one of the greatest films of all time, both in the action-adventure genre, and in general. The film also ranks #2 on Empires 2008 list of the 500 greatest movies of all time, in 1936, archaeologist Indiana Jones braves an ancient booby-trapped temple in Peru and retrieves a golden idol. He is confronted by rival archaeologist René Belloq and the indigenous Hovito people, surrounded and outnumbered, Indy surrenders the idol to Belloq and escapes aboard a waiting floatplane. Jones returns to his position at Marshall College, where he is interviewed by two Army Intelligence agents. They inform him that the Nazis are searching for his old mentor, Abner Ravenwood, the Staff of Ra is the key to finding the Well of Souls, a secret chamber in which the Ark is buried. The agents authorize Jones to recover the Ark to prevent the Nazis from obtaining it and he travels to Nepal and discovers that Abner has died, and the headpiece is in the possession of Ravenwoods daughter Marion. Jones visits Marion at her tavern, where she reveals her feelings toward him from a previous romantic affair. She physically rebuffs his offer to buy the headpiece, and Jones leaves, shortly after, a group of thugs arrive with their Nazi commander, Arnold Toht. Indy and Marion escape with the headpiece, and Marion decides to accompany Indy in his search for the Ark so he can repay his debt to her, the pair travels to Cairo, where they meet up with Indys friend Sallah, a skilled excavator. Sallah informs them that Belloq and the Nazis are digging for the Well of Souls with a replica of the headpiece and they quickly realize the Nazi headpiece is incomplete and that the Nazis are digging in the wrong place. The Nazis kidnap Marion and it appears to Jones that she is killed in an exploding truck, after a confrontation with Belloq in a local bar, Indy and Sallah infiltrate the Nazi dig site and use their staff to correctly locate the Ark. Indy discovers Marion is alive, bound and gagged in a tent, Indy, Sallah, and a small group of diggers unearth the Well of Souls and acquire the Ark. Belloq and Nazi officer Colonel Dietrich arrive, seize the Ark from Jones, Jones and Marion escape to a local airstrip, where Jones has a fistfight with a Nazi mechanic and destroys the flying wing that was to transport the Ark to Berlin
32.
Return of the Jedi
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This list of characters from the Star Wars franchise contains only those which are considered part of the official Star Wars canon. C-3PO and R2-D2 are the characters to appear in all films to date
33.
Indiana Jones and the Last Crusade
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Indiana Jones and the Last Crusade is a 1989 American action-adventure film directed by Steven Spielberg, from a story co-written by executive producer George Lucas. It is the installment in the Indiana Jones franchise. Harrison Ford reprises the role and Sean Connery plays Indianas father, Henry Jones. Other cast members featured include Alison Doody, Denholm Elliott, Julian Glover, River Phoenix, in the film, set largely in 1938, Indiana searches for his father, a Holy Grail scholar, who has been kidnapped by Nazis. After the mixed reaction to Indiana Jones and the Temple of Doom, Spielberg chose to compensate with a film that toned down the violence, during the five years between Temple of Doom and Last Crusade, he and executive producer Lucas reviewed several scripts before accepting Jeffrey Boams. Filming locations included Spain, Italy, the United Kingdom, Turkey, the film was released in North America on May 24,1989, to mostly positive reviews. It was a success, earning $474,171,806 at the worldwide box office totals. It won an Academy Award for Best Sound Editing, in 1912, thirteen-year-old Indiana Jones is horseback riding with his Boy Scout troop at Arches National Park in Utah. While scouting caves, Indy discovers a group of robbers who have found a golden crucifix belonging to Coronado and steals it from them. The men give chase through a circus train, leaving Indy with a bloody cut across his chin from a bullwhip. Indy escapes, but the local sheriff makes him return the cross to the robbers, impressed with Indys bravery, the leader of the robbers gives Indy his fedora, and encourages him to not give up. In 1938, Indy recovers the cross off the coast of Portugal, later, Indy is introduced to Walter Donovan, who informs him that Indys father, Henry Jones, Sr. has vanished while searching for the Holy Grail, using an incomplete inscription as his guide. Indy then receives Henrys Grail diary via mail from Venice, realizing that he would not have sent the diary unless he was in trouble, Indy and Marcus travel to Venice, where they meet Henrys Austrian colleague, Dr. Elsa Schneider. They flee, however, when the catacombs are set aflame by the Brotherhood of the Cruciform Sword, a secret society that protects the Grail from evildoers. Indy and Elsa capture one of the Brotherhood, Kazim, and Indy tells him that his goal is only to find his father, Kazim tells him that Henry is being held in Castle Brunwald on the Austrian-German border. Marcus later reveals a map drawn by Henry of the route to the Grail, at Castle Brunwald, Indy rescues Henry, but learns that Elsa and Donovan are actually working with the Nazis, and are using him to find the Grail for them. Meanwhile, Marcus is captured in Hatay, while waiting with Sallah for the Joneses, the Joneses escape from Castle Brunwald. Henry tells Indy that to reach the Grail, one must face three booby traps and his diary contains the clues to guide them through the challenges safely and they recover the diary from Elsa at a book burning rally in Berlin
34.
Battle droid
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This list of characters from the Star Wars franchise contains only those which are considered part of the official Star Wars canon. C-3PO and R2-D2 are the characters to appear in all films to date