|
FRACTRAN
FRACTRAN is a Turing-complete esoteric programming language invented by the mathematician John Conway. A FRACTRAN program is an ordered list of positive fractions together with an initial positive integer input ''n''. The program is run by updating the integer ''n'' as follows: #for the first fraction ''f'' in the list for which ''nf'' is an integer, replace ''n'' by ''nf'' #repeat this rule until no fraction in the list produces an integer when multiplied by ''n'', then halt. gives the following FRACTRAN program, called PRIMEGAME, which finds successive prime numbers: \left( \frac, \frac, \frac, \frac, \frac, \frac, \frac, \frac, \frac, \frac, \frac, \frac, \frac, \frac \right) Starting with ''n''=2, this FRACTRAN program generates the following sequence of integers: * 2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, ... After 2, this sequence contains the following powers of 2: 2^2=4,\, 2^3=8,\, 2^5=32,\, 2^7=128,\, 2^=2048,\, 2^=8192,\, 2^=131072,\, 2^=524288,\, \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Esoteric Programming Language
An esoteric programming language (sometimes shortened to esolang) is a programming language designed to test the boundaries of computer programming language design, as a proof of concept, as software art, as a hacking interface to another language (particularly functional programming or procedural programming languages), or as a joke. The use of the word ''wiktionary:esoteric, esoteric'' distinguishes them from languages that working developers use to write software. The creators of most esolangs do not intend them to be used for mainstream programming, although some esoteric features, such as live Data and information visualization, visualization of code, have inspired practical applications in the arts. Such languages are often popular among Hacker culture, hackers and hobbyists. Usability is rarely a goal for designers of esoteric programming languages; often their design leads to quite the opposite. Their usual aim is to remove or replace conventional language features while sti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Esoteric Programming Languages
An esoteric programming language (sometimes shortened to esolang) is a programming language designed to test the boundaries of computer programming language design, as a proof of concept, as software art, as a hacking interface to another language (particularly functional programming or procedural programming languages), or as a joke. The use of the word ''esoteric'' distinguishes them from languages that working developers use to write software. The creators of most esolangs do not intend them to be used for mainstream programming, although some esoteric features, such as live visualization of code, have inspired practical applications in the arts. Such languages are often popular among hackers and hobbyists. Usability is rarely a goal for designers of esoteric programming languages; often their design leads to quite the opposite. Their usual aim is to remove or replace conventional language features while still maintaining a language that is Turing-complete, or even one for wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Horton Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician. He was active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life. Born and raised in Liverpool, Conway spent the first half of his career at the University of Cambridge before moving to the United States, where he held the John von Neumann Professorship at Princeton University for the rest of his career. On 11 April 2020, at age 82, he died of complications from COVID-19. Early life and education Conway was born on 26 December 1937 in Liverpool, the son of Cyril Horton Conway and Agnes Boyce. He became interested in mathematics at a very early age. By the time he was 11, his ambition was to become a mathematician. After leaving sixth form, he studied mathematics at Gonville and Caius Coll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fraction (mathematics)
A fraction (from , "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A ''common'', ''vulgar'', or ''simple'' fraction (examples: and ) consists of an integer numerator, displayed above a line (or before a slash like ), and a division by zero, non-zero integer denominator, displayed below (or after) that line. If these integers are positive, then the numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. For example, in the fraction , the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole. The picture to the right illustrates of a cake. Fractions can be used to represent ratios and division (mathematics), division. Thus the fraction can be used to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collatz Conjecture
The Collatz conjecture is one of the most famous List of unsolved problems in mathematics, unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns integer sequence, sequences of integers in which each term is obtained from the previous term as follows: if a term is Parity (mathematics), even, the next term is one half of it. If a term is odd, the next term is 3 times the previous term plus 1. The conjecture is that these sequences always reach 1, no matter which positive integer is chosen to start the sequence. The conjecture has been shown to hold for all positive integers up to , but no general proof has been found. It is named after the mathematician Lothar Collatz, who introduced the idea in 1937, two years after receiving his doctorate. The sequence of numbers involved is sometimes referred to as the hailstone sequence, hailstone numbers or hailstone numerals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One-instruction Set Computer
A one-instruction set computer (OISC), sometimes referred to as an ultimate RISC, reduced instruction set computer (URISC), is an abstract machine that uses only one instructionobviating the need for a machine language opcode. With a judicious choice for the single instruction and given arbitrarily many resources, an OISC is capable of being a universal computer in the same manner as traditional computers that have multiple instructions. OISCs have been recommended as aids in teaching computer architecture and have been used as computational models in structural computing research. The first carbon nanotube computer is a 1-bit computing, 1-bit one-instruction set computer (and has only 178 transistors). Machine architecture In a Turing completeness, Turing-complete model, each memory location can store an arbitrary integer, anddepending on the mode, there may be arbitrarily many locations. The instructions themselves reside in memory as a sequence of such integers. There exists ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denominator
A fraction (from , "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A ''common'', ''vulgar'', or ''simple'' fraction (examples: and ) consists of an integer numerator, displayed above a line (or before a slash like ), and a non-zero integer denominator, displayed below (or after) that line. If these integers are positive, then the numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. For example, in the fraction , the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole. The picture to the right illustrates of a cake. Fractions can be used to represent ratios and division. Thus the fraction can be used to represent the ratio 3:4 (the ratio of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floor Function
In mathematics, the floor function is the function that takes as input a real number , and gives as output the greatest integer less than or equal to , denoted or . Similarly, the ceiling function maps to the least integer greater than or equal to , denoted or . For example, for floor: , , and for ceiling: , and . The floor of is also called the integral part, integer part, greatest integer, or entier of , and was historically denoted (among other notations). However, the same term, ''integer part'', is also used for truncation towards zero, which differs from the floor function for negative numbers. For an integer , . Although and produce graphs that appear exactly alike, they are not the same when the value of is an exact integer. For example, when , . However, if , then , while . Notation The ''integral part'' or ''integer part'' of a number ( in the original) was first defined in 1798 by Adrien-Marie Legendre in his proof of the Legendre's formula. Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Models Of Computation
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology. Categories Models of computation can be classified into three categories: sequential models, functional models, and concurrent models. Sequential models Sequential models include: * Finite-state machines * Post machines ( Post–Turing machines and tag machines). * Pushdown automata * Register machines ** Random-access machines * Turing machines * Decision tree model * External memory model Functional models Functio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor & Francis
Taylor & Francis Group is an international company originating in the United Kingdom that publishes books and academic journals. Its parts include Taylor & Francis, CRC Press, Routledge, F1000 (publisher), F1000 Research and Dovepress. It is a division of Informa, a United Kingdom-based publisher and conference company. Overview Founding The company was founded in 1852 when William Francis (chemist), William Francis joined Richard Taylor (editor), Richard Taylor in his publishing business. Taylor had founded his company in 1798. Their subjects covered agriculture, chemistry, education, engineering, geography, law, mathematics, medicine, and social sciences. Publications included the ''Philosophical Magazine''. Francis's son, Richard Taunton Francis (1883–1930), was sole partner in the firm from 1917 to 1930. Acquisitions and mergers In 1965, Taylor & Francis launched Wykeham Publications and began book publishing. T&F acquired Hemisphere Publishing in 1988, and the compa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Magazine
''Mathematics Magazine'' is a refereed bimonthly publication of the Mathematical Association of America. Its intended audience is teachers of collegiate mathematics, especially at the junior/senior level, and their students. It is explicitly a journal of mathematics rather than pedagogy. Rather than articles in the terse "theorem-proof" style of research journals, it seeks articles which provide a context for the mathematics they deliver, with examples, applications, illustrations, and historical background. Paid circulation in 2008 was 9,500 and total circulation was 10,000. ''Mathematics Magazine'' is a continuation of ''Mathematics News Letter'' (1926–1934) and ''National Mathematics Magazine'' (1934–1945). Doris Schattschneider became the first female editor of ''Mathematics Magazine'' in 1981. .. The MAA gives the Carl B. Allendoerfer Awards annually "for articles of expository excellence" published in ''Mathematics Magazine''. See also *''American Mathematical Mon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamming Weight
The Hamming weight of a string (computer science), string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a given set of bits, this is the number of bits set to 1, or the digit sum of the Binary numeral system, binary representation of a given number and the Taxicab geometry, ''ℓ''₁ norm of a bit vector. In this binary case, it is also called the population count, popcount, sideways sum, or bit summation. History and usage The Hamming weight is named after the American mathematician Richard Hamming, although he did not originate the notion. The Hamming weight of binary numbers was already used in 1899 by James Whitbread Lee Glaisher, James W. L. Glaisher to give a formula for Gould's sequence, the number of odd binomial coefficients in a single row of Pascal's triangle. Irving S. Reed introduced a concept, equivalen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
