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Arithmetic Billiards
In recreational mathematics, arithmetic billiards provide a geometrical method to determine the least common multiple (LCM) and the greatest common divisor (GCD) of two Natural number, natural numbers. It makes use of reflections inside a rectangle that has sides with length of the two given numbers. This is a simple example of trajectory analysis used in dynamical billiards. Arithmetic billiards can be used to show how two numbers interact. Drawing squares within the rectangle of length and width of the two natural numbers allows a reader to learn more about the relationship between the two numbers. Coprime integers interact with every unit square within the rectangle. Properties Arithmetic billiards is a name given to the process of finding both the LCM and the GCD of two integers using a geometric method. It is named for its similarity to the movement of a billiard ball. To create an arithmetic billiard, a rectangle is drawn with a base of the larger number, and height of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Billiard Table
A billiard table or billiards table is a bounded table on which cue sports are played. In the modern era, all billiards tables (whether for carom billiards, Pool (cue sports), pool, Russian pyramid, pyramid or snooker) provide a flat surface usually made of quarried slate, that is covered with cloth (usually of a tightly woven worsted wool called baize), and surrounded by vulcanized rubber cushions, with the whole thing elevated above the floor. More specific terms are used for specific sports, such as snooker table and pool table, and different-sized billiard balls are used on these table types. An obsolete term is billiard board, used in the 16th and 17th centuries. Parts and equipment Cushions Cushions (also sometimes called "rail cushions", "cushion rubber", or rarely "bumpers") are located on the inner sides of a table's wooden . There are several different materials and design philosophies associated with cushion rubber. These cushions are made from an elastic material suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Dynamics
Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory. Part of the inspiration comes from complex dynamics, the study of the Iterated function, iteration of self-maps of the complex plane or other complex algebraic varieties. Arithmetic dynamics is the study of the number-theoretic properties of integer point, integer, rational point, rational, p-adic number, -adic, or algebraic points under repeated application of a polynomial or rational function. A fundamental goal is to describe arithmetic properties in terms of underlying geometric structures. ''Global arithmetic dynamics'' is the study of analogues of classical diophantine geometry in the setting of discrete dynamical systems, while ''local arithmetic dynamics'', also called p-adic dynamics, p-adic or nonarchimedean dynamics, is an analogue of complex dynamics in which one replaces the complex numbers by a -adic field such as or and studies chaotic behavior and the Fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pool (cue Sports)
Pool is a series of cue sports played on a billiard table. The table has six Pocket (billiards), pockets along the , into which Billiard ball, balls are shot. "Pool billiards" is sometimes hyphenated and/or spelled with a singular "billiard". The WPA itself uses "pool-billiard" in its logo but "pool-billiards" in its legal notices. The organization compounds the words to result in an acronym of "WPA", "WPBA" having already been taken by the Women's Professional Billiards Association. Normal English grammar would not hyphenate here, and w:de:Poolbillard, the term is actually a Germanism. A general rules booklet on pool games in general, including eight-ball, nine-ball and several others. Of the many different pool games, the most popular include: eight-ball, Blackball (pool), blackball, nine-ball, ten-ball, seven-ball, straight pool, one-pocket, and bank pool. Eight-ball is the most frequently played discipline of pool, and it is often thought of as synonymous with "pool". The ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing magic, scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.Martin (2010) He was a leading authority on Lewis Carroll; '' The Annotated Alice'', which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies.Martin Gardner obituary (2010) He had a lifelong interest in magic and illusion and in 1999, ''MAGIC'' magazine named him as one of the "10 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Symmetric
In geometry, a point reflection (also called a point inversion or central inversion) is a geometric transformation of affine space in which every point is reflected across a designated inversion center, which remains fixed. In Euclidean or pseudo-Euclidean spaces, a point reflection is an isometry (preserves distance). In the Euclidean plane, a point reflection is the same as a half-turn rotation (180° or radians), while in three-dimensional Euclidean space a point reflection is an improper rotation which preserves distances but reverses orientation. A point reflection is an involution: applying it twice is the identity transformation. An object that is invariant under a point reflection is said to possess point symmetry (also called inversion symmetry or central symmetry). A point group including a point reflection among its symmetries is called ''centrosymmetric''. Inversion symmetry is found in many crystal structures and molecules, and has a major effect upon their p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Factorisation
In mathematics, integer factorization is the decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is a composite number, or it is not, in which case it is a prime number. For example, is a composite number because , but is a prime number because it cannot be decomposed in this way. If one of the factors is composite, it can in turn be written as a product of smaller factors, for example . Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer using mental or pen-and-paper arithmetic, the simplest method is trial division: checking if the number is divisible by prime numbers , , , and so on, up to the square root of . For larger numbers, especially when using a computer, various more sophistic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coprime Integers
In number theory, two integers and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides does not divide , and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. One says also ''is prime to'' or ''is coprime with'' . The numbers 8 and 9 are coprime, despite the fact that neither—considered individually—is a prime number, since 1 is their only common divisor. On the other hand, 6 and 9 are not coprime, because they are both divisible by 3. The numerator and denominator of a reduced fraction are coprime, by definition. Notation and testing When the integers and are coprime, the standard way of expressing this fact in mathematical notation is to indicate that their greatest common divisor is one, by the formula or . In their 1989 textbook ''Concrete Mathematics'', Ronald Graham, Donald Knuth, and Oren Patashnik proposed an alternative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
