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Magic Rectangle
In mathematics, a magic hypercube is the ''k''-dimensional generalization of magic squares and magic cubes, that is, an ''n'' × ''n'' × ''n'' × ... × ''n'' array of integers such that the sums of the numbers on each pillar (along any axis) as well as on the main space diagonals are all the same. The common sum is called the magic constant of the hypercube, and is sometimes denoted ''M''''k''(''n''). If a magic hypercube consists of the numbers 1, 2, ..., ''n''''k'', then it has magic number :M_k(n) = \frac. For ''k'' = 4, a magic hypercube may be called a magic tesseract, with sequence of magic numbers given by . The side-length ''n'' of the magic hypercube is called its ''order''. Four-, five-, six-, seven- and eight-dimensional magic hypercubes of order three have been constructed by J. R. Hendricks. Marian Trenkler proved the following theorem: A ''p''-dimensional magic hypercube of order ''n'' exists if and only if ''p'' > 1 and ''n'' is different from 2 or ''p'' = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Displaying A Formula
Display behaviour is a set of ritualized behaviours that enable an animal to communicate to other animals (typically of the same species) about specific stimuli. Such ritualized behaviours can be visual, but many animals depend on a mixture of visual, audio, tactical and chemical signals. Evolution has tailored these stereotyped behaviours to allow animals to communicate both conspecifically and interspecifically which allows for a broader connection in different niches in an ecosystem. It is connected to sexual selection and survival of the species in various ways. Typically, display behaviour is used for courtship between two animals and to signal to the female that a viable male is ready to mate. In other instances, species may make territorial displays, in order to preserve a foraging or hunting territory for its family or group. A third form is exhibited by tournament species in which males will fight in order to gain the 'right' to breed. Animals from a broad range of evolut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first meaning is the six permutations (orderings) of the set : written as tuples, they are (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). Anagrams of a word whose letters are all different are also permutations: the letters are already ordered in the original word, and the anagram reorders them. The study of permutations of finite sets is an important topic in combinatorics and group theory. Permutations are used in almost every branch of mathematics and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. The number of permutations of distinct objects is factorial, us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John R
John R. (born John Richbourg, August 20, 1910 – February 15, 1986) was an American radio disc jockey who attained fame in the 1950s and 1960s for playing rhythm and blues music on Nashville radio station WLAC. He was also a notable record producer and artist manager. Richbourg was arguably the most popular and charismatic of the four announcers at WLAC who showcased popular African-American music in nightly programs from the late 1940s to the early 1970s. (The other three were Gene Nobles, Herman Grizzard, and Bill "Hoss" Allen.) Later rock music disc jockeys, such as Alan Freed and Wolfman Jack, mimicked Richbourg's practice of using speech that simulated African-American street language of the mid-twentieth century. Richbourg's highly stylized approach to on-air presentation of both music and advertising earned him popularity, but it also created identity confusion. Because Richbourg and fellow disc jockey Allen used African-American speech patterns, many listeners thought t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Magic Cube
In mathematics, a perfect magic cube is a magic cube in which not only the columns, rows, pillars, and main space diagonals, but also the cross section (geometry), cross section diagonals sum up to the cube's magic constant. Perfect magic cubes of order one are trivial; cubes of orders two to four can be mathematical proof, proven not to exist, and cubes of orders five and six were first discovered by Walter Trump and Christian Boyer on November 13 and September 1, 2003, respectively. A perfect magic cube of order seven was given by A. H. Frost in 1866, and on March 11, 1875, an article was published in the Cincinnati Commercial newspaper on the discovery of a perfect magic cube of order 8 by Gustavus Frankenstein. Perfect magic cubes of orders nine and eleven have also been constructed. The first perfect cube of order 10 was constructed in 1988 (Li Wen, China). An alternative definition In recent years, an alternative definition for the perfect magic cube was proposed by John ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Cube
In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an ''n'' × ''n'' × ''n'' pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four main space diagonals are equal, the so-called magic constant The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is ... of the cube, denoted ''M''3(''n''). If a magic cube consists of the numbers 1, 2, ..., ''n''3, then it has magic constant :M_3(n) = \frac. If, in addition, the numbers on every cross section diagonal also sum up to the cube's magic number, the cube is called a perfect magic cube; otherwise, it is called a semiperfect magic cube. The number ''n'' is called the order of the magic cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Cube Classes
In mathematics, a magic cube of order n is an n\times n \times n grid of natural numbers satisfying the property that the numbers in the same row, the same column, the same pillar or the same length-n space diagonal, diagonal add up to the same number. It is a 3-dimensional generalisation of the magic square. A magic cube can be assigned to one of six magic cube classes, based on the cube characteristics. A benefit of this classification is that it is consistent for all orders and all dimensions of magic hypercubes. The six classes * Simple: The minimum requirements for a magic cube are: all rows, columns, pillars, and 4 space diagonals must sum to the same value. A simple magic cube contains no magic squares or not enough to qualify for the next class. The smallest magic square, normal simple magic cube is order 3. Minimum correct summations required = 3''m''2 + 4 * Diagonal: Each of the 3''m'' planar arrays must be a Magic_square#Classification_of_magic_squares, simple magic s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isomorphism
In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word is derived . The interest in isomorphisms lies in the fact that two isomorphic objects have the same properties (excluding further information such as additional structure or names of objects). Thus isomorphic structures cannot be distinguished from the point of view of structure only, and may often be identified. In mathematical jargon, one says that two objects are the same up to an isomorphism. A common example where isomorphic structures cannot be identified is when the structures are substructures of a larger one. For example, all subspaces of dimension one of a vector space are isomorphic and cannot be identified. An automorphism is an isomorphism from a structure to itself. An isomorphism between two structures is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinality
The thumb is the first digit of the hand, next to the index finger. When a person is standing in the medical anatomical position (where the palm is facing to the front), the thumb is the outermost digit. The Medical Latin English noun for thumb is ''pollex'' (compare ''hallux'' for big toe), and the corresponding adjective for thumb is ''pollical''. Definition Thumb and fingers The English word ''finger'' has two senses, even in the context of appendages of a single typical human hand: 1) Any of the five terminal members of the hand. 2) Any of the four terminal members of the hand, other than the thumb. Linguistically, it appears that the original sense was the first of these two: (also rendered as ) was, in the inferred Proto-Indo-European language, a suffixed form of (or ), which has given rise to many Indo-European-family words (tens of them defined in English dictionaries) that involve, or stem from, concepts of fiveness. The thumb shares the following with each of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Hypercubes
In mathematics, a magic hypercube is the ''k''-dimensional generalization of magic squares and magic cubes, that is, an ''n'' × ''n'' × ''n'' × ... × ''n'' array of integers such that the sums of the numbers on each pillar (along any axis) as well as on the main space diagonals are all the same. The common sum is called the magic constant of the hypercube, and is sometimes denoted ''M''''k''(''n''). If a magic hypercube consists of the numbers 1, 2, ..., ''n''''k'', then it has magic number :M_k(n) = \frac. For ''k'' = 4, a magic hypercube may be called a magic tesseract, with sequence of magic numbers given by . The side-length ''n'' of the magic hypercube is called its ''order''. Four-, five-, six-, seven- and eight-dimensional magic hypercubes of order three have been constructed by J. R. Hendricks. Marian Trenkler proved the following theorem: A ''p''-dimensional magic hypercube of order ''n'' exists if and only if ''p'' > 1 and ''n'' is different from 2 or ''p'' = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Most-perfect Magic Square
A most-perfect magic square of order ''n'' is a magic square containing the numbers 1 to ''n''2 with two additional properties: # Each 2 × 2 subsquare sums to 2''s'', where . # All pairs of integers distant ''n''/2 along a (major) diagonal sum to ''s''. There are 384 such combinations. Examples Two 12 × 12 most-perfect magic squares can be obtained adding 1 to each element of: [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [1,] 64 92 81 94 48 77 67 63 50 61 83 78 [2,] 31 99 14 97 47 114 28 128 45 130 12 113 [3,] 24 132 41 134 8 117 27 103 10 101 43 118 [4,] 23 107 6 105 39 122 20 136 37 138 4 121 [5,] 16 140 33 142 0 125 19 111 2 109 35 126 [6,] 75 55 58 53 91 70 72 84 89 86 56 69 [7,] 76 80 93 82 60 65 79 51 62 49 95 66 [8,] 115 15 98 13 131 30 112 4 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kathleen Ollerenshaw
Dame Kathleen Mary Ollerenshaw, (''née'' Timpson; 1 October 1912 – 10 August 2014) was a British mathematician and politician who was Lord Mayor of Manchester from 1975 to 1976 and an advisor on educational matters to Margaret Thatcher's government in the 1980s. Early life and education She was born Kathleen Mary Timpson in Withington, Manchester, where she attended Lady Barn House School (1918–26). She was a grandchild of the founder of the Timpson shoe repair business, who had moved to Manchester from Kettering and established the business there by 1870. She became fascinated with mathematics, inspired by the Lady Barn headmistress, Miss Jenkin Jones. While at Lady Barn, she met her future husband, Robert Ollerenshaw. Ollerenshaw became completely deaf at age eight and was taught to lip read. She gravitated toward the study of mathematics as it is not dependent on hearing. She was further inspired by a headmistress at Lady Barn House School who studied mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
