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Multimagic Cube
In mathematics, a ''P''-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their ''k'' th powers for 1 ≤ ''k'' ≤ ''P''. cubes are called bimagic, cubes are called trimagic, and cubes tetramagic. A cube is said to be semi-perfect if the ''k'' th power cubes are perfect for 1 ≤ ''k'' < ''P'', and the ''P'' th power cube is . If all ''P'' of the power cubes are perfect, the cube is said to be perfect. The first known example of a bimagic cube was given by in 2000; it is a |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Cube
In mathematics, a magic cube is the dimension, 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 to the same number, the so-called magic constant of the cube, denoted ''M''3(''n''). It can be shown that 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 (geometry), 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 cube. If the sums of numbers on a magic cube's broken space diagonals also equal the cube's magic number, the cube is called a pandiagonal magic cube. Alternative definition In recen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases: b^n = \underbrace_. The exponent is usually shown as a superscript to the right of the base. In that case, is called "''b'' raised to the ''n''th power", "''b'' (raised) to the power of ''n''", "the ''n''th power of ''b''", "''b'' to the ''n''th power", or most briefly as "''b'' to the ''n''th". Starting from the basic fact stated above that, for any positive integer n, b^n is n occurrences of b all multiplied by each other, several other properties of exponentiation directly follow. In particular: \begin b^ & = \underbrace_ \\ ex& = \underbrace_ \times \underbrace_ \\ ex& = b^n \times b^m \end In other words, when multiplying a base raised to one e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Magic Cube
Perfect commonly refers to: * Perfection, completeness, excellence * Perfect (grammar), a grammatical category in some languages Perfect may also refer to: Film * ''Perfect'' (1985 film), a romantic drama * ''Perfect'' (2018 film), a science fiction thriller Literature * ''Perfect'' (Friend novel), a 2004 novel by Natasha Friend * ''Perfect'' (Hopkins novel), a young adult novel by Ellen Hopkins * ''Perfect'' (Joyce novel), a 2013 novel by Rachel Joyce * ''Perfect'' (Shepard novel), a Pretty Little Liars novel by Sara Shepard * ''Perfect'', a young adult science fiction novel by Dyan Sheldon Music * Perfect interval, in music theory * Perfect Records, a record label Artists * Perfect (musician) (born 1980), reggae singer * Perfect (Polish band) * Perfect (American band), an American alternative rock group Albums * ''Perfect'' (Intwine album) (2004) * ''Perfect'' (Half Japanese album) (2016) * ''perfecT'', an album by Sam Shaber * ''Perfect'', an album by Tru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiperfect Magic Cube
In mathematics, a semiperfect magic cube is a magic cube that is not a perfect magic cube, i.e., a magic cube for which the cross section diagonals do not necessarily sum up to the cube's 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 .... References *. Magic squares {{combin-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Hendricks
John Samuel Hendricks (born March 29, 1952)"John Hendricks: An Oral History," The Cable Center, September 2, 2003. is an American businessman and is the founder and former chairman of Discovery, Inc. (now a part of Warner Bros. Discovery) a broadcasting and film production company which owned the Discovery Channel, TLC and Animal Planet networks, among other ventures. On March 20, 2014, after 32 years at the helm, he made public his decision to retire as chairman of Discovery Communications after the annual shareholders' meeting of May 16, 2014. He moved on to found CuriosityStream, an ad-free, on-demand nonfiction streaming service. Early life Born in Matewan, West Virginia, Hendricks' father was a home builder and his mother a clerk for city government. In 1958, the Hendricks family moved to Huntsville, Alabama, where Hendricks grew up. His father died when he was 20, and his mother died when he was 30. He attended S.R. Butler High School where he met his first wife, Patti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, a magic square which contains the numbers 1, 2, ..., ''n''2 – the magic constant is M = n \cdot \frac. For normal magic squares of orders ''n'' = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260 (sequence A006003 in the OEIS). For example, a normal 8 × 8 square will always equate to 260 for each row, column, or diagonal. The normal magic constant of order n is (n^3+n)/2. The largest magic constant of normal magic square which is also a: *triangular number is 15 (solve the Diophantine equation x^2=y^3+16y+16, where y is divisible by 4); *square number is 1 (solve the Diophantine equation x^2=y^3+4y, where y is even); * generalized pentagonal number is 171535 (solve the Diophan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign. History Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. Weisstein continuously improved the notes and accepted corrections and comments from online readers. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled "CRC Concise Encyclopedia of Mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Square
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number of integers along one side (''n''), and the constant sum is called the ' magic constant'. If the array includes just the positive integers 1,2,...,n^2, the magic square is said to be 'normal'. Some authors take magic square to mean normal magic square. Magic squares that include repeated entries do not fall under this definition and are referred to as 'trivial'. Some well-known examples, including the Sagrada Família magic square and the Parker square are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant this gives a ''semimagic square (sometimes called orthomagic square). The mathematical study of magic squares typically deals with their construction, classification, and enumeration. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multimagic Square
In mathematics, a ''P''-multimagic square (also known as a satanic square) is a magic square that remains magic even if all its numbers are replaced by their ''k''th powers for 1 ≤ ''k'' ≤ ''P''. squares are called bimagic, squares are called trimagic, squares tetramagic, and squares pentamagic. Constants for normal squares If the squares are normal, the constant for the power-squares can be determined as follows: Bimagic series totals for bimagic squares are also linked to the square-pyramidal number sequence is as follows :- Squares 0, 1, 4, 9, 16, 25, 36, 49, .... Sum of Squares 0, 1, 5, 14, 30, 55, 91, 140, 204, 285, ... )number of units in a square-based pyramid) The bimagic series is the 1st, 4th, 9th in this series (divided by 1, 2, 3, ''n'') etc. so values for the rows and columns in order-1, order-2, order-3 Bimagic squares would be 1, 15, 95, 374, 1105, 2701, 5775, 11180, ... The trimagic series would be related in the same way to the hyper-py ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
