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LUX Method For Magic Squares
Conway's LUX method for magic squares is an algorithm by John Horton Conway for creating magic squares of order 4''n''+2, where ''n'' is a natural number. Method Start by creating a (2''n''+1)-by-(2''n''+1) square array consisting of * ''n''+1 rows of Ls, * 1 row of Us, and * ''n''-1 rows of Xs, and then exchange the U in the middle with the L above it. Each letter represents a 2x2 block of numbers in the finished square. Now replace each letter by four consecutive numbers, starting with 1, 2, 3, 4 in the centre square of the top row, and moving from block to block in the manner of the Siamese method: move up and right, wrapping around the edges, and move down whenever you are obstructed. Fill each 2x2 block according to the order prescribed by the letter: :\mathrm: \quad \begin4&&1\\&\swarrow&\\2&\rightarrow&3\end \qquad \mathrm: \quad \begin1&&4\\\downarrow&&\uparrow\\2&\rightarrow&3\end \qquad \mathrm:\quad \begin1&&4\\&\searrow\!\!\!\!\!\!\nearrow&\\3&&2\end Example Let '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...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] |
Magic Square
In mathematics, especially History of mathematics, historical and 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, Sagrada Família magic square and the #Parker square, 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). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Siamese Method
The Siamese method, or De la Loubère method, is a simple method to construct any size of ''n''-odd magic squares (i.e. number squares in which the sums of all rows, columns and diagonals are identical). The method was brought to France in 1688 by the French mathematician and diplomat Simon de la Loubère, as he was returning from his 1687 embassy to the kingdom of Siam. The Siamese method makes the creation of magic squares straightforward. Publication De la Loubère published his findings in his book ''A new historical relation of the kingdom of Siam'' (''Du Royaume de Siam'', 1693), under the chapter entitled ''The problem of the magical square according to the Indians''. Although the method is generally qualified as "Siamese", which refers to de la Loubère's travel to the country of Siam, de la Loubère himself learnt it from a Frenchman named M.Vincent (a doctor, who had first travelled to Persia and then to Siam, and was returning to France with the de la Loubère embassy) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strachey Method For Magic Squares
The Strachey method for magic squares is an algorithm for generating magic squares of singly even order 4''k'' + 2. An example of magic square of order 6 constructed with the Strachey method: Strachey's method of construction of singly even magic square of order ''n'' = 4''k'' + 2. 1. Divide the grid into 4 quarters each having ''n''2/4 cells and name them crosswise thus 2. Using the Siamese method (De la Loubère method) complete the individual magic squares of odd order 2''k'' + 1 in subsquares A, B, C, D, first filling up the sub-square A with the numbers 1 to ''n''2/4, then the sub-square B with the numbers ''n''2/4 + 1 to 2''n''2/4,then the sub-square C with the numbers 2''n''2/4 + 1 to 3''n''2/4, then the sub-square D with the numbers 3''n''2/4 + 1 to ''n''2. As a running example, we consider a 10×10 magic square, where we have divided the square into four quarters. The quarter A contains a magic square of numbers from 1 to 25, B a magic square of numbers from 26 to 50 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Association Of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary education and research which awards academic degrees in several Discipline (academia), academic disciplines. ''University'' is derived from the Latin phrase , which roughly ..., college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. The MAA was founded in 1915 and is headquartered at 11 Dupont in the Dupont Circle, Washington, D.C., Dupont Circle neighborhood of Washington, D.C. The organization publishes mathematics journals and books, including the ''American Mathematical Monthly'' (established in 1894 by Benjamin Finkel), the most widely read mathematics journal in the world according to re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
