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- Magic squares

Simple magic cube

A simple magic cube is the lowest of six basic classes of magic cubes. These classes are based on extra features required. The simple magic cube requires only the basic features a cube requires to be

Trimagic square

No description available.

Bimagic square

No description available.

Ahmad al-Buni

Sharaf al-Din or Shihab al-Din or Muḥyi al-Din Abu al-Abbas Aḥmad ibn Ali ibn Yusuf al-Qurashi al-Sufi, better known as Ahmad al-Buni (Arabic: أحمد البوني), born in Buna, in present-day Annaba, Algeri

Magic cube classes

Every magic cube may be assigned to one of six magic cube classes, based on the cube characteristics. This new system is more precise in defining magic cubes. But possibly of more importance, it is co

Most-perfect magic square

A most-perfect magic square of order n is a magic square containing the numbers 1 to n2 with two additional properties: 1.
* Each 2 × 2 subsquare sums to 2s, where s = n2 + 1. 2.
* All pairs of inte

Claude Gaspar Bachet de Méziriac

Claude Gaspar Bachet Sieur de Méziriac (9 October 1581 – 26 February 1638) was a French mathematician and poet born in Bourg-en-Bresse, at that time belonging to Duchy of Savoy. He wrote Problèmes pla

Bernard Frénicle de Bessy

Bernard Frénicle de Bessy (c. 1604 – 1674), was a French mathematician born in Paris, who wrote numerous mathematical papers, mainly in number theory and combinatorics. He is best remembered for Des q

John R. Hendricks

John Robert Hendricks (September 4, 1929 – July 7, 2007) was a Canadian amateur mathematician specializing in magic squares and hypercubes. He published many articles in the Journal of Recreational Ma

Space diagonal

In geometry, a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals contrast with face diagonals, w

Pandiagonal magic square

A pandiagonal magic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional property that the broken diagonals, i.e. the di

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

Arthur Cayley

Arthur Cayley FRS (/ˈkeɪli/; 16 August 1821 – 26 January 1895) was a prolific British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics. As a ch

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 kth powers for 1 ≤ k ≤ P. 2-multimagic squares

Manuel Moschopoulos

Manuel Moschopoulos (Latinized as Manuel Moschopulus; Greek: Mανουὴλ Μοσχόπουλος), was a Byzantine commentator and grammarian, who lived during the end of the 13th and the beginning of the 14th centur

Nasik magic hypercube

No description available.

Diagonal magic cube

The class of diagonal magic cubes is the second of the six magic cube classes (when ranked by the number of lines summing correctly), coming after the simple magic cubes. In a diagonal magic cube of o

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 eac

Pantriagonal magic cube

A pantriagonal magic cube is a magic cube where all 4m2 pantriagonals sum correctly. There are 4 one-segment pantriagonals, 12(m − 1) two-segment pantriagonals, and 4(m − 2)(m − 1) three-segment pantr

Associative magic square

An associative magic square is a magic square for which each pair of numbers symmetrically opposite to the center sum up to the same value. For an n × n square, filled with the numbers from 1 to n2, t

D. R. Kaprekar

Dattatreya Ramchandra Kaprekar (Marathi: दत्तात्रेय रामचंद्र कापरेकर; 17 January 1905 – 1986) was an Indian recreational mathematician who described several classes of natural numbers including the Ka

Sriramachakra

Sriramachakra (also called Sri Rama Chakra, Ramachakra, Rama Chakra, or Ramar Chakra) is a mystic diagram or a yantra given in Tamil almanacs as an instrument of astrology for predicting one's future.

Geometric magic square

A geometric magic square, often abbreviated to geomagic square, is a generalization of magic squares invented by Lee Sallows in 2001. A traditional magic square is a square array of numbers (almost al

Broken diagonal

In recreational mathematics and the theory of magic squares, a broken diagonal is a set of n cells forming two parallel diagonal lines in the square. Alternatively, these two lines can be thought of a

Pandiagonal magic cube

In recreational mathematics, a pandiagonal magic cube is a magic cube with the additional property that all broken diagonals (parallel to exactly two of the three coordinate axes) have the same sum as

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). T

Magic series

A magic series is a set of distinct positive integers which add up to the magic constant of a magic square and a magic cube, thus potentially making up lines in magic tesseracts. So, in an n × n magic

Philippe de La Hire

Philippe de La Hire (or Lahire, La Hyre or Phillipe de La Hire) (18 March 1640 – 21 April 1718) was a French painter, mathematician, astronomer, and architect. According to Bernard le Bovier de Fonten

Frénicle standard form

A magic square is in the Frénicle standard form, named for Bernard Frénicle de Bessy, if the following two conditions hold: 1.
* the element at position [1,1] (top left corner) is the smallest of the

Conway's 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 4n+2, where n is a natural number.

Prime reciprocal magic square

A prime reciprocal magic square is a magic square using the decimal digits of the reciprocal of a prime number. Consider a unit fraction, like 1/3 or 1/7. In base ten, the remainder, and so the digits

Lo Shu Square

Lo Shu Square (or Nine Halls Diagram), named for the Luo (River) scroll, is the unique normal magic square of order three (every normal magic square of order three is obtained from the Lo Shu by rotat

Yang Hui

Yang Hui (simplified Chinese: 杨辉; traditional Chinese: 楊輝; pinyin: Yáng Huī, ca. 1238–1298), courtesy name Qianguang (謙光), was a Chinese mathematician and writer during the Song dynasty. Originally, f

Yellow River Map

The Yellow River Map, Scheme, or Diagram (河圖, with variants for the second character) is an ancient Chinese concept. It is related to the Lo Shu Square. The origins of the two from the rivers Luo and

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 consta

Magic hypercube

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 pill

Magic hyperbeam

No description available.

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. 2-multimagic cubes are called bimagic, 3-multimagic cube

Alphamagic square

An alphamagic square is a magic square that remains magic when its numbers are replaced by the number of letters occurring in the name of each number. Hence 3 would be replaced by 5, the number of let

Antimagic square

An antimagic square of order n is an arrangement of the numbers 1 to n2 in a square, such that the sums of the n rows, the n columns and the two diagonals form a sequence of 2n + 2 consecutive integer

Broken space diagonal

In a magic cube, a broken space diagonal is a sequence of cells of the cube that follows a line parallel to a space diagonal of the cube, and continues on the corresponding point of an opposite face w

W. W. Rouse Ball

Walter William Rouse Ball (14 August 1850 – 4 April 1925), known as W. W. Rouse Ball, was a British mathematician, lawyer, and fellow at Trinity College, Cambridge, from 1878 to 1905. He was also a ke

Luca Pacioli

Fra Luca Bartolomeo de Pacioli (sometimes Paccioli or Paciolo; c. 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to

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. T

Strachey method for magic squares

The Strachey method for magic squares is an algorithm for generating magic squares of singly even order 4k + 2. An example of magic square of order 6 constructed with the Strachey method: Strachey's m

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 diagonals sum up to the cube's magic constant. P

Simon de la Loubère

Simon de la Loubère (French: [simɔ̃ də la lubɛʁ]; 21 April 1642 – 26 March 1729) was a French diplomat to Siam (Thailand), writer, mathematician and poet. He is credited with bringing back a document

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