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The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3. In mathematics, especially 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.
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 quarrez ou tables magiques, a treatise on magic squares published posthumously in 1693, in which he described all 880 essentially different normal magic squares of order 4.
Sallows is an expert on the theory of magic squares [1] and has invented several variations on them, including alphamagic squares [2] [3] and geomagic squares. [4] The latter invention caught the attention of mathematician Peter Cameron who has said that he believes that "an even deeper structure may lie hidden beyond geomagic squares" [5]
A geometric magic square, often abbreviated to geomagic square, is a generalization of magic squares invented by Lee Sallows in 2001. [1] A traditional magic square is a square array of numbers (almost always positive integers ) whose sum taken in any row, any column, or in either diagonal is the same target number .
Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathematics includes the aesthetics and culture of mathematics, peculiar or amusing stories and coincidences about mathematics, and the personal lives of mathematicians.
The Chinese also made use of the complex combinatorial diagram known as the magic square and magic circles, described in ancient times and perfected by Yang Hui (AD 1238–1298). [ 121 ] Even after European mathematics began to flourish during the Renaissance , European and Chinese mathematics were separate traditions, with significant Chinese ...
A common method of creating the sigils of certain spirits was to use kameas, a special use case of magic squares—the names of the spirits were converted to numbers, which were then located on the magic square. The locations were then connected by lines, forming an abstract figure. [4] The word sigil [...] has a long history in Western magic.
The earliest known magic squares of order greater than three are attributed to Yang Hui (fl. ca. 1261–1275), who worked with magic squares of order as high as ten. [47] "The same "Horner" device was used by Yang Hui, about whose life almost nothing is known and who work has survived only in part.