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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.
Ramanujan magic square construction: Image title: Construction of Ramanujan's magic square from a mutually orthogonal Latin square, its transpose and day (D), month (M), century (C) and year (Y) values, and Ramanujan's example, drawn by CMG Lee. Width: 100%: Height: 100%
Construction of Ramanujan's birthday magic square from a 4×4 Latin square with distinct diagonals and day (D), month (M), century (C) and year (Y) values, and Ramanujan's birthday example. The problem of determining if a partially filled square can be completed to form a Latin square is NP-complete. [22]
[14] [15] In their conversation, Hardy stated that the number 1729 from a taxicab he rode was a "dull" number and "hopefully it is not unfavourable omen", but Ramanujan remarked that "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways". [16]
Srinivasa Ramanujan Aiyangar [a] (22 December 1887 – 26 April 1920) was an Indian mathematician.Often regarded as one of the greatest mathematicians of all time, though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then ...
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.
Construction of Ramanujan's magic square from Latin squares and day (D), month (M), century (C) and year (Y) values, and Ramanujan's example. What is the "magic" behind magic squares? Why does it work? Is there a mathematical formula explaining why it works?
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 example, the magic square shown below has a magic constant of 15.