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  2. Magic constant - Wikipedia

    en.wikipedia.org/wiki/Magic_constant

    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 ...

  3. Magic square - Wikipedia

    en.wikipedia.org/wiki/Magic_square

    The second square is a corresponding non-normal magic square with r = 8, s = 2, a = 1, c = 1, and d = 10 such that the new magic constant is M = 38. The third square is an order 5 normal magic square, which is a 90 degree clockwise rotated version of the square generated by De la Loubere method. On the right most side is a corresponding non ...

  4. Prime reciprocal magic square - Wikipedia

    en.wikipedia.org/wiki/Prime_reciprocal_magic_square

    In contrast with its rows and columns, the diagonals of this square do not sum to 27; however, their mean is 27, as one diagonal adds to 23 while the other adds to 31.. All prime reciprocals in any base with a period will generate magic squares where all rows and columns produce a magic constant, and only a select few will be full, such that their diagonals, rows and columns collectively yield ...

  5. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    DeVicci's tesseract constant: 1.00743 47568 84279 37609 [OEIS 69] The largest cube that can pass through a 4D hypercube. Positive root of + + = 1966 [OEIS 69] Lieb's square ice constant [80] 1.53960 07178 39002 03869 [Mw 61] [OEIS 70]

  6. Magic graph - Wikipedia

    en.wikipedia.org/wiki/Magic_graph

    A semimagic square is an n × n square with the numbers 1 to n 2 in its cells, in which the sum of each row and column is the same. A semimagic square is equivalent to a magic labelling of the complete bipartite graph K n,n. The two vertex sets of K n,n correspond to the rows and the columns of the square, respectively, and the label on an edge ...

  7. Siamese method - Wikipedia

    en.wikipedia.org/wiki/Siamese_method

    For example the following sequence can be used to form an order 3 magic square according to the Siamese method (9 boxes): 5, 10, 15, 20, 25, 30, 35, 40, 45 (the magic sum gives 75, for all rows, columns and diagonals). The magic sum in these cases will be the sum of the arithmetic progression used divided by the order of the magic square.

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  9. Magic series - Wikipedia

    en.wikipedia.org/wiki/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 square using the numbers from 1 to n 2, a magic series is a set of n distinct numbers adding up to n(n 2 + 1)/2.