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For example, a normal 8 × 8 square will always equate to 260 for each row, column, or diagonal. 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 ...
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.
Magic angle [75] 0.95531 66181 245092 ... Lieb's square ice constant [80] 1.53960 07178 39002 03869 ... Foias constant is the unique real number such that if x 1 = ...
Example of a Magic Square: Date: 6 April 0008: ... Magic circle (mathematics) Magic constant; ... Most-perfect magic square; Multimagic square; Number Scrabble;
For each square, cells with the same colour (excluding grey) sum to the magic constant. Note *: The second requirement of most-perfect magic squares imply that any 2 cells that are 2 cells diagonally apart (including wraparound) sum to half the magic constant, hence any 2 such pairs also sum to the magic constant. Width: 100%: Height: 100%
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 ...
A magic circle can be derived from one or more magic squares by putting a number at each intersection of a circle and a spoke. Additional spokes can be added by replicating the columns of the magic square. In the example in the figure, the following 4 × 4 most-perfect magic square was copied into the upper part of the magic circle. Each number ...
Since each 2 × 2 subsquare sums to the magic constant, 4 × 4 pandiagonal magic squares are most-perfect magic squares. In addition, the two numbers at the opposite corners of any 3 × 3 square add up to half the magic constant. Consequently, all 4 × 4 pandiagonal magic squares that are associative must have duplicate cells.