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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 normal magic square of order n – that is, a magic square which contains the numbers 1, 2, ..., n 2 – the magic constant is = +.
1+13 = 2+12 = 3+11 = 4+10 = 5+9 = 14 1 2 + 3 2 + 9 2 + 10 2 + 12 2 = 2 2 + 4 2 + 5 2 + 11 2 + 13 2 = 335 (equal partitioning of squares; semi-bimagic property) This leads to squares having a maximum element of 169 and a pandiagonal magic constant of 850, which are also semi-bimagic with each row or column sum of squares equal to 102,850.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
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 ...
The 3×3 magic square in different orientations forming a non-normal 6×6 magic square, from an unidentified 19th century Indian manuscript. The 3×3 magic square first appears in India in Gargasamhita by Garga, who recommends its use to pacify the nine planets (navagraha). The oldest version of this text dates from 100 CE, but the passage on ...
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 r i s j is the value in row i, column j of the semimagic square. The definition of semimagic squares differs from the definition of ...
The fact that this square is a pandiagonal magic square can be verified by checking that all of its broken diagonals add up to the same constant: 3+12+14+5 = 34 10+1+7+16 = 34 10+13+7+4 = 34. One way to visualize a broken diagonal is to imagine a "ghost image" of the panmagic square adjacent to the original:
9855 is also the Magic constant of a Magic square of order 27. [3] In a magic square, the magic constant is the sum of numbers in each row, column, and diagonal, which is the same. For magic squares of order n, the magic constant is given by the formula (+). [4] The magic constant 9855 [5] for the magic square of order 27 can be calculated [2 ...