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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 = +.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, ... Square root of 3, Theodorus' constant [6] ... Magic angle [75] 0.95531 ...
The square consists of 9 nine power magic squares. It has been noted that the number of days in 27 years (365 days per year) is 9855, the constant of the larger square. [6] [2] This was first discovered and solved by ancient Greeks: Aristotle understood this magic square, but it is noted from numeris Platonics nihil obscuris that Cicero was ...
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.
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 ...
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A most-perfect magic square of order n is a magic square containing the numbers 1 to n 2 with two additional properties: Each 2 × 2 subsquare sums to 2 s , where s = n 2 + 1. All pairs of integers distant n /2 along a (major) diagonal sum to s .