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Posted by / 18-May-2016 05:58

The dating guy 2x2

In modern times they have been generalized a number of ways, including using extra or different constraints, multiplying instead of adding cells, using alternate shapes or more than two dimensions, and replacing numbers with shapes and addition with geometric operations. For normal magic squares of orders n = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260 (sequence A006003 in the OEIS).

The 1×1 magic square, with only one cell containing the number 1, is called trivial, because it is typically not under consideration when discussing magic squares; but it is indeed a magic square by definition, if we regard a single cell as a square of order one.

For the order-3 case the moment of inertia is always 60, while for the order-4 case the moment of inertia is always 340.

In general, for the n×n case the moment of inertia is and to Islamic mathematicians possibly as early as the seventh century AD.

Moreover, the term "magic squares" is sometimes also used to refer to various types of word squares.

While the great king Yu was trying to channel the water out to sea, a turtle emerged from it with a curious pattern on its shell: a 3×3 grid in which circular dots of numbers were arranged, such that the sum of the numbers in each row, column and diagonal was the same: 15.

According to the legend, thereafter people were able to use this pattern in a certain way to control the river and protect themselves from floods.

It is essentially the same as the Lo Shu Square, but with 19 added to each number, giving a magic constant of 72.

The earliest unequivocal occurrence of magic square is found in a work called Kaksaputa, composed by the alchemist Nagarjuna around 1st century AD.

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For the 6×6 case, there are estimated to be approximately 1.8 × 10 The moment of inertia of a magic square has been defined as the sum over all cells of the number in the cell times the squared distance from the center of the cell to the center of the square; here the unit of measurement is the width of one cell.

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