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In the mass model, the value in each cell specifies the mass for that cell. This model has two notable properties. First it demonstrates the balanced nature of all magic squares. If such a model is suspended from the central cell the structure balances. (consider the magic sums of the
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However, there are infinitely many rational triangular numbers, rational generalized pentagonal numbers and rational tetrahedral numbers which are also magic constants of rational order.
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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
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119:). For example, a normal 8 × 8 square will always equate to 260 for each row, column, or diagonal. The normal magic constant of order
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261:. Number shapes on a triangular grid divided into equal polyiamond areas containing equal sums give polyiamond magic constant.
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rows/columns .. equal mass at an equal distance balance). The second property that can be calculated is the
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Note that 0 and 1 are the only normal magic constants of rational order which are also rational squares.
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111:= 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260 (sequence
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polytope. The number of unique sequences that form the magic constant is now known up to
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http://www.sciencenews.org/view/generic/id/7485/description/Magic_Square_Physics/
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260 as a magic constant for the 8-queens problem and 8x8 magic square
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39:– that is, a magic square which contains the numbers 1, 2, ...,
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Magic number (programming) § Unnamed numerical constants
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is similarly applied to other "magic" figures such as
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90:{\displaystyle M=n\cdot {\frac {n^{2}+1}{2}}}
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16:For unnamed numerical constants, see
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185:(solve the Diophantine equation
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316:In 2013 Dirk Kinnaes found the
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273:-pointed normal magic star is
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571:Prime reciprocal magic square
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269:The magic constant of an
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369:Magic number (physics)
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339:{\displaystyle n=1000}
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301:{\displaystyle M=4n+2}
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245:The term
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363:See also
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115:in the
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31:of a
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23:The
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51:M
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