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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
370:. Summing the individual moments of inertia (distance squared from the center × the cell value) gives the moment of inertia for the magic square, which depends solely on the order of the square.
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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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130:). For example, a normal 8 × 8 square will always equate to 260 for each row, column, or diagonal. The normal magic constant of order
272:. 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.
122:= 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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156:. The largest magic constant of normal magic square which is also a:
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50:– 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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101:{\displaystyle M=n\cdot {\frac {n^{2}+1}{2}}}
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221:is 171535 (solve the Diophantine equation
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27:For unnamed numerical constants, see
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196:(solve the Diophantine equation
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327:In 2013 Dirk Kinnaes found the
284:-pointed normal magic star is
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582:Prime reciprocal magic square
219:generalized pentagonal number
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596:Higher dimensional shapes
587:Most-perfect magic square
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280:The magic constant of an
641:Pandiagonal magic square
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457:Hypercube Math formulae
380:Magic number (physics)
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350:{\displaystyle n=1000}
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312:{\displaystyle M=4n+2}
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386:References
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256:The term
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18:Magic sum
374:See also
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126:in the
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423:Heinz
236:where
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34:The
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65:=
62:M
52:n
48:n
31:.
20:)
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