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Magic triangle (mathematics)

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For other uses, see Magic triangle.

A magic triangle (also called a perimeter magic triangle[1]) is an arrangement of the integers from 1 to n on the sides of a triangle with the same number of integers on each side, called the order of the triangle, so that the sum of integers on each side is a constant, the magic sum of the triangle.[1][2][3][4] Unlike magic squares, there are different magic sums for magic triangles of the same order.[1] Any magic triangle has a complementary triangle obtained by replacing each integer x in the triangle with 1 + n − x.[1]

Examples

Order-3 magic triangles

Order-3 magic triangles are the simplest (except for trivial magic triangles of order 1).[1]

See also

References

  1. ^ a b c d e "Perimeter Magic Triangles". www.magic-squares.net. Retrieved 2016-12-27.
  2. ^ "Perimeter Maghic Polygons". www.trottermath.net. Retrieved 2016-12-27.
  3. ^ "Magic Triangle : nrich.maths.org". nrich.maths.org. Retrieved 2016-12-27.
  4. ^ "P4W8: Magic Triangles and Other Figures" (PDF). Retrieved December 27, 2016.
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