Magic triangle (mathematics)

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. This means that only half of the triangles for any order need to be checked for the magic property.[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. 1 2 3 4 5 "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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