Magic triangle (mathematics)

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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 + nx. [1]

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Examples

Order-3 magic triangles Order 3 Magic Triangles.gif
Order-3 magic triangles

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

See also

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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.