Magic triangle (mathematics)
A magic triangle is an magic arrangement of the integers from 1 to n to triangular figure.
perimeter magic triangle
A magic triangle or 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 are the simplest (except for trivial magic triangles of order 1).[1]
Other magic triangles
Other magic triangles use Triangular number or square number of vertices to form magic figure.[5]
See also
References
- ^ a b c d e "Perimeter Magic Triangles". www.magic-squares.net. Retrieved 2016-12-27.
- ^ "Perimeter Maghic Polygons". www.trottermath.net. Retrieved 2016-12-27.
- ^ "Magic Triangle : nrich.maths.org". nrich.maths.org. Retrieved 2016-12-27.
- ^ "P4W8: Magic Triangles and Other Figures" (PDF). Retrieved December 27, 2016.
- ^ https://www.mlwright.org/docs/magic_triangles.pdf, (sequence A355119 in the OEIS)
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