Magic triangle (mathematics)
A magic triangle is a magic arrangement of the integers from 1 to in a triangular figure.
Perimeter magic triangle
A magic triangle or perimeter magic triangle is an arrangement of the integers from 1 to 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. Unlike magic squares, there are different magic sums for magic triangles of the same order. Any magic triangle has a complementary triangle obtained by replacing each integer in the triangle with.Examples
Order 3 magic triangles are the simplest.Other magic triangles
Other magic triangles use a triangular number or square number of vertices to form magic figure. Matthew Wright and his students in St. Olaf College developed magic triangles with square numbers. In their magic triangles, the sum of the th row and the th row is same for all. Its one modification uses triangular numbers instead of square numbers. Another magic triangle form is magic triangles with triangular numbers with different summation. In this magic triangle, the sum of the th row and the th row is the same for all .
Another magic triangle form is magic triangles with square numbers with different summation. In this triangle, the sum of the 2×2 subtriangles is the same for all subtriangles.
Generalized perimeter-magic types are defined which do not require a consecutive set of integers starting at 1 along the sides,.