Langley’s Adventitious Angles Langley’s Adventitious Angles Langley’s Adventitious Angles is a mathematical problem posed by Edward Mann Langley in "The Mathematical Gazette" in 1922. In its original form the problem was as follows: formula_1 is an isosceles triangle. A solution was developed by James Mercer in 1923. This solution involves drawing one additional line, and then making repeated use of the fact that the internal angles of a triangle add up to 180° to prove that several triangles drawn within the large triangle are all isosceles. Many other solutions are possible. Cut the Knot list twelve different solutions and several alternative problems with
Magic triangle (mathematics) Magic triangle (mathematics) A magic triangle (also called a 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 . This means that only half of the triangles