Langley’s Adventitious Angles the first of the three unsolved problems listed by Rigby in his 1978 paper. 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
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