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
Schwarz triangle angle is "d"/"n" of the half-circle. "2" means a right triangle. When these are whole numbers, the triangle is called a Möbius triangle, and corresponds to a "non"-overlapping tiling, and the symmetry group is called a triangle group. In the sphere there are three Möbius triangles plus one one-parameter family; in the plane there are three Möbius triangles, while in hyperbolic space there is a three-parameter family of Möbius triangles, and no exceptional objects. A fundamental domain triangle ("p" "q" "r"), with vertex angles /"p", /"q", and /"r", can exist in different spaces depending on the value of the sum