Hyperbolic triangle relations between the sides "s" and the angles "A" of an equilateral triangle (a triangle where all sides have the same length and all angles are equal). The relations are: Whether "C" is a right angle or not, the following relationships hold: The hyperbolic law of cosines is as follows: Its dual theorem is There is also a "law of sines": and a four-parts formula: For hyperbolic trigonometry: Hyperbolic triangle In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called "sides" or "edges" and three points called "angles" or "vertices".
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