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
Facial Angles (Camper) for Philipp von Stosch's "Pierres Antiques Gravées". The facial angles of Moors and Kalmyks was calculated to be 70 degrees, and that of a European 80 degrees. The original report of these lectures in the proceedings of the literature society is listed as one of the 1000 most important texts in the Canon of Dutch Literature. Facial Angles (Camper) Facial Angles refers to the content of two lectures on this subject by the Amsterdam professor of anatomy Petrus Camper on the 1st and 8 August in 1770 to the Amsterdam Drawing Academy called the "Teken-akademie". Camper was a competent artist