Special right triangle : , which follows immediately from the Pythagorean theorem. Of all right triangles, the 45°–45°–90° degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, namely . Of all right triangles, the 45°–45°–90° degree triangle has the greatest ratio of the altitude from the hypotenuse to the sum of the legs, namely . Triangles with these angles are the only possible right triangles that are also isosceles triangles in Euclidean geometry. However, in spherical geometry and hyperbolic geometry, there are infinitely many different shapes of right isosceles triangles. This is a triangle whose three angles
Alan (given name) century, where it was about even with "Simon", and more numerous than "Henry". Early occurrences of the name in British records include: "Alanus" in 1066 (in the "Domesday Book"); and "Alain" in 1183. The name became popular in Scotland in part through the Stewarts. This family descends from Alan fitz Flaad, an Anglo-Breton knight, who possessed lands in what is modern day Shropshire, England. Alan (given name) Alan is a masculine given name in the English language. There are numerous differing etymologies attributed to the name. The name was first introduced into England by Bretons who took part in the