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
Gauss's Pythagorean right triangle proposal Gauss's Pythagorean right triangle proposal Gauss's Pythagorean right triangle proposal is an idea attributed to Carl Friedrich Gauss for a method to signal extraterrestrial beings by constructing an immense right triangle and three squares on the surface of the Earth. The shapes would be a symbolical representation of the Pythagorean theorem, large enough to be seen from the Moon or Mars. Although credited in numerous sources as originating with Gauss, with exact details of the proposal set out, the specificity of detail, and even whether Gauss made the proposal, have been called into question. Many of the earliest sources do