Elliptic geometry geometry is that the sum of the interior angles of a triangle is greater than 180 degrees. In the spherical model, for example, a triangle can be constructed with vertices at the locations where the three positive Cartesian coordinate axes intersect the sphere, and all three of its internal angles are 90 degrees, summing to 270 degrees. For sufficiently small triangles, the excess over 180 degrees can be made arbitrarily small. The Pythagorean theorem fails in elliptic geometry. In the 90°–90°–90° triangle described above, all three sides have the same length, and consequently do not satisfy formula_1. The Pythagorean result
Many-angled ones a result, when they manifest in our universe they appear as disconnected floating body parts of some larger beast that is complete in the higher dimension (similar to how a three dimensional being would appear in flatland as its parts pass through the plane of that two-dimensional world). More recently, they have appeared in books by British authors or comics and video games from British comics writers who have worked for "2000 AD". The many-angled ones were mentioned in Charles Stross's "The Atrocity Archives". This work features the usual appearances by "nameless horrors of the abyss," which may or may