Equiangular polygon Equiangular polygon In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths. The only equiangular triangle is the equilateral triangle. Rectangles, including the square, are the only equiangular quadrilaterals (four-sided figures). For a convex equiangular "n"-gon each internal angle is 180(1-2/n)°; this is the "equiangular polygon theorem". Viviani's theorem holds for equiangular polygons: A rectangle (equiangular quadrilateral) with integer side lengths may be tiled
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