Golden triangle (mathematics) Golden triangle (mathematics) A golden triangle, also known as the sublime triangle,is an isosceles triangle in which the duplicated side is in the golden ratio to the distinct side: Golden triangles are found in the nets of several stellations of dodecahedrons and icosahedrons. Also, it is the shape of the triangles found in the points of pentagrams. The vertex angle is equal to Since the angles of a triangle sum to 180°, base angles are therefore 72° each. The golden triangle can also be found in a regular decagon, or an equiangular and equilateral ten-sided polygon, by connecting any two
Ideal triangle circle. Note that in the Beltrami-Klein model, the angles at the vertices of an ideal triangle are not zero, because the Beltrami-Klein model, unlike the Poincaré disk and half-plane models, is not conformal i.e. it does not preserve angles. The real ideal triangle group is the reflection group generated by reflections of the hyperbolic plane through the sides of an ideal triangle. Algebraically, it is isomorphic to the free product of three order-two groups (Schwarz 2001). Ideal triangle In hyperbolic geometry an ideal triangle is a hyperbolic triangle whose three vertices all are ideal points. Ideal triangles are also sometimes