In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle. The triangle can be an ordinary Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle. Each triangle group is the symmetry group of a tiling of the Euclidean plane, the sphere, or the Hyperbolic plane by congruent triangles, a fundamental domain for the action, called a Möbius triangle.
Read more about Triangle Group: Definition, Classification, Von Dyck Groups, Overlapping Tilings, History, Applications
Famous quotes containing the word group:
“Remember that the peer group is important to young adolescents, and there’s nothing wrong with that. Parents are often just as important, however. Don’t give up on the idea that you can make a difference.”
—The Lions Clubs International and the Quest Nation. The Surprising Years, I, ch.5 (1985)