geodesic triangle

Let M be a differentiable manifold (at least two times differentiableMathworldPlanetmathPlanetmath) and A,B,CM (not necessarily distinct). Let x1,x2,x3[0,). Let γ1:[0,x1]M, γ2:[0,x2]M, and γ3:[0,x3]M be geodesics such that all of the following hold:

  • γ1(0)=A;

  • γ1(x1)=B;

  • γ2(0)=A;

  • γ2(x2)=C;

  • γ3(0)=B;

  • γ3(x3)=C.

Then the figure determined by γ1, γ2, and γ3 is a geodesic triangle.

Note that a geodesic triangle need not be a triangle. For example, in 2, if A=(0,0), B=(1,2), and C=(3,6), then the geodesic triangle determined by A, B, and C is {(x,2x):x[0,3]}, which is not a triangle.


geodesic metric space (

Title geodesic triangle
Canonical name GeodesicTriangle
Date of creation 2013-03-22 17:11:31
Last modified on 2013-03-22 17:11:31
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 7
Author Wkbj79 (1863)
Entry type Definition
Classification msc 53C22