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Everyone learns the number one rule about triangles in high school: the angles of a triangle add up to 180 degrees. But did you know that sometimes they don't? Triangles are much more interesting than ...

This paper gives the exact evaluation of the shape density on the shape space Σ (S2,3) for a labelled random spherical triangle whose vertices are i.i.d.-uniform in a 'cap' of S2 bounded by a 'small' ...

This media is in the public domain (free of copyright restrictions). You can copy, modify, and distribute this work without contacting the Smithsonian. For more information, visit the Smithsonian's ...