The shortest distance between two points is a straight line. This is one of the basic principles of Euclidean geometry. But we live on a spherical Earth, so we cannot travel the straight line path ...

One hypothesis about the shape of the universe is that the universe is in the space of Euclidean geometry and flat. In Euclidean geometry, it is assumed that straight lines extend everywhere, planes ...

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' ...