Positive curvature, like that on a sphere, implies a finite universe, while zero curvature, as on a flat plane or negative ...

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' ...

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 ...

A: The short answer is gravity. This ‘force’, by virtue of the large masses of planets and stars, forces them into a spherical shape. Part of the answer is also geometry: a sphere is the most compact ...