Most trigonometry students look at triangles on a flat surface. However, people from ancient astronomers to modern navigators calculated the arc lengths and angles of triangles on a sphere. They used ...

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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 ...