Inflation for Beginners #2 But it was Bernhard Riemann, a pupil of Gauss, who put the notion of non-Euclidean geometry on a comprehensive basis in the 1850s, and who realised the possibility of yet another variation on the theme, the geometry that applies on the closed surface of a sphere (including the surface of the Earth). In spherical geometry, the angles of a triangle always add up to more than 180o, and although all "lines of longitude" cross the equator at right angles, and must therefore all be parallel to one another, they all cross each other at the poles.
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