Birthday

Happy birthday, yamazikikun!

Ramble, Part 45: Making Models

Though Gauss, Bolyai, and Lobachevsky had been unable to find contradictions in hyperbolic geometry, the question still remained whether there actually were any such contradictions. The same was true of the elliptic geometry studied by Gauss's student Bernhard Riemann. (In that geometry, Saccheri's "hypothesis of the obtuse angle", there are no parallels, and lines have finite length.) The question of how to show that the new geometries were not self-contradictory was dealt with in the next generation or so, most notably by Henri Poincaré.

( Models )

Ramble Contents