Non-Euclidean (hyperbolic) geometry
Geometría no euclidiana (hiperbólica)
- Date
- 1829-1832 · confidence high
- Place
- Kazan, Russia
- Credited to
- Nikolai Lobachevsky (1829), János Bolyai (1832) and Carl Friedrich Gauss (unpublished)
- People
- 👤 Carl Friedrich Gauss1777–1855👤 János Bolyai1802–1860👤 Nikolái Lobachevski1792–1856
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
A consistent geometry in which infinitely many parallels pass through a point outside a line, obtained by denying Euclid's fifth postulate. It showed that Euclidean geometry is not a necessary truth and freed mathematics from spatial intuition.
An independent discovery by Lobachevsky (Kazan) and Bolyai (Marosvásárhely, Transylvania); Gauss claimed to have developed it earlier without publishing it for fear of the outcry of the Boeotians. Relative consistency was proved with Beltrami's model (1868).
What it led to
- Riemannian geometry
- the Erlangen programme
- relativity
- the models of Beltrami, Klein and Poincaré
- modern axiomatics
Built on
- Saccheri (1733)
- Lambert
- Legendre (attempts to prove the fifth postulate)