Differential geometry of surfaces and Theorema Egregium
Geometría diferencial de superficies y Theorema Egregium
- Date
- 1827 · confidence high
- Place
- Göttingen, Germany
- Credited to
- Carl Friedrich Gauss (Disquisitiones generales circa superficies curvas)
- People
- 👤 Carl Friedrich Gauss1777–1855
- Field
- Knowledge & symbols
What was discovered
The Gaussian curvature of a surface is intrinsic: it can be measured from within, without reference to the ambient space. It explains why no flat map of the Earth preserves distances and paves the way for Riemannian geometry.
The work arose from the geodetic triangulation of the Kingdom of Hanover directed by Gauss.
What it led to
- Riemannian geometry
- general relativity
- cartography and geodesy
- the Gauss-Bonnet theorem
Built on
- calculus
- Euler's and Monge's work on surfaces
Made possible
- Mirzakhani's moduli space volumes and simple geodesics2004-2014
- Hanover geodetic survey
- engineering surface design