🔬 Discovery

Pseudosphere

Pseudoesfera

Date
1868 · confidence medium
Place
Bologna, Italy
Credited to
Eugenio Beltrami (surface previously studied by Ferdinand Minding)
Field
Knowledge & symbols

What was discovered

A surface of constant negative Gaussian curvature, the most famous example of a pseudospherical surface; Beltrami used it in 1868 as a model of hyperbolic geometry.

The surface (the tractoid) had already been studied by Ferdinand Minding in 1839; the name "pseudosphere" was introduced by Beltrami in 1868.

What it led to

  • The first concrete models of hyperbolic geometry
  • Later development of non-Euclidean geometry

Links

Sources✓ verified 2026-09-28