Pseudosphere

In geometry, a pseudosphere is a surface with constant negative Gaussian curvature.

A pseudosphere of radius R is a surface in ${\displaystyle \mathbb {R} ^{3}}$ having curvature −1/R² at each point. Its name comes from the analogy with the sphere of radius R, which is a surface of curvature 1/R². The term was introduced by Eugenio Beltrami in his 1868 paper on models of hyperbolic geometry.^[1]