Pseudosphere

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

A pseudosphere of radius $R$ is a surface in $\mathbb {R} ^{3}$ having curvature $−.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}1/R2$ in each point. Its name comes from the analogy with the sphere of radius $R$ , which is a surface of curvature $1 / R 2$ . The term was introduced by Eugenio Beltrami in his 1868 paper on models of hyperbolic geometry.

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