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Reference.org
Pseudosphere
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<p>In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a pseudosphere is a surface with constant negative <a href="/facts/Gaussian_curvature/ARdhnb7o">Gaussian curvature</a>. </p><p>A pseudosphere of radius R is a surface in R 3 {\displaystyle \mathbb {R} ^{3}} having <a href="/facts/Gaussian_curvature/ARdhnb7o">curvature</a> −1/<i>R</i>2 at each point. Its name comes from the analogy with the sphere of radius R, which is a surface of curvature 1/<i>R</i>2. The term was introduced by <a href="/facts/Eugenio_Beltrami/vkp9UPR9">Eugenio Beltrami</a> in his 1868 paper on models of <a href="/facts/Hyperbolic_geometry/DjTMKdgy">hyperbolic geometry</a>. </p>