Pseudosphere

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In geometry, a pseudosphere is a surface in R 3 {\displaystyle \mathbb {R} ^{3}} . It is the most famous example of a pseudospherical surface. A pseudospherical surface is a surface piecewise smoothly immersed in R 3 {\displaystyle \mathbb {R} ^{3}} with constant negative Gaussian curvature. A "pseudospherical surface of radius R" is a surface in R 3 {\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. Examples include the tractroid, Dini's surfaces, breather surfaces, and the Kuen surface. The term "pseudosphere...

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