pseudosphere
Sign in to saveIn geometry, a pseudosphere is a surface in \mathbb{R}^3. It is the most famous example of a pseudospherical surface. A pseudospherical surface is a surface piecewise smoothly immersed in \mathbb{R}^3 with constant negative Gaussian curvature. A "pseudospherical surface of radius " is a surface in \mathbb{R}^3 having curvature −1/R2 at each point. Its name comes from the analogy with the sphere of radius , which is a surface of curvature 1/R2. Examples include the tractroid, Dini's surfaces, breather surfaces, and the Kuen surface.
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9 sectionsContents
- Tractroid
- Line congruence
- Universal covering space
- Hyperboloid
- Relation to solutions to the sine-Gordon equation
- See also
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In geometry, a pseudosphere is a surface in \mathbb{R}^3. It is the most famous example of a pseudospherical surface. A pseudospherical surface is a surface piecewise smoothly immersed in \mathbb{R}^3 with constant negative Gaussian curvature. A "pseudospherical surface of radius " is a surface in \mathbb{R}^3 having curvature −1/R2 at each point. Its name comes from the analogy with the sphere of radius , which is a surface of curvature 1/R2. Examples include the tractroid, Dini's surfaces, breather surfaces, and the Kuen surface.
The term "pseudosphere" was introduced by Eugenio Beltrami in his 1868 paper on models of hyperbolic geometry.