Kuen surface

The Kuen surface is a mathematical surface of constant negative unit Gaussian curvature, making it an example of a pseudospherical surface. It can be described as a parametric surface in terms of the parametric equations x = 2 cosh ⁡ v ( cos ⁡ u + u sin ⁡ u ) / w {\displaystyle x=2\cosh v\,(\cos u+u\sin u)/w} y = 2 cosh ⁡ v ( sin ⁡ u − u cos ⁡ u ) / w {\displaystyle y=2\cosh v\,(\sin u-u\cos u)/w} z = v − ( 2 sinh ⁡ v cosh ⁡ v ) / w {\displaystyle z=v-(2\sinh v\cosh v)/w} where w = ( cosh ⁡ v ) 2 + u 2 {\displaystyle w=(\cosh v)^{2}+u^{2}} It is named after, and was first described by, the German mathematician Theodor Kuen in 1884.

Source: Wikipedia — Kuen surface (CC BY-SA 4.0)

Kuen surface

The Kuen surface is a mathematical surface of constant negative unit Gaussian curvature, making it an example of a pseudospherical surface. It can be described as a parametric surface in terms of the parametric equations x = 2 cosh ⁡ v ( cos ⁡ u + u sin ⁡ u ) / w {\displaystyle x=2\cosh v\,(\cos u+u\sin u)/w} y = 2 cosh ⁡ v ( sin ⁡ u − u cos ⁡ u ) / w {\displaystyle y=2\cosh v\,(\sin u-u\cos u)/w} z = v − ( 2 sinh ⁡ v cosh ⁡ v ) / w {\displaystyle z=v-(2\sinh v\cosh v)/w} where w = ( cosh ⁡ v ) 2 + u 2 {\displaystyle w=(\cosh v)^{2}+u^{2}} It is named after, and was first described by, the German mathematician Theodor Kuen in 1884.

Source: Wikipedia "Kuen surface" · CC BY-SA 4.0

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