Английская Википедия:Dini's surface

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Файл:Mathematica dinis surface.png
Dini's surface plotted with adjustable parameters by Wolfram Mathematica program
Файл:Dini Surface.png
Dini's Surface with constants a = 1, b = 0.5 and 0 ≤ u ≤ 4Шаблон:Pi and 0<v<1.

In geometry, Dini's surface is a surface with constant negative curvature that can be created by twisting a pseudosphere.[1] It is named after Ulisse Dini[2] and described by the following parametric equations:[3]

<math>\begin{align}

x&=a \cos u \sin v \\ y&=a \sin u \sin v \\ z&=a \left(\cos v +\ln \tan \frac{v}{2} \right) + bu \end{align}</math>

Файл:Dini's Surface.svg
Dini's surface with 0 ≤ u ≤ 4Шаблон:Pi and 0.01 ≤ v ≤ 1 and constants a = 1.0 and b = 0.2.

Another description is a generalized helicoid constructed from the tractrix.[4]

See also

References

Шаблон:Reflist