CATENOID

 

\[ X(u,v)=(\cos u\cosh v,\sin u\cosh v,v),\quad 0\le u\le 2\pi,\ -2\le v\le 2 \]

generated with ps-tricks

Interactive catenoid

Parametric representation

$$ \mathbf{x}(u,v)=\bigl(c\,\cosh(\tfrac{v}{c})\cos (u),\; c\,\cosh(\tfrac{v}{c})\sin (u),\; v\bigr), \quad u\in[0,2\pi),\; v\in\mathbb{R}. $$
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Created by Yannick Häberlin with WebGL (part of his Bachelor thesis)