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Maeder's Owl Minimal Surface


A Minimal Surface which resembles a Cross-Cap. It is given by the polar equations

$\displaystyle x$ $\textstyle =$ $\displaystyle 1$ (1)
$\displaystyle y$ $\textstyle =$ $\displaystyle \sqrt{z}$ (2)
$\displaystyle z$ $\textstyle =$ $\displaystyle z,$ (3)

or the parametric equations
$\displaystyle x$ $\textstyle =$ $\displaystyle r\cos\theta-{\textstyle{1\over 2}}r^2\cos(2\theta)$ (4)
$\displaystyle y$ $\textstyle =$ $\displaystyle -r\sin\theta-{\textstyle{1\over 2}}r^2\sin(2\theta),$ (5)
$\displaystyle z$ $\textstyle =$ $\displaystyle {\textstyle{4\over 3}} r^{3/2}\cos({\textstyle{3\over 2}}\theta).$ (6)

See also Cross-Cap, Minimal Surface


Maeder, R. Programming in Mathematica, 3rd ed. Reading, MA: Addison-Wesley, pp. 29-30, 1997.

© 1996-9 Eric W. Weisstein