Difference between revisions of "Enneper surface"
From Encyclopedia of Mathematics
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An algebraic [[Minimal surface|minimal surface]] covering a surface of revolution. Its parametric equation is | An algebraic [[Minimal surface|minimal surface]] covering a surface of revolution. Its parametric equation is | ||
| − | + | $$ | |
| + | x = | ||
| + | \frac{1}{4} | ||
| + | ( u ^ {3} - 3 u - 3 u v ^ {2} ) , | ||
| + | $$ | ||
| − | + | $$ | |
| + | y = | ||
| + | \frac{1}{4} | ||
| + | ( 3 v + 3 u ^ {2} v - v ^ {3} ) , | ||
| + | $$ | ||
| − | + | $$ | |
| + | z = | ||
| + | \frac{3}{4} | ||
| + | ( v ^ {2} - u ^ {2} ) . | ||
| + | $$ | ||
It was discovered by A. Enneper in 1864. | It was discovered by A. Enneper in 1864. | ||
| − | |||
| − | |||
====Comments==== | ====Comments==== | ||
| − | |||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> J.C.C. Nitsche, "Vorlesungen über Minimalflächen" , Springer (1975)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> J.C.C. Nitsche, "Vorlesungen über Minimalflächen" , Springer (1975)</TD></TR></table> | ||
Revision as of 19:37, 5 June 2020
An algebraic minimal surface covering a surface of revolution. Its parametric equation is
$$ x = \frac{1}{4} ( u ^ {3} - 3 u - 3 u v ^ {2} ) , $$
$$ y = \frac{1}{4} ( 3 v + 3 u ^ {2} v - v ^ {3} ) , $$
$$ z = \frac{3}{4} ( v ^ {2} - u ^ {2} ) . $$
It was discovered by A. Enneper in 1864.
Comments
References
| [a1] | J.C.C. Nitsche, "Vorlesungen über Minimalflächen" , Springer (1975) |
How to Cite This Entry:
Enneper surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Enneper_surface&oldid=46824
Enneper surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Enneper_surface&oldid=46824
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article