Strophoid
From Encyclopedia of Mathematics
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A third-order plane algebraic curve whose equation takes the form
 |
in Cartesian coordinates, and
 |
in polar coordinates. The coordinate origin is a node with tangents 
(see Fig.). The asymptote is 
. The area of the loop is
 |
The area between the curve and the asymptote is
 |
A strophoid is related to the so-called cusps (cf. Cusp).
Figure: s090630a
References
| [1] | A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian) |
| [2] | A.S. Smogorzhevskii, E.S. Stolova, "Handbook of the theory of planar curves of the third order" , Moscow (1961) (In Russian) |
Comments
References
| [a1] | F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971) |
| [a2] | J.D. Lawrence, "A catalog of special planar curves" , Dover, reprint (1972) |
How to Cite This Entry:
Strophoid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Strophoid&oldid=15202
Strophoid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Strophoid&oldid=15202
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article