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2020 Mathematics Subject Classification: Primary: 53A04 [MSN][ZBL]

of a curve

The planar curve obtained by increasing or decreasing the position vector of each point of a given planar curve by a segment of constant length $l$. If the equation of the given curve is $\rho=f(\phi)$ in polar coordinates, then the equation of its conchoid has the form: $\rho=f(\phi)\pm l$.

Examples: the conchoid of a straight line is called the Nicomedes conchoid; the conchoid of a circle is called the Pascal limaçon.


[a1] J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972) Zbl 0257.50002
How to Cite This Entry:
Conchoid. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article