# Difference between revisions of "Conchoid"

From Encyclopedia of Mathematics

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− | 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 | + | 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|Nicomedes conchoid]]; the conchoid of a circle is called the [[Pascal limaçon|Pascal limaçon]]. |

## Revision as of 17:53, 11 April 2014

*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.

#### Comments

#### References

[a1] | J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972) |

**How to Cite This Entry:**

Conchoid.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Conchoid&oldid=18606

This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article