# Difference between revisions of "Conchoid"

From Encyclopedia of Mathematics

(Importing text file) |
(MSC 53A04) |
||

(2 intermediate revisions by 2 users not shown) | |||

Line 1: | Line 1: | ||

+ | {{TEX|done}} | ||

+ | {{MSC|53A04}} | ||

+ | |||

''of a curve'' | ''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 | + | 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]]. |

Line 9: | Line 12: | ||

====References==== | ====References==== | ||

− | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)</TD></TR></table> | + | <table> |

+ | <TR><TD valign="top">[a1]</TD> <TD valign="top"> J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972) {{ZBL|0257.50002}}</TD></TR> | ||

+ | </table> |

## Latest revision as of 00:10, 13 December 2015

2010 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.

#### Comments

#### References

[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: 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