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 $l$. If the equation of the given curve is $\rho=f(\phi)$ in polar coordinates, then the equation of its conchoid has the form: $\rho=f(\phi)\pm l$. | + | 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: $\rho=f(\phi)\pm l$. |
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| + | Examples: the conchoid of a straight line is called the [[Nicomedes conchoid]]; the conchoid of a circle is called the [[Pascal limaçon]]. | ||
====References==== | ====References==== | ||
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| − | <TR><TD valign="top">[a1]</TD> <TD valign="top"> J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)</TD></TR> | + | <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> |
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Latest revision as of 05:42, 9 April 2023
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.
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://encyclopediaofmath.org/index.php?title=Conchoid&oldid=34013
Conchoid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conchoid&oldid=34013
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article