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Difference between revisions of "Conchoid"

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''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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024420/c0244201.png" />. If the equation of the given curve is <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024420/c0244202.png" /> in polar coordinates, then the equation of its conchoid has the form: <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c024/c024420/c0244203.png" />. 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]].
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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: $\rho=f(\phi)\pm l$. 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]].
  
  
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====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>
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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) {{ZBL|0257.50002}}</TD></TR>
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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