Namespaces
Variants
Actions

Difference between revisions of "Conchoid"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
(details)
 
(3 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 <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]].
+
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: $\rho=f(\phi)\pm l$.
 
 
 
 
 
 
====Comments====
 
  
 +
Examples: the conchoid of a straight line is called the [[Nicomedes conchoid]]; the conchoid of a circle is called the [[Pascal limaçon]].
  
 
====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 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=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