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Difference between revisions of "Kappa"

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$$\rho=a\operatorname{cotan}\phi.$$
 
$$\rho=a\operatorname{cotan}\phi.$$
  
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/k055110a.gif" />
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[[File:Kappa curve.svg|center|300px|Kappa curve for a=1]]
 
 
Figure: k055110a
 
  
 
The origin is a nodal point with coincident tangents $x=0$ (see Fig.). The asymptotes are the lines $y=\pm a$. It is related to the so-called nodes (cf. [[Node|Node]] in geometry).
 
The origin is a nodal point with coincident tangents $x=0$ (see Fig.). The asymptotes are the lines $y=\pm a$. It is related to the so-called nodes (cf. [[Node|Node]] in geometry).
  
 
====References====
 
====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.A. Savelov,  "Planar curves" , Moscow  (1960)  (In Russian)</TD></TR></table>
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<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.A. Savelov,  "Planar curves" , Moscow  (1960)  (In Russian)</TD></TR>
 
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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></table>
 
 
 
 
====Comments====
 
 
 
 
 
====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>
 

Latest revision as of 08:22, 17 March 2023

A plane algebraic curve of order four whose equation in Cartesian rectangular coordinates has the form

$$(x^2+y^2)y^2=a^2x^2;$$

and in polar coordinates:

$$\rho=a\operatorname{cotan}\phi.$$

Kappa curve for a=1

The origin is a nodal point with coincident tangents $x=0$ (see Fig.). The asymptotes are the lines $y=\pm a$. It is related to the so-called nodes (cf. Node in geometry).

References

[1] A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)
[a1] J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)
How to Cite This Entry:
Kappa. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Kappa&oldid=32006
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article