Namespaces
Variants
Actions

Difference between revisions of "Kappa"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
(TeX)
Line 1: Line 1:
 +
{{TEX|done}}
 
A plane algebraic curve of order four whose equation in Cartesian rectangular coordinates has the form
 
A plane algebraic curve of order four whose equation in Cartesian rectangular coordinates has the form
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055110/k0551101.png" /></td> </tr></table>
+
$$(x^2+y^2)y^2=a^2x^2;$$
  
 
and in polar coordinates:
 
and in polar coordinates:
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055110/k0551102.png" /></td> </tr></table>
+
$$\rho=a\operatorname{cotan}\phi.$$
  
 
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/k055110a.gif" />
 
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/k055110a.gif" />
Line 11: Line 12:
 
Figure: k055110a
 
Figure: k055110a
  
The origin is a nodal point with coincident tangents <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055110/k0551103.png" /> (see Fig.). The asymptotes are the lines <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055110/k0551104.png" />. 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====

Revision as of 21:17, 30 April 2014

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:

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

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 in geometry).

References

[1] A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)


Comments

References

[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