Difference between revisions of "Kappa"
From Encyclopedia of Mathematics
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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 | ||
| − | + | $$(x^2+y^2)y^2=a^2x^2;$$ | |
and in polar coordinates: | and in polar coordinates: | ||
| − | + | $$\rho=a\operatorname{cotan}\phi.$$ | |
<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" /> | ||
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Figure: k055110a | Figure: k055110a | ||
| − | The origin is a nodal point with coincident tangents | + | 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=12175
Kappa. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Kappa&oldid=12175
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article