# Nicomedes conchoid

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A plane algebraic curve of order 4 whose equation in Cartesian rectangular coordinates has the form

and in polar coordinates

Figure: n066620a

Outer branch (see Fig.). Asymptote . Two points of inflection, and .

Inner branch. Asymptote . The coordinate origin is a double point whose character depends on the values of and . For it is an isolated point and, in addition, the curve has two points of inflection, and ; for it is a node; for it is a cusp. The curve is a conchoid of the straight line .

The curve is named after Nicomedes (3rd century B.C.), who used it to solve the problem of trisecting an angle.

#### References

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

#### References

 [a1] J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)
How to Cite This Entry:
Nicomedes conchoid. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Nicomedes_conchoid&oldid=13493
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article