A plane algebraic curve of order 4 whose equation in Cartesian rectangular coordinates has the form
and in polar coordinates
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.
|||A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)|
|[a1]||J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)|
Nicomedes conchoid. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Nicomedes_conchoid&oldid=13493