## Conchoid of Nicomedes

A curve studied by the Greek mathematician Nicomedes in about 200 BC , also called the Cochloid. It is the Locus of points a fixed distance away from a line as measured along a line from the Focus point (MacTutor Archive). Nicomedes recognized the three distinct forms seen in this family. This curve was a favorite with 17th century mathematicians and could be used to solve the problems of Cube Duplication and Angle Trisection.

 (1)

In Cartesian Coordinates,
 (2)

The conchoid has as an asymptote and the Area between either branch and the Asymptote is infinite. The Area of the loop is

 (3)

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 135-139, 1972.

Lee, X. Conchoid of Nicomedes.'' http://www.best.com/~xah/SpecialPlaneCurves_dir/ConchoidOfNicomedes_dir/conchoidOfNicomedes.html.

MacTutor History of Mathematics Archive. Conchoid.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Conchoid.html.

Pappas, T. Conchoid of Nicomedes.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 94-95, 1989.

Yates, R. C. Conchoid.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 31-33, 1952.