info prev up next book cdrom email home


Given two curves $C_1$ and $C_2$ and a fixed point $O$, let a line from $O$ cut $C_1$ at $Q$ and $C_2$ at $R$. Then the Locus of a point $P$ such that $OP = QR$ is the cissoid. The word cissoid means ``ivy shaped.''

Curve 1 Curve 2 Pole Cissoid
Line Parallel Line any point line
Line Circle center Conchoid of Nicomedes
Circle tangent line on Circumference oblique cissoid
Circle tangent line on Circumference opp. tangent Cissoid of Diocles
Circle radial line on Circumference strophoid
Circle concentric Circle center Circle
Circle same Circle $(a\sqrt{2}, 0)$ Lemniscate

See also Cissoid of Diocles


Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 53-56 and 205, 1972.

Lee, X. ``Cissoid.''

Lockwood, E. H. ``Cissoids.'' Ch. 15 in A Book of Curves. Cambridge, England: Cambridge University Press, pp. 130-133, 1967.

Yates, R. C. ``Cissoid.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 26-30, 1952.

© 1996-9 Eric W. Weisstein