(generalized) cissoid

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last updated: 2003-12-09

Given curves C1 and C2 and a fixed point O. Draw lines l through O that intersect C1 in Q1, and C2 in Q2. Then the cissoid is defined as the collection of points P (on l) for which OP is equal to the distance between the intersections (Q1Q2).

Some special cases of the cissoid:

curve C1	curve C2	pole O	cissoid
line	line parallel to C1	any point	line
	circle	center of the circle	conchoid (of Nicomedes)
circle	concentric circle	center	circle
	line tangent to the circle	on circle, opposite the tangent	cissoid (of Diocles)
	line tangent to the circle	on circle	oblique cissoid
	radial line	on circle	(right) strophoid
	circle of equal size	any point	hippopede

The first cissoid to be discovered was the cissoid of Diocles.