(generalized) cissoid


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.