Cissoid

In geometry, a cissoid is a curve generated from two given curves C₁, C₂ and a point O (the pole). Let L be a variable line passing through O and intersecting C₁ at P₁ and C₂ at P₂. Let P be the point on L so that OP = P₁P₂. (There are actually two such points but P is chosen so that P is in the same direction from O as P₂ is from P₁.) Then the locus of such points P is defined to be the cissoid of the curves C₁, C₂ relative to O.

Slightly different but essentially equivalent definitions are used by different authors. For example, P may be defined to be the point so that OP = OP₁ + OP₂. This is equivalent to the other definition if C₁ is replaced by its reflection through O. Or P may be defined as the midpoint of P₁ and P₂; this produces the curve generated by the previous curve scaled by a factor of 1/2.

The word "cissoid" comes from the Greek kissoeidēs "ivy shaped" from kissos "ivy" and -oeidēs "having the likeness of".