Cissoid
In geometry, a
cissoid is a curve generated from two given curves
C1,
C2 and a point
O. 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 =
P1
P2. 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".