Cissoid
A cissoid is a curve derived from a fixed point O and two other curves α and β. Every line through O cutting α at A and β at B cuts the cissoid at the midpoint of 
.
The simplest expression uses polar coordinates with O at the origin. If r = α(θ) and r = β(θ) express the two curves then 
expresses the cissoid.
Sometimes ths cissoid is described as a sum r = β(θ) + α(θ) or difference r = β(θ) - α(θ); these are basically equivalent except for doubling the size and possibly needing one curve reflected through O.
Every conchoid is a cissoid with the other curve a circle centered on O.
The cissoid of Diocles was the prototype for this general construction.
A cissoid of Zahradnik replaced Diocles' circle with a conic section.
The often-so-called conchoid of de Sluze has α a circle passing through O less O itself and β a line parallel to α's tangent at O. It is, in fact, not a conchoid.
External links
- Mathworld (http://mathworld.wolfram.com/Cissoid.html)
- 2D Curves (http://www.2dcurves.com/derived/cissoid.html)
- [1] (http://www.mathcurve.com/courbes2d/cissoidale/cissoidale) in French but nicely illustrated
Graphics!
Categories: Curves | Math stubs