Cassinian curve


last updated: 20030725 
It is the curve for which the product of multiple polar radii is constant.
The curve is an algebraic curve of degree 2n.
In the case of a regular polygon the curve can be written in polar
coordinates as
1)
For a < 1, the curve consists of n pieces.
For a > 1, the curve is just one closed curve.
For a = 1, the curve is a sinusoidal spiral.
For n = 2 we see the Cassinian oval.
Think about a magnetic field created by n parallel threads with the same
current.
The magnetic field lines in a plane orthogonal to the threads are Cassinian
curves for which the foci are the intersections of the threads with the plane.
The Cassinian curve has been studied by Serret (in 1843), and the curve is named
after Cassini.
notes
1) In other words:
