EggMath: The Shape of an Egg
Cassini Ovals
Giovanni Cassini, an astronomer who discovered
the moons of Saturn, was interested in oval curves
as descriptions of orbits. Like the Cartesian Ovals, the
ovals of Cassini are based on a modification of
the pinsandstring
construction for ellipses and produce more
eggshaped curves. The Cassini ovals are defined
by the condition that for all points on the curve,
the product of the distances to two fixed points
(foci) is a constant:
An Oval of Cassini is the figure
consisting of all those points for which
the product of their distances to two
fixed points (called the foci) is a
constant.

Unfortunately, we don't know of any way to
modify a real life pinand string device to draw
these ovals of Cassini. But what can't be done in
the real world can easily be done in the virtual
world! Our computer simulation of the
pinandstring device has no trouble with
Cassini's definition.
In this drawing, you can:
 Click and drag
the pins (green and yellow dots), or
 Click and drag
around the oval, or
 Look at other
members of the family of Cassini's ovals by
adjusting the slider at the bottom.
 The
product of the distance from the left pin
times the distance to the right pin is given by
the slider. This can yield one convex curve, or a
curve with a pinch in the middle, or two curves,
depending on the distanceproduct and the
separation between the pins.
When you drag in the area around the oval, the
lengths of the two segments are shown at upper
left, and their product appears below them,
colored in red if you're on (or outside) the
oval.
FOR FURTHER
READING...
 Page 7 of 15 
