||last updated: 2005-04-23
Hippopede means literally 'foot of a horse'; the curve is also known as the horse
Because of the work done by J. Booth (1810-1878), the curve is also named the curve
The curve has three forms:
For a < 1, the curve is the oval of Booth.
For a > 1, the curve is the lemniscate of
When the parameter a has the value 2, the curve is the lemniscate
Proclus (75 BC) and Eudoxus were the first to investigate the curve.
After Proclus the curve has been named hippopede of Proclus.
In Cartesian coordinates the curve has the form: (x2 + y2)2
= b x2 + y2 with b = 1 - a.
And we see that the curve is a bicircular
The hippopede can be seen as:
- the cissoid of two
circles of equal size
- a Watt's curve for which the length
of the rod and the distance between the circles are equal
- a special case of the spiric section for which
the plane is tangent to the interior of the torus