The besace is a Lissajous curve.
In 1750 Cramer gave the curve its name ^{1}^{)}.
The curve can be constructed as follows: given a circle C and a point O draw
horizontal lines l which cut the circle in R. Q is the projection of O on l.
Then the Besace is the set of points P for which PQ = OR.
The curve is the result of the projection of the pancake
curve on a plane through the central zaxis of the curve.
For large a, the curve approximates the parabola.
For a = 0 the lemniscate of Gerono results:
The form of the curve is that of ribbon ^{2}^{)},
as the other lemniscate, the more famous lemniscate of
Bernoulli. Because of the resemblance with the digit 8, the curve is also called the (figure)
eight curve.
But I think the figure eight curve that is formed by the hippopede
makes a better eight.
Its Cartesian equation resembles the equation of the kampyle of Eudoxus.
The curve was studied by CamilleChristophe Gerono.
notes
1) In German: Quersackkurve.
2) lemniskos (Gr.) = ribbon
