Astroid

This section features the  Astroid also known as the hypocycloid of four cusps, tetracuspid, cubocycloid, paracycle and still other names.

MATHEMATICA®Code

In one quadrant, the astroid may  be thought of as a falling ladder, a problem often found in introductory Calculus.  In this case, the curve is also  known as a glissette.

Yates writes the cycloidal curves, including the Astroid, were discoverd by Roemer (1674) in his search for the best form for gear teeth.  The equation can be found in Leibniz's correspondence as early as 1715 and was further investigated by Daniel Bernoulli in 1725.  We suggest you also view the cyloid of three cusps.