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This section features the 


also known as the

hypocycloid of four cusps,

tetracuspid, cubocycloid,

paracycle and still other names.


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.

Historical Sketch:

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.
Useful Links and Books
Gray, Alfred.  Modern Differential Geometry of Curves and Surfaces with MATHEMATICA® ,2nd ed., CRC Press, 1998.
Yates, Robert.  CURVES AND THEIR PROPERTIES, The National Council of Teachers of Mathematics, 1952.
MATHEMATICA® Code and animation
contributed by
Gus Gordillo, 2002.