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Text "the parametric formula for the astroid curve.
Astroid is defined as the trace of a point on a circle of radius r rolling inside a fixed circle of radius 4 r or 4/3 r. The latter is known as double generation.
The cycloidal curves, including the astroid, were discovered by Roemer (1674) in his search for the best form for gear teeth. Double generation was first noticed by Daniel Bernoulli in 1725.
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