A hypocycloid with four cusps (like a square with concave sides).
- The astroid was first discussed by Johann Bernoulli in 1691-92.
- The caustic of the tricuspoid, where the rays are parallel and in any direction, is an astroid.
- The cycloidal curves, including the astroid, were discovered by Roemer (1674) in his search for the best form for gear teeth.
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