MediumCurves in space

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §12.2 Plane Motion: Projectiles and Cycloids, #32 · Multivariable Calculus · Curves in space

For a hypocycloid the fixed circle has radius … and the circle…

This problem is about cycloids and related curves

For a hypocycloid the fixed circle has radius $c + 1$ and the circle rolling inside has radius 1. There are $c + 1$ cusps if $c$ is an integer. How many cusps (use computer graphics if possible) for $c = 1/2$ ? $c = 3/2$ ? $c = 2$ ? What curve for $c = 1$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.2 Plane Motion: Projectiles and Cycloids, #32

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