DeepCurves in space

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §12.2 Plane Motion: Projectiles and Cycloids, #34 · Multivariable Calculus · Curves in space

For the point … on the astroid, explain why … and

This problem is about cycloids and related curves

For the point $P$ on the astroid, explain why $x = 3 cos θ + cos 3 θ$ and $y = 3 sin θ - sin 3 θ$ . The angle in the figure is $3 θ$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.2 Plane Motion: Projectiles and Cycloids, #34

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