A Rolling Circle Drawing Ellipses

The path traced by a point attached at distance d from the center of a circle of radius r rolling around the inside of a fixed circle of radius R is an ellipse when R = 2r and d ≠ r.

The Tusi couple is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle.

Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along the diameter of the larger circle. However, the points on the inner circle that are not on the circumference trace ellipses.

These ellipses, and the straight lines traced by the Tusi couple, are special cases of hypotrochoids.

Interactive animation of Tusi couple in desmos: https://www.desmos.com/calculator/bad8rtx0ab

This video is produced using the animation engine Manim [Manim Community v0.17.2] https://www.manim.community

Code Snippets https://link.curiouswalk.com/manim

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