Get smart curated videos delivered to your inbox.   SUBSCRIBE
The Kid Should See This

Hypocycloid circular motion optical illusion

A circle made of points, shown here with small white balls, appears to roll around the inside edge of a larger circle, but is that what’s really happening? File under: Cycloids, hypocycloids, and optical illusions. This mechanical gear design, demonstrated by the Visual Education Project and originally developed by Italian polymath Girolamo Cardano (1501-1576), demonstrates how circular motion can result from linear motion.

Copernicus’ Theorem states a surprising result that a point on the circumference of the small circle traces a straight line segment – a diameter of the big circle, to be precise…

Cardano’s work with hypocycloids led him to the Cardan joint or gear mechanism, in which a pair of gears with the smaller being one-half the size of the larger gear is used converting rotational motion to linear motion.

Read more about rolling hypocycloids, not to be confused with the hypotrochoids made with a Spirograph, in this blog post by John Baez.

Read about Copernicus’ Theorem at Wolfram.com and Cut the Knot. Plus, a color path demo with the mathematical proof from Mind Your Decisions:

Here’s another video demonstration: Brusspup’s Crazy Circle Illusion.

Plus, more math videos, including Types of Triangles, Mathematica – A World of Numbers… and Beyond, Professor Kokichi Sugihara creates his mind-blowing illusions with math, How High Can You Count on Your Fingers? and How Many Ways Are There to Prove the Pythagorean Theorem?

Bonus: Spirograph pancakes.

This Webby award-winning video collection exists to help teachers, librarians, and families spark kid wonder and curiosity. TKSST features smarter, more meaningful content than what's usually served up by YouTube's algorithms, and amplifies the creators who make that content.

Curated, kid-friendly, independently-published. Support this mission by becoming a sustaining member today.