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The Perfect Road for a Square Wheel and How to Design It

How do you design a road that a square wheel will roll smoothly over? And what about other wheel shapes? How do you even approach such a problem? =Chapters= 0:00 - Intro 1:36 - The Dynamics of Rolling 4:05 - Vertical Alignment Property 7:16 - Stationary Rim Property 8:29 - Describing the Road and Wheel 13:04 - The Road-Wheel Equations 17:02 - The Perfect Road for a Square Wheel 22:40 - Building the Road Visually 25:54 - Wrap Up =============================== Many of the ideas in this video came from, or were inspired by, "Roads and Wheels," an article by Leon Hall and Stan Wagon that appeared in Mathematics Magazine, Vol. 65, No. 5 (Dec 1992). If you want a deeper dive (or if you want spoilers for the next video), I encourage you to read it yourself. As far as math papers go, it's fairly easy to read: https://web.mst.edu/~lmhall/Personal/... =============================== CREDITS ► The song at the beginning of this video is "Rubix Cube" and comes from Audionautix.com ► Thumbtack icon comes from Mister Pixel of the Noun Project. =============================== Want to support future videos? Become a patron at   / morphocular   Thank you for your support! =============================== The animations in this video were mostly made with a homemade Python library called "Morpho". I consider it a pretty amateurish tool, but if you want to play with it, you can find it here: https://github.com/morpho-matters/mor...