The Perfect Road for a Square Wheel and How to Design It
Morphocular
View ChannelAbout
The name rhymes with "binocular", and it's a channel intended to teach math with the help of visuals and animation wherever possible. Henri Poincaré once said about mathematicians, "Matter does not engage their attention, they are interested in form alone." And in one sense, math can be defined as the study of pure form ("morphḗ"). This channel is meant to be a morphocular, a lens on math, that clarifies and illuminates its often confusing and daunting concepts to reveal the beautiful thing it really is. I hope this channel lets a little of that beauty shine through to you. Note about business inquiries: The channel is currently in a less active state for the time being and so I have less energy to investigate sponsorship opportunities. Inquiries are still welcome, but I may not respond.
Latest Posts
No results found. Try different keywords.
Video Description
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/RoadsWheels/RoadsWheels.pdf =============================== 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 https://www.patreon.com/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/morpholib
Design Your Dream Track Now
AI-recommended products based on this video

acer Aspire Premium Laptop | 15.6" FHD Display | AMD Ryzen 7 5700U (Beats i7-1250U) | 64GB RAM | 4TB SSD | Long Battery Life | Sleek Design | Ethernet Port | Windows 11 Pro | w/WOWPC Bundle

Funny Cute Mouse Pad with Wrist Rest, Dumpster on Fire Ergonomic Mouse Pads Wrist Support for Desk, Mousepad for Wireless Mouse Gaming Laptop Work Home Desk Accessories Office Supplies Decor

Lenovo IdeaPad 3 Laptop| Intel Core i7-1255U Processor| Touchscreen| 15.6 inch Full HD Display| 40GB RAM, 1TB PCIe SSD|USB-C, HDMI, Card Reader| Office Trial| Backlit Keyboard| Windows 11

Lenovo IdeaPad 15.6" FHD Touchscreen Laptop – Powerful 10-Core Intel i7 (Turbo Up to 4.7GHz), 40GB RAM, 1TB SSD, Backlit Keyboard, Fingerprint Reader, Wi-Fi 6, Windows 11 Pro + WOWPC Recovery USB

acer Nitro V 15 Gaming Laptop, 15.6" 144Hz FHD Display, Intel 10-Core i7-13620H, NVIDIA GeForce RTX 4060, 64 GB DDR5 RAM, 4 TB SSD, Backlit Keyboard, Microsoft Office Lifetime License, Windows 11 Pro
