AMAZING CIRCLE ILLUSION! Optical Illusion Explained With Math

This incredible optical illusion shows how circular motion can result from linear motion! The reason we see the circle has to do with high school geometry. I explain why and give a formal mathematical proof in the video.\r
\r
My blog post for this video\r
\r
\r
Thanks to all Patrons! Special thanks to:\r
Kyle\r
Shrihari Puranik\r
Marlon Forbes\r
\r
If you like my videos, you can support me at Patreon: \r
\r
Sources\r
You can try it for yourself in this GeoGebra interive rolling circles. Set a = 6, b = 3, and remove the click mark for the outside circle. Mark the box for path or trace and click roll.\r
\r
\r
Copernicus Theorem proof\r
\r
\r
Proof from Lines and Curves: A Prical Geometry Handbook. \r
By Victor Gutenmacher, N.B. Vasilyev. Preview\r
\r
\r
Inscribed angle theorem\r
\r
\r
You can create this illusion in Powerpoint with a tutorial from the YouTube channel The Teacher:\r
\r
\r
Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.\r
\r
My Blog: \r
Twitter: \r
Facebook: \r
Google+: \r
Pinterest: \r
Tumblr: \r
Instagram: \r
Patreon: \r
\r
Newsletter (sent about 2 times a year): \r
\r
My Books\r
\r
The Joy of Game Theory shows how you can use math to out-think your competition. (rated 3.8/5 stars on 27 reviews) \r
\r
The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 2 reviews) \r
\r
Math Puzzles Volume 1 features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews. \r
\r
Math Puzzles Volume 2 is a sequel book with more great problems. (rated 5/5 stars on 3 reviews) \r
\r
Math Puzzles Volume 3 is the third in the . (rated 5/5 stars on 3 reviews) \r
\r
40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated 4.7/5 stars on 12 reviews) \r
\r
The Best Mental Math Tricks teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews) \r
\r
Multiply Numbers By Drawing Lines This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews)