The Circular Motion Illusion Explained Mathematically

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by Super User, 2 months ago
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The green dots appear to be moving as a circle and rolling perfectly inside the blue circle. But what is the true path of each dot, and what is the geometric proof for why this happens? Watch the video for a mathematical proof of this amazing optical illusion.

My blog post for this video
https://wp.me/p6aMk-5aG

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Sources
You can try it for yourself in this GeoGebra interactive 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.
https://www.geogebra.org/m/RPx3ne5v

Copernicus' Theorem proof
http://www.cut-the-knot.org/pythagoras/Copernicus.shtml

Proof from Lines and Curves: A Practical Geometry Handbook.
By Victor Gutenmacher, N.B. Vasilyev. Preview
https://books.google.com/books?id=LuUlBQAAQBAJ&lpg=PA4&dq=Copernicus'%20Theorem&pg=PA5#v=onepage&q&f=false

Inscribed angle theorem
https://en.wikipedia.org/wiki/Inscribed_angle

You can create this illusion in Powerpoint with a tutorial from the YouTube channel "The Teacher":
https://www.youtube.com/watch?v=EB6YSddogmY

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