The Helicone Numberscope: Mathematical Superpowers Hidden in a Simple Toy

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This is a corrected version of a video that I uploaded two days ago. After a critical mistake was discovered in the "Nature's Numbers" part of the video, I decided to scrap the original video, fix the errors and republish the video (many more hours down the drain :( Anyway, had to be done. Just in case you are wondering my list of best approximations of pi did not fit in with my definition. This was first pointed out by @typha I've collected the comments on the original video in this pdf file https://www.qedcat.com/phyl/comments_collection.pdf If you've got access to Mathematica, you can down