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The wheel part reminds me of something I learned from 3blue1brown:
"Pi seems to magically appear everywhere, until you realize that wherever it appears there is usually a circle hiding"
Usually. Sometimes it really does seem magical. Sometimes the circle is very well hidden. Maybe we just haven't found it yet.
Honestly I've learned more math from that guy than any math teacher I ever had - one of the few YouTube channels I would absolutely recommend to anyone scientifically inclined at all. He's an incredible explainer.
Blow your mind with the video where he calculates pi through the repeated elastic collision of a pair of blocks... One digit at a time. If that sounds bizarre - yeah, watch the video.
Pi in the normalizing factor of the normal distribution was a surprise to me
But it is in fact due to circles hiding very well.
Yuuuuuh I was often confused about Eigenvectors and then watched their video on it and the visualisation of scaling just made everything so simple, I felt stupid for not getting it before.