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How to fold a circle into an ellipse

Believe it or not, I used to be a mathematician. And stupidly, I didn’t apply myself to applied math, stuff that uses computers and makes money. I was interested in 1) formal logic 2) the history of mathematics 3) the foundations of geometry, all of which quickly routed me into philosophy, i.e., obscurity.

But it does mean that I remain stupidly interested in things like ruler-and-compass constructions, axioms for foldable geometries, and the difference between Euclidean and non-Euclidean spaces. Folding is especially interesting because it’s tactile, it doesn’t require tools, and it sort of requires you to mentally balance the idea of the paper as representative of the geometric plane AND paper as the tool you use to inscribe that plane… oh, forget it. Let me just show you this cool GIF:

I’m not sure how this fits into foldable geometries exactly since it imagines an infinite procedure, and geometric constructions are typically constrained to be finite. But still. It’s really cool to look at, play with, and think about.