TIL that there is no formula for the exact perimeter of an ellipse, but that you could make an arbitrarily close approximation of a formula for the perimeter of a *given* ellipse, and that such a formula would depend on the sum of an infinite series.

TIL that this is technically how we have a formula for the perimeter of a circle, but don't notice the messiness because the circle's "axes" are of equal length and thus a single sum of an infinite series works. We call it "pi" to keep it unmessy.

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Oh, heavens. This has already been favorited and boosted more times than any other toot I've made. It's sure to hit some real mathematician who's bound to tell me how I'm wrong wrong wrong. To that future person, I am apologizing in advance. I fake all my math.

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@roadriverrail circle: a very specific and commonly occuring ellipse

@darius It's been a long time since I took analytic geometry, but I do remember a number of formulae for circles basically are special cases of those for ellipses, which is why I must have spent the last 25 years just casually assuming there was a formula for the perimeter of ellipses.

@roadriverrail Did.... YouTube suggest this topic to you? It recommended me a ~20 minute video about exactly this last night.

@touk It sure did, and it's one of the people from Numberphile that I liked, so I had a watch while I hacked at things.

@roadriverrail Not sure if that's better or worse, that it was just The Algorithm and not a Fun Coincidence. Definitely a good video though!

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