Does Pi Equal 2?? (Spoiler: no)

In this short, we show a thought experiment that arises by doubling the number of semicircles drawn in a semicircle but halving their radii. The process produces an infinite collection of smaller and smaller chains of more and more semicircles that always have combined circumference length equal to pi. If we think about the limiting process, it seems like maybe this technique shows that pi = 2. But Pi can definitely be shown to be greater than 3 - so where does this argument fail?

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Here is a related false proof that shows root 2 is equal to 2:
https://youtube.com/shorts/owFwvyozcn8

This false argument was suggested to me by Jeff Stuart as a nice alternative to the more classic Pi = 4 argument.

#math #manim #visualproof #proofwithoutwords #circle #circumference #radius #pi #piday #shorts #infinite #falseproof

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Тэги:

#Semicircle #Pi #Pi_day #Pi_equals_2 #Visual_proof #False_proof #Logical_fallacy

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