Here’s a mathematical paper of which I can smugly say I understood *every word*.

Ha ha. No, seriously, I like it. A visual proof that .

But as Math with Bad Drawings pointed out someone else pointed out, the proof doesn’t depend on but can be generalized to any number , and as Math with Bad Drawings pointed out, a similar proof works for any positive number . That is, for all and , .

Proof here if you don’t want to click through to MwBD:

If ,

so

or

or

and similarly, if ,

so

or

or

QED

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