Basel Problem

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23 pointspiinbinary6 comments

My favorite consequence of this problem is a rather unintuitive answer to the following problem:

You find yourself in a circular arena with a hungry lion that will hunt you through whatever strategy it likes. You are able to run at exactly the speed of the lion. Assuming that you don't get exhausted and that both you and the lions are point-shaped, is there a strategy that allows you to avoid the lion forever?

Wouldn't running to the perimeter and then always running whichever way creates distance from the lion along the perimeter achieve this?

The lion could follow your path in a circle with a smaller circumference, and use the extra time to move closer to you.

No. The fundamental problem with that strategy is that moving along the curvature of the perimeter forces you closer to the lion, and it turns out that that's just barely enough for the lion to catch up in finite time.

Oh I see. The lion shaves the circle if I stay at the wall. It's less intuitive than I imagined. I feel almost compelled to code it just to see how different strategies pan out.

This video is a nice illustration of a geometric proof: https://www.youtube.com/watch?v=d-o3eB9sfls

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