
Basel Problem - piinbinary
https://en.wikipedia.org/wiki/Basel_problem
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atq2119
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?

~~~
3pt14159
Wouldn't running to the perimeter and then always running whichever way
creates distance from the lion along the perimeter achieve this?

~~~
atq2119
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.

~~~
3pt14159
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.

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10xr
This video is a nice illustration of a geometric proof:
[https://www.youtube.com/watch?v=d-o3eB9sfls](https://www.youtube.com/watch?v=d-o3eB9sfls)

