So the story by Leo Tolstoy goes, that a man has a limited amount to time to run a closed loop in an open field and when the time is up, he will get all the land that he has enclosed. If he cannot run an enclosed loop, then he will get nothing.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that the man has a fixed speed that he runs at, and which he has already calculated. What shape could he run in so that he could get the most land possible? I would imagine a circle, but there are infinite possible shapes with all sorts of twists and turns so I can't prove my answer, but was wondering if someone here knew the proof or even whether a solution actually exists?

What branch of mathematics would this fall under? Calculus of variations?

Circle sounds quite elegant though.

BiP

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# How much land does a man need?

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