Some years back a friend of mine dug out this problem - I've a first-class honours degree in maths so I smiled smugly to myself, preparing to solve the problem in only a few minutes... and got horribly stumped (serves me right!).
Here's the problem: a farmer has a square field (let's say 100m on each side). He tethers a cow to the mid-point of one side. How long should the rope be so that the cow ends up eating exactly half the grass in the field?
I remember creating awful-looking trigonometric expressions constaining the answer, but never being able to reduce it to a
length of rope = (nasty expression)
kind of formula.
(BTW I'm not interested in approximations or iterative methods.)
I got it into my head that it was impossible to reduce to such a formula - and if so, that would be an interesting proof in itself.
Anyone got a solution or a way of proving that there's no simple expression?
2006-12-04
23:44:49
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7 answers
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asked by
Anonymous
in
Mathematics