Dean Hoffman writes

I don't remember either of those names at sci.physics. I think that's
where I saw this puzzle. Take a circular pasture with grass growth even
over the full area. Put a stake at the edge of the pasture with a rope on
it. Tie a hungry critter on the other end. How long should the rope be so
the critter can get to only 1/3 of the pasture? Express the length in
relation to one of the circle's dimensions such as radius, diameter or
circumference.

1) Take the radius, r. That is the original length of the rope.

Now we know from elementary geometry that area is pi*r^2,
so for 1/3 area we need a radius of 1/(square root 3).

2) Take a right angled triangle of side r and hypotenuse 2r.
Again this is elementary geometry, compass and straight edge stuff.
You can use a 3:4:5 triangle for a 90deg if you like.

The other side will be square root of 3r in length.
Cut a length of string off at sqrt(3).

3) Divide the string into three equal parts by folding it (free ends at
opposite ends).

This will have length sqrt(3)/3 = 1/sqrt(3) which is what we want,

so cut the string into three equal lengths. Each gives you the length
you require for your string.

Easy ....

--
Oz
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