3 ms·

I initially assumed that the goat was tied to the fence in such a way that the non-goat rope-end could move completely around the circumference of the fence and

• acqq 6y ago
  I was also at first confused, and I find the problem as published in 1894 (i.e. almost 130 years ago) much clearer: "A circle containing one acre is cut by another whose centre is on the circumference of the given circle, and the area common to both is one-half acre. Find that radius of the cutting circle." I think that formulation had to be at least mentioned near the beginning of the text, when not used in the first sentence.
• shmageggy 6y ago
  Your goat eats the "donut" and GP's goat eats the "hole", each eating half of the area. Not a blade of grass was wasted; how satisfying!
  • thaumasiotes 6y ago
    > Your goat eats the "donut" and GP's goat eats the "hole", each eating half of the area. Assuming the two goats are on equally long leashes, this doesn't come close to being true. They each eat circular arcs which run through half a radius. But the outside goat's circles are huge and the inside goat's circles are tiny; the inside goat covers 25% of the area. This is related to https://en.wikipedia.org/wiki/Bertrand_paradox_(probability) https://en.wikipedia.org/wiki/Bertrand_paradox_(probability) and https://mathworld.wolfram.com/DiskPointPicking.html https://mathworld.wolfram.com/DiskPointPicking.html