61199829-131c-4509-bf1d-1f0540966fd8 14 4 5 true true 0 decimal

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I hate FindRoot ! f init GivenFind f init FindRoot :

http://mathworld.wolfram.com/GoatProblem.html

Tieing a goat to a point on the interior of the fence with radius a=1 using a chain of length L=r, consider the length of chain that must be used in order to allow the goat to graze exactly one half the area of the field. The answer is obtained by using the equation for a circle-circle intersection ... which cannot be solved exactly, but which has approximate solution: L= 1.15872847

R 1 :

The solve bloc fails miserably ...  use "solve" instead. f 212 / R 2^* 2 L 2 R * / asin * 2 L 2 R * / asin * sin - (* (* L 2^L 2 R * / acos * + π R 2^* 2 / ≡ :

init L 1.1401 ≡ :

f init GivenFind 1.15872837

R L Goat 212 / R 2^* 2 L 2 R * / asin * 2 L 2 R * / asin * sin - (* (* L 2^L 2 R * / acos * + :

x c 10 x ≤ (x 2 R * ≤ (& cases :

R x Goat x c * 1.1587 π R 2 ^ * 2 / + 15 red 1 5 mat 2 1 sys

... a more mathematical competitive solution R L Goat π R 2^* 2 / - 0 ≡ L 1 1.2 solve 1.15872847

x D R / ≡

21 x 2^2 / - asin * 2 x 2^* x 2 / asin * + 4 x 2^* x 4^- sqrt + π x 2^* - 0 ≡

21 x 2^2 / - asin * 2 x 2^* x 2 / asin * + 4 x 2^* x 4^- sqrt + π x 2^* - 0 ≡ x 02 solve 1.15872847