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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.6 Properties of the Integral and Average Value, #29 · Calculus · Integrals

(A classic way to compute …) A … needle is tossed onto…

(A classic way to compute $π$ ) A $2^{''}$ needle is tossed onto a floor with boards $2^{''}$ wide. Find the probability of falling across a crack. (This happens when $cos θ > y$ = distance from midpoint of needle to nearest crack. In the rectangle $0 \leq θ \leq π /2$ , $0 \leq y \leq 1$ , shade the part where $cos θ > y$ and find the fraction of area that is shaded.)

(A classic way to compute $π$ ) A $2^{''}$ needle is tossed onto a floor with boards $2^{''}$ wide. Find the probability of falling across a crack. (This happens when $cos θ > y$ = distance from midpoint of needle to nearest crack. In the rectangle $0 \leq θ \leq π /2$ , $0 \leq y \leq 1$ , shade the part where $cos θ > y$ and find the fraction of area that is shaded.)

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.6 Properties of the Integral and Average Value, #29

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