How likely is Buffon’s needle to meet a Cantor square? - Microsoft Research
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Microsoft
How likely is Buffon’s needle to meet a Cantor square? - Microsoft Research
Let Cn be the n’th generation in the construction of the middle-half Cantor set. The Cartesian square Kn of Cn consists of 4n squares of side-length 1/(4n). The chance that a long needle thrown at random in the unit square will meet Kn is essentially the average length of the projections of Kn. It is […]
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SOLVED:The Buffon needle problem is one of the oldest and most famous of probability problems. Suppose that a series of horizontal lines are spaced one unit apart and a needle of length one is placed randomly. What is the probability that the needle intersects one of the horizontal lines? (FIGURE CANNOT COPY) In the figure, y is the distance from the center of the needle to the nearest line and θis the positive angle that the needle makes with the horizontal. Show that the needle intersects the
SOLVED:The Buffon needle problem is one of the oldest and most famous of probability problems. Suppose that a series of horizontal lines are spaced one unit apart and a needle of length one is placed randomly. What is the probability that the needle intersects one of the horizontal lines? (FIGURE CANNOT COPY) In the figure, y is the distance from the center of the needle to the nearest line and θis the positive angle that the needle makes with the horizontal. Show that the needle intersects the
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SOLVED:The Buffon needle problem is one of the oldest and most famous of probability problems. Suppose that a series of horizontal lines are spaced one unit apart and a needle of length one is placed randomly. What is the probability that the needle intersects one of the horizontal lines? (FIGURE CANNOT COPY) In the figure, y is the distance from the center of the needle to the nearest line and θis the positive angle that the needle makes with the horizontal. Show that the needle intersects the
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