Compte de Buffon in the 18^th century posed and solved the very first problem of geometric probability. A needle of a given length L is thrown on a wooden floor with evenly spaced cracks at the distance D from each other. What is the probability of the needle hitting a crack? This problem became appropriately known as Buffon's Needle.

There is an interesting observation that also leads to a simplified solution of the problem. As a matter of fact, it's not important that Buffon's needle was a needle - a straight line segment. Any piece of wire, or a noodle, of the same length would produce exactly same result. (It appears that Buffon's Noodle is an even more appropriate appellation for the experiment.)

The applet below serves to demonstrate this point. Originally, the needle is the straight line segment whose length equals the distance between two neighboring cracks. Check the Draw box on the right to try another shape. Shapes are drawn as broken lines (drag-click-drag-click-...). When you close the popup window by pressing Save the shape you drew is resized to the same length as before.

(In the lower right corner the applet shows the number of crossings and the total number of throws.)

Explanation

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