Buffon's Noodle Simulation

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.

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This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

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

Explanation

Geometric Probability

• Geometric Probabilities
• Are Most Triangles Obtuse?
  • Eight Selections in Six Sectors
• Barycentric Coordinates and Geometric Probability
  • Stick Broken Into Three Pieces (Trilinear Coordinates)
  • Stick Broken Into Three Pieces. Solution in Cartesian Coordinatess
• Bertrand's Paradox
• Birds On a Wire (Problem and Interactive Simulation)
  • Birds on a Wire: Solution by Nathan Bowler
  • Birds on a Wire. Solution by Mark Huber
  • Birds on a Wire: a probabilistic simulation. Solution by Moshe Eliner
  • Birds on a Wire. Solution by Stuart Anderson
• Buffon's Noodle Simulation
• Averaging Raindrops - an exercise in geometric probability
  • Averaging Raindrops, Part 2
• Rectangle on a Chessboard: an Introduction

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Copyright © 1996-2012 Alexander Bogomolny