Support for the
Java 2 runtime environment (version 1.4 or later). Click on the icon to download the appropriate
plug-in.Object Library > Applets > Buffon's Needle Experiment
Buffon's needle experiment consists of dropping a needle on hardwood floor, with floorboards of width 1. The experiment is shown graphically in the first graph box. The angle X of the needle relative to the floorboard cracks and the distance Y from the center of the needle to the lower crack are recorded in the first table on each update. Each point (X, Y) is shown as a red dot in the scatterplot. The variable I indicates the event that the needle crosses a crack. The density of I is shown in blue in the distribution graph and is recorded in the distribution table. On each update, the empirical density of I is shown in red in the distribution graph and is also recorded in the distribution table. Finally, pi is shown in blue in the last graph and is recorded in the last table, and on each update, Buffon's estimate of pi is shown in red in the last graph and is recorded in the last table. The parameter is the needle length L, which can be varied with a scrollbar.
This experiment is historically important and illustrates a number of basic concepts in a conceptually simple setting: random experiment, event, random variable, the simple version of the law of large numbers, point estimation, and more generally the interplay between probability and statistics. For a more detailed mathematical analysis, see
Click on the link below to download the Java archive file:
To add the applet to your web page, insert the following in the html file, at the point where you want the applet to appear:
<applet code="edu.uah.math.experiments.BuffonNeedleExperiment.class"
archive="BuffonNeedleExperiment.jar" width="600" height="400"></applet>
The jar file and the html file must be in the same folder.
This width and height dimensions are simply suggestions and can be varied. Generally, components such as graphs and tables expand and contract proportionally, while components such as buttons, scrollbars, dice, and coins are fixed in size.
Support for the
Java 2 runtime environment (version 1.4 or later). Click on the icon to download the appropriate
plug-in.Copyright © 2001-2003 Kyle Siegrist, Dawn Duehring
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public License for more details.
If you are interested in the Java source code or the Java documentation and object model for this applet, please visit BuffonNeedleExperiment in the Object section of the Library.