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 > Bertrand's Experiment
Bertrand's experiment is to generate a random chord of a circle. In the simulation, one point of the chord is fixed at (1, 0) and the other random point (X, Y) is recorded on each update in the first table. Also recorded are D, the length of the line segment from the center of the circle to the center of the chord, and A, the angle that this line segment makes with the horizontal. Variable I indicates the event that the chord is longer than the length of a side of the inscribed equilateral triangle. The density of I is shown in blue in the distribution graph and and is recorded in the distribution table. On each update, the empirical density of I is shown in red in the distribution graph graph and is recorded in the distribution table. Three differnt models can be selected with the list box:
Bertrand's experiment is historically interesting and illustrates the difficulty of properly modeling a random experiment. This experiment also illustrates the concept of event and random variable, and the simple version of the law of large numbers. For a more complete 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.BertrandExperiment.class"
archive="BertrandExperiment.jar" width="450" height="450"></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
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 BertrandExperiment in the Object section of the Library.