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Center of Mass

Philip Crooke and Steven Tschantz

This tool computes the center of mass (centroid) of a lamina of uniform density occupying the region f(x) < x < g(x), a < x < b in the plane, and it plots both the region and the center of mass.

This mathlet is part of the MathServ Calculus Toolkit (see link at left). The authors have provided the following information about the toolkit.

Philip Crooke is Professor of Mathematics and Education and Steven Tschantz is Associate Professor of Mathematics, both at Vanderbilt University


  1. In-class demonstration
  2. Calculus laboratories
  3. Out-of-class homework and study


  1. Algebra and Trigonometry
  2. Calculus

The only requirement is a WWW browser.  For one of the tools, the browser must be Java enabled.

Operating systems supported: MAC OS 7/8/9, Windows95/98/NT/ME

Browsers: Netscape 4/4.7/6, Internet Explorer 4/4.5/5/5.5

Availability of code:

  • The source code for the tools (.html and .def files) can be downloaded.
  • The cgi script, parsing, and security software are proprietary, although the use of the Calculus Toolkit is totally free.

Open Center of Mass  in a new window.


The Department of Mathematics and the Owen Graduate School of Management developed the MathServ technology to provide web access to the computer algebra system Mathematica, running on a remote server. MathServ allows the user to perform sophisticated, focused calculations with Mathematica without learning the Mathematica language and without purchasing the software. The Calculus Toolkit is a collection of programs that perform basic calculations using Mathematica, such as graphing, differentiating, and integrating. Each tool is composed of an html file and one or more def files. The html file permits the user to enter in standard mathematical notation the information necessary to perform a particular task, and the def file(s) contains the Mathematica program(s) to execute the task and format the output for the user. For example, to graph a function of a single variable, the information entered would be the function and its domain. Most of the tools are very simple, but one is highly interactive -- the Integration Assistant -- which guides the student through the process of finding an antiderivative.

©Crooke & Tschantz, 2001
Published January, 2001

Philip Crooke and Steven Tschantz, "Center of Mass," Convergence (September 2004)