Phillip Brown is a student co-enrolled at Georgia Southern University and the Georgia Institute of Technology. His mathematical background includes calculus (I and II) and linear algebra. Phillip enjoys playing video games and working out.
Jim Braselton has been teaching math in the Department of Mathematical Sciences at Georgia Southern since 1990. He is interested in incorporating various technologies, especially computer algebra systems like Mathematica and Maple, into the college mathematics curriculum and areas of applied mathematics. Besides teaching calculus, Jim enjoys canning vegetables and touring the AKC dog show circuit with his German Shepherds, Rose and Ted.
For some students, using the methods of washers or cylindrical shells to find the volume of a solid obtained by revolving a given region about a given line is difficult to understand because of the abstraction involved. In this article, we use on-line resources and computational tools to approximate the measure of the volume of the space occupied by each planet as it orbits the Sun.
Teachers and students of calculus
Technologies Used in This Article
This article is given in two forms.
The HTML version uses GIF images for mathematical expressions.
The XML version uses MathML (the Mathematics Markup Language) for mathematical expressions.
The XML/MathML version is supported by the Mozilla Firefox browser (version 1.5 or later) with the MathML fonts installed, and on the Microsoft Windows platform by the Internet Explorer browser (version 6.0 or later) with the MathPlayer plug-in (version 2.0b or later). We encourage you to upgrade your browser so that it supports MathML (click on the links above). The MathML version is superior in several respects:
The mathematical expressions look better.
Expressions can be resized, and in general behave like the surrounding text.
In some cases expressions can be exported into other applications.
This article uses also has several animations in MP4 format; you will need a helper application such as QuickTime to view the animations. The animations enhance the article but are not essential.
Published August, 2006. Article ID: 1275
Copyright © 2006 by Phillip Brown and James Braselton