ma056 - Exploding the Ellipse Arnold Good Mathematics...

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Arnold Good Mathematics Teacher, March 1999, Volume 92, Number 3, pp. 186–188 Mathematics Teacher is a publication of the National Council of Teachers of Mathematics (NCTM). More than 200 books, videos, software, posters, and research reports are available through NCTM’S publication program. Individual members receive a 20% reduction off the list price. For more information on membership in the NCTM, please call or write: NCTM Headquarters Office 1906 Association Drive Reston, Virginia 20191-9988 Phone: (703) 620-9840 Fax: (703) 476-2970 Internet: E-mail: Article reprinted with permission from Mathematics Teacher, copyright May 1991 by the National Council of Teachers of Mathematics. All rights reserved. Arnold Good, Framingham State College, Framingham, MA 01701, is experimenting with a new approach to teaching second-year calculus that stresses sequences and series over integration techniques. R eaders are advised to proceed with caution. Those with a weak heart may wish to consult a physician first. What we are about to do is explode an ellipse. This risky business is not often undertaken by the professional mathematician, whose polytechnic endeavors are usually limited to encounters with administrators. Ellipses of the standard form of where are not suitable for exploding because they just move out of view as they explode. Hence, before the ellipse explodes, we must secure it in the neighborhood of the origin by translating the left vertex to the origin and anchoring the left focus to a point on the x -axis. Then a portion of the ellipse will always remain in view. At this point, recall that the ellipse is characterized by two focal points that lie on the horizontal axis; their distance from the center of the ellipse is c , where Figure 1 shows the graph of an ellipse in standard form. The equation of the ellipse after translation is s x 2 a d 2 a 2 1 y 2 b 2 5 1. c
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This note was uploaded on 03/05/2010 for the course MAT 1740 taught by Professor Staff during the Winter '08 term at Oakland CC.

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ma056 - Exploding the Ellipse Arnold Good Mathematics...

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