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The Proof of the Century!

Procedures for Teachers is divided into three sections:
Prep -- Preparing for the Lesson.
Steps -- Conducting the Lesson.

Prep

Student Prerequisites:
Prior knowledge of the Pythagorean theorem is not required. Students will be asked to use the exponential function keys on their scientific calculators.

Materials:
• Videotape: THE PROOF. Available from NOVA Videos, c/o WGBH Boston Video, PO Box 2284, South Burlington, VT 05407-2284, (800) 255-9424. Information about the video is available on NOVA Web site
(http://www.pbs.org/wgbh/nova/proof/).
• Videotape: THE THEOREM OF PYTHAGORAS. Available from Project MATHEMATICS!, c/o Joyce, California Institute of Technology Bookstore, I-51, Pasadena, CA 9125, (626) 395-6161. Information about the video is available on Project MATHEMATICS!
(http://www.projmath.caltech.edu).
• Copies of the article, "Fermat's Last Stand," by Simon Singh and Kenneth A. Ribet, SCIENTIFIC AMERICAN, November, 1997.
• Scientific calculators.
• Construction paper for the proof cutout exercise.
• Scissors.
• Tape or glue.
Computer Resources:
You will need at least one computer with Internet access to complete this lesson. While many configurations will work, we recommend:

• Modem: 28.8 Kbps or faster.
• Browser: Netscape Navigator 3.0 or above or Internet Explorer 3.0 or above.
• Macintosh computer: System 7.0 or above and at least 16 MB of RAM.
• IBM-compatible computer: 386 or higher processor with at least 16 MB of RAM, running Windows 3.1. Or, a 486/66 or Pentium with at least 16 MB of RAM, running Windows 95.

For more information, visit What You Need to Get Connected in wNetSchool's Internet Primer.

Bookmarks:
The following sites should be bookmarked:

Information Concerning the Pythagorean Theorem:

• Pythagorean Theorem Site
http://www.cut-the-knot.com/pythagoras/

This site contains 28 geometric proofs of the Pythagorean theorem and links to more.

• United States Naval Academy Mathematics Department

The site includes an animated proof of the Pythagorean theorem.

• Math Forum
http://mathforum.org/library/problems/sets/middle_pythagorean.html

Several good animated proofs of the Pythagorean theorem are displayed.

Information Concerning Pythagorean Triples:

• Plimpton 322
http://www.math.ubc.ca/~cass/courses/m446-03/pl322/pl322.html

This site provides information about an ancient Babylonian, baked clay tablet written in cuneiform script called Plimpton 322. The tablet, dating from 1900-1600 BCE, contains a list of 15 Pythagorean triples.

• Picturing Pythagorean Triples
http://nrich.maths.org/public/viewer.php?obj_id=1332&part=index&refpage=articles.php

The site includes examples and diagrams of Pythagorean triples.

Information Concerning Mathematical Proofs:

• University of Idaho
http://www.cs.uidaho.edu/~casey931/mega-math/gloss/math/proof.html
The site provides explanations of what a mathematical proof entails.

• Ask Dr. Math--What is Math?
http://forum.swarthmore.edu/dr.math/faq/faq.why.math.html

The site provides explanations of practical applications of mathematics.

Information Concerning Fermat's Last Theorem:

• NOVA Web site
http://www.pbs.org/wgbh/nova/proof/

This site provides information on the NOVA program, THE PROOF, about Fermat's Last Theorem and Wiles' proof.

• MacTutor History of Mathematics Archive
http://www-groups.dcs.st-and.ac.uk/~history/
HistTopics/Fermat's_last_theorem.html

An exploration of the history of the Fermat problem that includes a brief chronology of the famous mathematicians who tried to prove this theorem. The site includes links to biographies of the mathematicians mentioned.

• Charles Daney's Fermat Page
http://www.best.com/~cgd/home/flt/flt01.htm

This site contains information about Fermat's Last Theorem that is beyond the scope of high school mathematics but is useful for answering students' questions about why the problem was so difficult to solve.

• Wiles, Ribet, Shimura-Taniyama-Weil and Fermat's Last Theorem
gopher://gopher.math.albany.edu:70/h0/.DEPTS/math/fermat/view

This site provides information about mathematicians' research activities.

• Earth/matriX -- Science in Ancient Artwork: The Pythagorean Problem
http://www.earthmatrix.com/Pitagor3.htm

This site investigates the Pythagorean problem.

• Earth/matriX -- Science in Ancient Artwork Series
http://www.earthmatrix.com/series.htm#SS.

This site investigates extensions of the Pythagorean problem.

Extensions

Fermat's Last Theorem is an ideal departure point for history lessons. Some interesting Internet projects could include researching the lives of Pierre de Fermat, Rene Descartes, Blaise Pascal, Evariste Galois, and Sophie Germain. Students should consider the mathematics that they invented as well as the circumstances of their lives and the societies in which they lived.

These URLs may be useful:

NOVA Web site
http://www.pbs.org/wgbh/nova/proof/

MacTutor History of Mathematics Archive
http://www-groups.dcs.st-and.ac.uk/~history/
HistTopics/Fermat's_last_theorem.html

Charles Daney's Fermat Page
http://www.best.com/~cgd/home/flt/flt01.htm

Wiles, Ribet, Shimura-Taniyama-Weil and Fermat's Last Theorem
gopher://gopher.math.albany.edu:70/h0/.DEPTS/math/fermat/view

The following sites are useful for investigating related mathematics beyond the Pythagorean theorem and Fermat's Last Theorem:

Earth/matriX -- Science in Ancient Artwork: The Pythagorean Problem
http://www.earthmatrix.com/Pitagor3.htm

Earth/matriX -- Science in Ancient Artwork Series
http://www.earthmatrix.com/series.htm#SS.

Submit a Comment: We invite your comments and suggestions based on how you used the lesson in your classroom.

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