MIT Massachusetts Institute of Technology

The Pythagorean Theorem: Geometry’s Most Elegant Theorem

Sandra Haupt
Mathematics teacher
Concord-Carlisle High School
Concord, Massachusetts

This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra and addresses the following national standards of the National Council of Teachers of Mathematics and the Mid-continent Research for Education and Learning: 1) Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; 2) Use visualization, spatial reasoning, and geometric modeling to solve problems; 3) Understand and apply basic and advanced properties of the concepts of geometry; and 4) Use the Pythagorean theorem and its converse and properties of special right triangles to solve mathematical and real-world problems. The video portion is about thirty minutes, and with breaks could be completed in 50 minutes. (You may consider completing over two classes, particularly if you want to allow more time for activities or do some of the enrichment material). These activities could be done individually, in pairs, or groups. I think 2 or 3 students is optimal. The materials required for the activities include scissors, tape, string and markers. An origami proof of the Pythagorean Theorem can be viewed here: http://www.youtube.com/watch?v=ncNt15SNlZE

Sandra Haupt has been a math teacher at Concord-Carlisle High School in Concord, Massachusetts for the past 10 years. Before that she was a geophysicist in the petroleum industry in Colorado and worked in environmental law in Vermont. Sandra has always been interested in the history of mathematical thinking and the development of mathematical concepts, and makes a point in her teaching to emphasize contributions from both Western and non-Western civilizations. 

In this YouTube video, Linda Perry - a former math teacher - uses the power of Origami to demonstrate the Pythagorean Theorem.
https://www.youtube.com/watch?v=ncNt15SNlZE

This Youtube video presents an origami proof of the Pythagorean Theorem.
http://www.youtube.com/watch?v=ncNt15SNlZE

This site, developed by Wolfram Math World, presents extensive resources for the study of Geometry.
http://mathworld.wolfram.com/topics/Geometry.html 

This Khan Academy site presents extensive resources for learning about the Pythagorean Theorem.
https://www.khanacademy.org/math/geometry/triangles/v/introduction-to-the-pythagorean-theorem

These two sites are preparatory sites for the New York State Regents exam. In addition to example problems, these sites explore the Pythagorean Theorem’s relation to the Distance Formula and to the Law of Cosines
http://www.regentsprep.org/Regents/math/ALGEBRA/AT1/Pythag.htm
http://www.regentsprep.org/Regents/math/geometry/GP13/indexGP13.htm

"Words and Pictures:  New Light on Plimpton 322," (2002) by Eleanor Robson. This paper explores the historical mathematical artifact, Plimpton 322.
http://www.maa.org/news/monthly105-120.pdf

Eleanor Robson, “Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322”, published in /Historia Mathematica,/ Vol 28, pages 167 - 206, 2001 
http://www.academia.edu/1261668/Neither_Sherlock_Holmes_nor_Babylon_a_reassessment_of_Plimpton_322

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This Lesson is in the following clusters: Geometry, Pythagorean Theorem