Five Reasons to Love the Pythagorean Theorem

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On this episode of My Favorite Theorem, we were happy to get to talk with Fawn Nguyen, a middle school math teacher in California. You can listen to the episode here or at kpknudson.com, where there is also a transcript.

Fawn Nguyen. Credit: Fawn Nguyen

Ms. Nguyen chose the Pythagorean theorem as her favorite theorem. It’s one of the most famous theorems, and it states that in a right triangle with legs of lengths a and b and a hypotenuse of length c, a2+b2=c2. She talked us through five reasons she loves this theorem. You’ll have to listen to the episode to hear them all, but I wanted to draw your attention to a few of the things we mentioned in the episode.

Oliver Byrne’s edition of Euclid, which uses brightly colored diagrams to replace letters for unknowns, is available for your perusal here.

The Pythagorean Proposition by Elisha Scott Loomis has 370 proofs of the Pythagorean theorem. You can read the full text here. I wrote about James Garfield’s proof of the Pythagorean theorem here. Steven Strogatz wrote about Einstein’s elegant proof here. For a compilation of more proofs than you can shake a stick out, check out Cut the Knot. The proof she refers to from November 2017 is here.

We also touched a little bit on the history of the theorem. The relationship between the sides of right triangles was known to many ancient cultures, including Navajo (as Henry Fowler told us on a previous episode of the podcast), Babylonian (I wrote about Plimpton 322, a table of Pythagorean triples from around 1800 BCE), Chinese, and Indian. Eli Maor’s book The Pythagorean Theorem: A 4,000 Year History delves into some of these cultures more fully.

Ms. Nguyen mentions tearing up at a student’s beautiful construction of √7. You can read her post and marvel at how clever her student was here.

The Pythagorean Theorem is reminiscent of Fermat’s Last Theorem, which states that an+bn=cn is not solvable in integers for integer exponents n greater than 2. You can learn more about the history of that theorem here and here.

Ms. Nguyen’s last reason for loving the Pythagorean theorem is that she likes sharing the story of what a weird guy Pythagoras was. Vi Hart has an entertaining video on the topic. For a more staid take on the Pythagoreans, you can start here.

In each episode of the podcast, we ask our guest to pair their theorem with something. Ms. Nguyen picked one of her great loves: football. Specifically, check out this magnificent hypotenuse run by Ben Watson, which thwarted Champ Bailey’s attempted 99-yard touchdown after interception.

You can find Ms. Nguyen at her website, where she shares beautiful writing about teaching, and on Twitter. You can find more information about the mathematicians and theorems featured in this podcast, along with other delightful mathematical treats, at kpknudson.com and here at Roots of Unity. A transcript is available here. You can subscribe to and review the podcast on iTunes and other podcast delivery systems. We love to hear from our listeners, so please drop us a line at myfavoritetheorem@gmail.com. Kevin Knudson’s handle on Twitter is @niveknosdunk, and mine is @evelynjlamb. The show itself also has a Twitter feed: @myfavethm and a Facebook page. Join us next time to learn another fascinating piece of mathematics.

Previously on My Favorite Theorem:

Episode 0: Your hosts’ favorite theorems

Episode 1: Amie Wilkinson’s favorite theorem

Episode 2: Dave Richeson’s favorite theorem

Episode 3: Emille Davie Lawrence’s favorite theorem

Episode 4: Jordan Ellenberg’s favorite theorem

Episode 5: Dusa McDuff’s favorite theorem

Episode 6: Eriko Hironaka’s favorite theorem

Episode 7: Henry Fowler’s favorite theorem

Episode 8: Justin Curry’s favorite theorem

Episode 9: Ami Radunskaya’s favorite theorem

Episode 10: Mohamed Omar’s favorite theorem

Episode 11: Jeanne Clelland’s favorite theorem

Episode 12: Candice Price’s favorite theorem

Episode 13: Patrick Honner’s favorite theorem

Episode 14: Laura Taalman’s favorite theorem

Episode 15: Federico Ardila’s favorite theorem

Episode 16: Jayadev Athreya’s favorite theorem

Episode 17: Nalini Joshi’s favorite theorem

Episode 18: John Urschel’s favorite theorem

Episode 19: Emily Riehl’s favorite theorem

Episode 20: Francis Su’s favorite theorem

Episode 21: Jana Rordiguez Hertz’s favorite theorem

Episode 22: Ken Ribet’s favorite theorem

Episode 23: Ingrid Daubechies’s favorite theorem

Episode 24: Vidit Nanda’s favorite theorem

Episode 25: Holly Krieger’s favorite theorem

Episode 26: Erika Camacho’s favorite theorem

Episode 27: James Tanton’s favorite theorem

Episode 28: Chawne Kimber’s favorite theorem

Episode 29: Mike Lawler’s favorite theorem

Episode 30: Katie Steckles’ favorite theorem

Episode 31: Yen Duong’s favorite theorem

Episode 32: Anil Venkatesh’s favorite theorem

Episode 33: Michèle Audin’s favorite theorem

Episode 34: Skip Garibaldi’s favorite theorem

Episode 35: Nira Chamberlain’s favorite theorem

Episode 36: Nikita Nikolaev and Beatriz Navarro Lameda’s favorite theorem

Episode 37: Cynthia Flores’ favorite theorem

Episode 38: Robert Ghrist’s favorite theorem



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