Five Reasons to Love the Pythagorean Theorem

Five Reasons to Love the Pythagorean Theorem

April 6, 2019 Off By readly

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, 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 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 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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