Skip to main content

Five Reasons to Love the Pythagorean Theorem

Middle school math teacher Fawn Nguyen tells us why a classic right triangle fact is her favorite mathematical result

An illustration of the Pythagorean Theorem from Oliver Byrne's edition of Euclid's Elements.

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American


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


On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.


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