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.

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.