In this episode of My Favorite Theorem, Kevin Knudson and I were happy have Patrick Honner, a math teacher at Brooklyn Technical High School, as our guest. You can listen to the episode here or at I rarely have cause to include a spoiler warning on this podcast, but this theorem is so fun, you might want to stop the episode around the 4:18 mark and play with the ideas a little bit before finishing the episode. Parents and teachers may want to listen to it alone before sharing the ideas with their kids or students.


Mr. Honner decided to share Varignon’s theorem with us. This is a theorem about quadrilaterals. Take a quadrilateral and connect the midpoints of the four sides. When you do that, you will get another quadrilateral. Varignon’s theorem says that no matter what quadrilateral you start with—regular or irregular, convex or concave, even a quadrilateral that is bent somehow into a three-dimensional object—you will always get a particular type of quadrilateral. I don’t want to spoil it here, either, so feel free to play with it for yourself or listen to the podcast to find out more.

As a high school teacher, Mr. Honner loves to use this theorem in the classroom because it leads to rich, open-ended explorations for his students, as well as allowing them to see and ponder some of their quadrilateral-related biases. He has some good ideas about using it in the classroom that might appeal to parents, teachers, and other people who work on math with kids.

In each episode, we ask our guest to pair their theorem with a food, beverage, or other delight in life. Mr. Honner chose crusty bread and a glass of red wine (grape juice for his students and others who don’t drink). You’ll have to listen to the episode to learn why he thinks they pair so well with Varignon’s theorem.

You can find Mr. Honner online at,, and on Twitter @MrHonner. His post about his favorite proof of Varignon's Theorem includes helpful illustrations.

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