Learning More about Conway’s Rational Tangles

I just led the Philly Area Math Teachers’ Circle and did a version of John Conway’s Rational Tangles.  I don’t claim to know everything about them by a long shot, but I put this together in case some of the participants want to explore more beyond what we covered in math circle.


My interest in this started when my husband traveled with me to the Northwest Math Conference in Whistler in 2018. He’s a retired high school math teacher, so I told him to go to Fawn’s session because she would make him do math.  They did this activity in her session, so I decided I’d do it when I was leading our local math circle this February.

Fawn Nguyen: Students Embroiled in Conway’s Rational Tangles [Blog post]. Fawn learned about this activity in a math circle.  Here she reports out on trying it with her students.  Be sure to watch the charming video at the end!

Tom Davis: Conway’s Rational Tangles [PDF]. Everyone seems to point to this or at least mention it, so I figured I better too.

Tom Davis: Conway’s Rational Tangles [Video]. Don’t want to read the PDF above? Head on over to YouTube and watch all 21 videos in the playlist of Tom leading this activity in a math circle.

James Tanton: Understanding Rational Tangles [PDF].  Want to dig into the math of this?  So did James, and he wrote about it.

Matthew Salomone: Math 596: Topics in Algebra and Knots [Video]. Ever wondered what an non-Abelian group is? Check out these support materials for Matthew’s course. (Hint: non-Abelian comes up in the third video and you will totally understand it.)  Oh, and it also explains, with visual aids, a bunch of the math about rational tangles.