The latest Relatively Prime podcast is fantastic:

The short description from the podcast’s website is:

“Sure DNA is important, some might even claim it is absolutely integral to life itself, but does it contain any interesting math? Samuel is joined by UC-Davis Professor of Mathematics, Microbiology, and Molecular Genetics Mariel Vazquez for a discussion proves conclusively that mathematically DNA is fascinating. They talk about the topology of DNA, how knot theory can help us understand the problems which occur during DNA replication, and how some antibiotics are really pills of weaponized mathematics.”

Since it is only 20 min long, I thought it would be fun to share with the boys. We listened to it in the car when we went out to breakfast this morning. Upon returning home I asked the kids what they thought and what were somethings they learned. Here’s what they had to say:

Next we looked at an interesting process described in the podcast. That process was an example by Mariel Vazquez of how you can go from a link with 6 crossings to two unlinked circles.

The process in the podcast seems simple – maybe even obvious – but I think that the process is actually much more subtle than it seems listening to it.

Here we followed the steps to go from the trefoil knot to the two unlinked circles. I think the ideas we followed here are a great way for kids to explore the process described in the podcast:

The next thing we looked at was the idea that when you cut a loop with an even number of twists in half, the halves would be linked. We took a long strip of paper and gave it 6 twists, taped the ends together, and then cut it down the middle.

I fast forwarded through the taping and cutting part, but forgot to remove the sound. Sorry for the “Alvin and the Chipmunks” middle part of this video.

I think both the podcast and the follow up projects are a great way for kids to explore some math ideas that wouldn’t normally be part of a school curriculum.

We’ve done a few other projects with knots and with paper cutting. Here’s a link to those collections:

A collection of some of our paper cutting (and folding) projects

It was really neat to hear about how knot theory applies to biology.