Recently I became aware that the Museum of Math in NYC has videos of more than 50 lectures given at the Museum in the last year (or maybe few years). The lectures discuss the use of math in an astonishing variety of fields ranging from pure theory to every day life (a recent lecture was about math and cooking, for example, though I don’t know if that one is online yet). The collection of lectures is here (click on the “Math Encounters” link at the top of this video to see the list):

One of the lectures that caught my eye was Terry Tao’s “The Cosmic Distance Ladder.” That talk is here:

It caught my eye for a couple of different reasons. First, Tao is one of the top mathematicians in the world and it is a rare treat to see him speak. An even rarer treat to see him deliver a lecture designed (quite successfully) to be accessible to the public. Having watched this talk several times now, I think many parts of it provide fun and exciting examples for kids of how math has been used to advance science.

I hope to use many pieces of his lecture to show my own kids some important math and science. I began with two fun, and frankly amazing, examples today:

(1) The approximation of the radius of the Earth by Eratosthenes (beginning around 17:20 in the video of the lecture), and

(2) The approximation of the radius of the orbit of the Moon by Aristarchus (beginning around 25:45)

Both of these are obviously remarkable scientific achievements, and Tao’s lecture does a wonderful job of explaining the ideas behind the discoveries. The lecture doesn’t dive too deep into the calculation of these results, though. That was not the point of the lecture – not at all – so my point isn’t even remotely a criticism. Rather I took it as an exciting opportunity to use the videos to teach. Exploring the calculations in the lecture a little more carefully seems to me to be a great way to use this lecture to help kids learn a bit of math, a bit of physics, and a bit of history. Only some basic geometry is needed to understand the calculations. Diving in a little deeper into the math this morning with the boys was really fun.

First off is the approximation of the radius of the Earth:

Second is the approximation of the radius of the orbit of the Moon:

The calculations we do are slight simplifications (as is noted in the original lecture), but I think the important mathematical ideas are here. Discussing the limitations of these calculations and ways to improve them could be a fun student project.

I’m really happy to have stumbled on this collection of lectures at the Museum of Math, and am super excited to spend some time over the next few months trying to figure out fun ways to used them to help kids see interesting examples of how math is used (and has been used) in the world.