Sharing John Urschel’s great video on rational and irrational numbers with my son

Yesterday I learned about a fantastic video that John Urschel made:

Here’s the video on youtube:

This morning I asked my younger son (going into 9th grade) to watch the video so we could talk about it. Here are his initial thoughts and what he thought was interesting:

Now we talked through three of the ideas he thought were interesting. The first was how to find the rational representation of a number like 0.64646464…..

Next he talked about the proof that \sqrt{2} is irrational:

Finally, we talked about a really neat proof in Urschel’s video -> why log base 2 of 3 is irrational:

I love Urschel’s video and think it is an absolutely terrific one to share with kids. It is a great way for kids to see some advanced mathematical proof ideas, but also a great way to review some important ideas in math. We had a really fun morning going through it.