Yesterday we played around with continued fractions and showed that the square root of 2 is irrational:

https://mikesmathpage.wordpress.com/2021/02/13/my-favorite-proof-that-the-square-root-of-2-is-irrational-continued-fractions/

Today we explored continued fractions a bit more using Mathematica. I started by showing my son the relatively simple commands at taking a closer look at the continued fraction for the square root of 2:

Now we explored a few other continued fractions for other square roots and looked for a few patterns – he did notice that there always seemed to be a repeating pattern:

Next we looked at pi and found a few, fun surprises:

Finally, we looked at e. We only had about 2 min of recording time left, so this last part was, unfortunately, a little rushed:

The last few days exploring continued fractions has been really fun – hoping to do a few more projects over February break studying them.