3 ideas involving e we saw this week

We had a little surprise this week as we saw e show up three different times. Since each kid only saw one of the ideas, I thought reviewing all three this morning would make for a great math project.

The first thing I did was introduce and review the ideas. Those ideas are:

(1) The proof that e is irrational,

(2) This idea from a Nassim Taleb Twitter thread:

(3) The idea in this twitter post from Sonia on Twitter:

Here’s the introduction to the ideas:

First we talked about the proof that e is irrational. My younger son saw this idea as an exercise in the number theory book he’s working through right now. The proof is accessible to kids, though a bit more difficult than some of the other proofs of irrationality the boys seen before:

Next we moved to the idea in Nassim Taleb’s tweet. The idea that (1.01)^{365} and e^{365/100} are so close together is a really important idea from calculus and the general idea has many important applications:

Finally, we looked at the tweet from Sonia and discussed the simplified mathematical problem in the tweet and the surprising relationship to e:

I think these three ideas are fun ones for kids to see. The proof that e is irrational is something that I’m pretty sure I didn’t see until college, but is definitely accessible to kids. The other two ideas are really important ideas from calculus and probability and definitely worth exploring many times!