I asked a kid what his favorite number was, you won’t believe what happened next :)

A friend from graduate school and her son stopped by yesterday on their way down to NYC.  Her son and my kids have a lot of common interests, including math.  Chit chatting over dinner I asked him what his favorite number was and got quite a surprise:

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Now that’s a favorite number!

Although his particular favorite number is a little difficult to talk about without getting into things like cos(1) and sin(1), I though that it would be fun to show the kids a little bit about complex numbers.   My end goal was to show the kids the value of rather than , but first we had to have a little discussion about powers:

With some of the simple properties of exponents out of the way, the one last thing we needed to touch on before taking about was square roots. Despite intending to be informal here, I was unfortunately a little too informal and I think that caused a little bit of confusion. It took a few extra examples to get us back on track.

Next up was the fun identity I didn’t have any interest in deriving this equation, rather I just wanted to use it as a starting point. With just a few manipulations of this equation we can come to a value for It was super fun to see all three kids react to the surprising value of At the end I mention the approximate value of as well.

So, a nice little math talk this morning sparked by this surprise favorite number!