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e to the pi i for dummies

For this Christmas video the Mathologer sets out to explain Euler’s identity e to the pi i = -1, the most beautiful identity in math to our clueless friend Homer Simpson. Very challenging to get this right since Homer knows close to no math!

Here are a couple of other nice videos on Euler’s identity that you may want to check out:

https://youtu.be/Yi3bT-82O5s (one of our Math in the Simpsons videos)
https://youtu.be/F_0yfvm0UoU (by 3Blue1Brown)

And for those of you who enjoy some mathematical challenges here is your homework assignment on Euler’s identity:
1. How much money does Homer have after Pi years if interest is compounded continuously?
2. How much money does Homer have after an imaginary Pi number of years?
3. As we’ve seen when you let m go to infinity the function (1+x/m)^m turns into the exponential function. In fact, it turns into the infinite series expansion of the exponential function that we used in our previous video. Can you explain why?
4. Can you explain the e to pi i paradox that we’ve captured in this video on Mathologer 2: https://youtu.be/Sx5_QGdFmq4.

If you own Mathematica you can play with this Mathematica notebook that I put together for this video

Thank you very much to Danil Dmitriev the official Mathologer translator for Russian for his subtitles.

Merry Christmas!

Burkard Polster