How does Euler's identity work? How can it possible be the case that five such fundamental constants of mathematics come together to form such a simple identity? Euler's formula has been called the most beautiful in all of mathematics, but what does it really mean?

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For today's math minute, I am taking a page out of Carlo Cellucci's book (literally, you can see his article here: https://www.researchgate.net/publicat...) in trying to explain the geometry behind e to the i pi plus one equals zero. This video doesn't quite dive into the details of the calculus, complex analysis, or other work (though there are two videos below that go into more detail), but it's the best intuition I've ever seen for what's actually going on when you combine the exponential function, multiplication, addition, Euler's number, π, the imaginary unit, one, and zero. Oh, and addition!

I'll leave the details to the video, but here are a couple links you might be interested in:

+ Desmos Graph: https://bit.ly/etotheipidesmos
+ Video on the e Limit:    • Using L'Hopital's Rule to Find the e ...  
+ Video on a Special Arctangent Limit:    • Using L'Hopital's Rule to find a Spec...  

#EulersIdentity #etotheipi #EulersFormula

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This was originally going to be my submission to @3blue1brown's SoME2 summer of math exposition 2 contest, but time got the best of me!

Euler's Theorem? some2 3blue1brown?