Understanding e to the pi i
Improved version here: https://youtu.be/mvmuCPvRoWQ The enigmatic equation e^{pi i} = -1 is usually explained using Taylor's formula during a calculus class.
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e to the pi i equals negative 1 is one of the most famous equations in math, but it's also one of the most confusing. Those watching this video likely fall into one of three categories 1) you know what each term means, but the statement as a whole seems nonsensical, 2) you were lucky enough to see what this means and some long formulae explaining why it works in a calculus class, but it still feels like black magic, or 3) it's not entirely clear with the terms themselves are. Those in this last category might be in the best position to understand the explanation I'm about to give since it doesn't require any calculus or advanced math, but will instead require an open-minded to reframing how we think about numbers. Once we do this, it will become clear what the question mea...
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e to the pi i equals negative 1 is one of the most famous equations in math, but it's also one of the most confusing. Those watching this video likely fall into one of three categories 1) you know what each term means, but the statement as a whole seems nonsensical, 2) you were lucky enough to see what this means and some long formulae explaining why it works in a calculus class, but it still feels like black magic, or 3) it's not entirely clear with the terms themselves are. Those in this last category might be in the best position to understand the explanation I'm about to give since it doesn't require any calculus or advanced math, but will instead require an open-minded to reframing how we think about numbers. Once we do this, it will become clear what the question mea...
