How e to the pi i can be made more intuitive with some perspectives from group theory, and why exactly e^(pi i) = -1. Apply to work at Emerald Cloud Lab: ...
========== two years ago, almost to the day actually I've put up the first video on this channel about Euler's formula e^(pi i) = -1 as an anniversary of sorts, I want to revisit that same idea for one thing, I always kindda wanted to improve on the presentation but I wouldn't rehash an old topic if there wasn't something new teach you see, the idea underlying that video was to take certain concepts from a field of maths group theory and show how to give Euler's formula a much richer interpretation than a mere association between numbers and, two years ago, I thought it might be fun to use those ideas without referencing group theory itself or any of the technical terms within it but, I've come to see that you all actually quite like getting into the maths itself even if it tak...