Euler's identity unifies five of the fundamental ingredients of mathematics: 0, 1, π e, and i.
The value e is the foundation of the natural logarithm. But even the most technically astute engineer or mathematician can be forgiven for not recognizing it:
e i π + 1 = 0
Solving, you get e = 2.718281828459...
(It's one of those numbers that goes on forever.)
You may say this is one of those tedious math things that means nothing to a pilot and perhaps that's true. But it is one of those things that comes up now and then so I keep it in my notes. If you really want to see it in action, the best explanation I've ever found appeared in the book The Simpsons and Their Mathematical Secrets, by Simon Singh.
Everything here is from the references shown below, with a few comments in an alternate color.
[Singh, pp. 132-135]
Singh, Simon, The Simpsons and Their Mathematical Secrets, 2013, Thomson-Shore Inc., Dexter, Michigan.
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