alt Hacker NewsPersonally, I prefer the version with tau (2 times pi) in it rather than the one with pi:
e^(i*tau) = 1
I won't reproduce https://www.tauday.com/tau-manifesto here, but I'll just mention one part of it. I very much prefer doing radian math using tau rather than pi: tau/4 radians is just one-fourth of a "turn", one-fourth of the way around the circle, i.e. 90°. Which is a lot easier to remember than pi/2, and would have made high-school trig so much easier for me. (I never had trouble with radians, and even so I would have had a much easier time grasping them had I been taught them using tau rather than pi as the key value).
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Ah, one of these battles that are very hard to fight to gain essentially nothing.
Edit: or, when you can't do actual math, you complain about notation.
This!
I've been posting the manifesto to friends and colleagues every tau day for the past ten years. Let's keep chipping away at it and eventually we won't obfuscate radians for our kids anymore.
Friends don't let friends use pi!
Which would be e^(i*tau) - 1 = 0 if you wanted to honor the spirit of the Identity.
535.491…^i = 1
Though the argument is technically correct, it is unnecessary at this point of time. Same as renaming cities and countries to "correct" history.
The one place where radians are more convenient is when you are at the centre of the circle. Then something which is as wide (or tall) as it is far away subtends one radian in your view. (And correspondingly, if it subtends half a radian it is half as wide as it is far away, etc.)
This happens to be the most common situation in which I measure angles.