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I'm in favor of keeping pi because of one simple equation: e^{i\pi} + 1 = 0 This is, IMHO, the most beautiful equation I've come across. It's concise and i
by kerkeslager 10y ago
I'm in favor of keeping pi because of one simple equation:
e^{i\pi} + 1 = 0
This is, IMHO, the most beautiful equation I've come across. It's concise and it relates all the most basic constants in mathematics. It's also useful, for example, for operating on the logarithm of a negative number:
e^{i\pi} + 1 = 0
e^{i\pi} = -1
i\pi = \ln{-1}
\ln{x} + i\pi = \ln{x} + \ln{-1}
\ln{x} + i\pi = \ln{-x}
For more see Euler's Identity[1].
[1] https://en.wikipedia.org/wiki/Euler%27s_identity https://en.wikipedia.org/wiki/Euler%27s_identity
- karmakaze 10y agoThis simultaneously illustrates how e^(180') is halfway round a unit. Tau (literally/numerically?) > Pi