simplicio comments on Open Thread: March 2010, part 2 - Less Wrong
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Maybe because e^0 = 1?
Well making pi=2pi would just mean the complex exponential function would repeat itself every pi radians instead of every 2pi radians. e^0 would still = 1 in either case. Note that in the current definition, e^jn(2pi) = 1 for any integer n.