I don't think there is much to discuss here, tau=2pi is clearly the more sensible constant for almost every use case. The only question is whether we give in to conventions, or pay the one-time technical debt of switching.
We (in the US) may never convert to metric, but the much smaller community who works with pi regularly should know better.
To my eye as a mathematician, the tau version I provided looks better.
e^i * tau = 1, has a much nicer geometric interperatation, of e^i * tau representing a full rotation (which is just the identity), whereas e^i * pi = -1 represents half a rotation, and it is not quite as immediately obvious that -1 is a 1/2 rotation (although this is not particularly opaque).
While I am on the subject, surely the equation you want to discuss is e^i * pi * x, = cos(pi * x)+isin(pi * x), which clearly represents a rotation of x/2 of a complete circle. Of course, viewing it this way, it seems even clearer why one would want to use tau.
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[ 3.2 ms ] story [ 26.3 ms ] threadWe (in the US) may never convert to metric, but the much smaller community who works with pi regularly should know better.
No way we mess with that.
To my eye as a mathematician, the tau version I provided looks better.
e^i * tau = 1, has a much nicer geometric interperatation, of e^i * tau representing a full rotation (which is just the identity), whereas e^i * pi = -1 represents half a rotation, and it is not quite as immediately obvious that -1 is a 1/2 rotation (although this is not particularly opaque).
While I am on the subject, surely the equation you want to discuss is e^i * pi * x, = cos(pi * x)+isin(pi * x), which clearly represents a rotation of x/2 of a complete circle. Of course, viewing it this way, it seems even clearer why one would want to use tau.