Re: Show us your builds!
Posted: Tue Jun 26, 2012 12:35 pm
Yeah, I always thought the magic was that it involved both addition and the additive and multiplicative identities. Things equalling 1 aren't that special: take, for instance, e^0. The layman would think tau*i = 0 which appears nonsensical, vs the mystery of e^(whatever) being negative that e^ipi arouses.Heilkaiba wrote: I always write it as e^iπ +1 = 0.
In trig, while sin and cos periodicity would be cleaner, tan would be tau/2 periodic, sin(x) = sin(tau/2 - x), cos(tau/2) = -cos(0). Certainly 2pi is more common in use, but fractions in place of concatenation-denoted multiplication are more of a pain (especially to typeset properly).
Furthermore, even if tau were introduced, it would create an unpalatable rift in the literature far outweighing any ivory-tower theoretical nicety.
Hell, if one could change one mathematical convention for "free", the pi-tau change would be fairly low on the list. Think how much pain standard hexadecimal use or RPN would alleviate. No more BEDMAS!
Maybe a compromise could be some sort of 2pi ligature, which would be visually similar enough to 2pi written normally to be understood as such, but nonetheless be a single typeset and handwritten character.
Anyway, this is the math forum, right? What's with the wolf logo in the corner?