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A Note To All Mathematicians - January 7, 2010Rating: 4.1/5 (51 votes cast)
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I'm puzzling over one of these at the moment :/
e iπ + 1 = 0 or eiπ = -1 ? Both are insufficiently ordered. It should be eπi + 1 = 0. Get it right!
That's how I would write it too when given a choice. Just the convention I'm used to when dealing with complex numbers, a+bi, a=0, b=pi.
I believe the i is normally placed first?
I dunno, I learned it the proper way, Pi x i. See also: http://xkcd.com/179/ and http://www.math.toronto.edu/mathnet/questionCorner/epii.html OK, other sites have it i x Pi.
Thank goodness Disgruntled Mathematician sent this memo; I concur!
I thoroughly agree!
On the i*pi vs pi*i argument, in engineering the i (or "j" as we call it, because we're crazy) comes before the number. I think it's largely an issue of context.
Yeah like in circuits were the impedance of a capacitor is 1/(jwC). btw j makes perfect sense since i is current.
If it isn't taken care of, he's got a formula... FOR DESTRUCTION!
Wouldn't e^(-i*pi)+1=0 be even nicer? You get the "-" sign as well as the "+", the "0" and all ather stuff.
And from now on, we should say E-mc^2=0.
Why would we say something so blatently wrong though? It'd make much more sense to say E/(mc^2)=0
And when I say 0 I definitely mean 1.
So i = (ln(-1))/pi = sqrt(-1) ? Or is it another i I'm thinking about?
Thinking I've read all of xkcd there is, I clicked on bmonk's great links only after I posted. Big mistake.
Problem (theoretically) resolved.
While the i being used is the imaginary unit, it's incorrect to say that i=ln(-1)/pi because the natural log function does not extend canonically to negative numbers, or any complex numbers besides positive reals. It's possible to define ln(-1) only up to integer multiples of 2 pi i.
The beauty about e^(i * pi) + 1 = 0 is that is that one equation clearly demonstrates relationship between e, i , pi, 1 and 0. While in the other representation, 0 is kinda lost.
Except that the relationship doesn't actually involve 0, that's just a construct. Writing e^{i\pi}=-1 more clearly demonstrates its origin in Euler's formula.
So, nothing is lost by using e^(i*pi)=-1 ?
Haha nice!
Uugh! That's a terrible pun. I wish I'd thought of it!
Ditto :D
e^(i*pi)+1=0 gives a relation to e pi i 1 and 0, e^(i*pi) = -1 only to e i pi and -1, and -1 isnt even that interesting.
yay! i recognize the gmail format anywhere :)
(yep, im more of a computer geek than a mathematician, but hey, from thanksgiving, if they didnt have complexity theory, i wouldn't have any fun :)
And of course the second way of writing it includes a 0, making it an equation with each of the 5 most important numbers in mathematics exactly once in it.
It really should be e^(i*tau) = 1 + 0, i.e. a rotation through one complete turn comes back to the original number.
Pi is the wrong circle constant! Embrace the tau! http://tauday.com/
what about e^(tau*i)=1? its balanced.
How about e^((Tau)i)=1?