## Thursday, April 21, 2011

### The Tao Manifesto: The War against Euler and Pi

 The Most Beautiful Equation in Mathematics, is about to get ugly.
Have you seen "The Tao Manifesto"? Pretty funny. It says Euler and Archimedes screwed up, and we should be using tau = 2 x pi instead of pi, the reason being 2(pi) comes up quite a bit in analysis, AND ... it stresses that talking about the ratio of the circumference of a circle divided by its radius (which is tau), seems more appealing than talking about the circumference of a circle to its diameter (which is pi).

Interestingly (or not, given the whole 'beauty is in the eye of the beholder" thing), I ran into this as being useful in reading J. Richard Gott and Robert J. Vanderbei's Sizing Up The Universe, which I consider to be the most beautiful book of 2010, and in Fourier Analysis. But enough of that ....

Sure, but look what that would do to Euler's Equation (pictured on the ring above, in original pure form). Won't be so pretty if "TAU" is adopted, hmm?

It would certainly make Euler's Equation, generally considered the most beautiful equation in Mathematics, more interesting. Remove pi, replace with tau/2. Messier, though. Less elegant. Ew. So instead of having e, pi, i, 0, 1 and the operators +, x, =, and exponentiation, we would have e, tau, i, 0, 1, 2, and the operators +,x, /, =, and exponentiation. I dunno, can't we work subtraction in there somewhere? Oh, right, subtract one from both sides. But then it's not the tightest, and you lose addition! Arghh! Math Jokes <=== if you understand them, you probably don't have any friends. ;-) I'll stick with 1+e^(i(pi))=0, thanks.

 Leonhard Euler. Second most prolific mathematician after Paul Erdos, and second most intelligent man of all time after William Sidis. "WE are not amused. Then again, WE are quite dead. It is YOUR problem, now. Sheesh, do I have to do EVERYTHING for you people ?!  Let me rest in peace, kthnx, lol."

Anonymous said...

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Chris and Sandy Boothe

Anton said...

e^(i*pi) + 1 = 0 is nice, but...

e^(i*tau) = 1

?

It's very elegant, connecting e, i, tau, and 1. Also, it shows nicely the periodicity of certain complex expressions. Consider:

e^0 = 1
e^(i*tau) = 1
e^(i*2*tau) = 1
e^(i*k*tau) = 1, where k is any integer
... etc

Yes, there's no zero in there, but it's still beautiful. Besides, in the original e^(i * pi) + 1 = 0,
the 0 is tacked on, anyway. A simpler way to write the expression would be:

e^(i * pi) = -1

To me,

e^(i * pi) = -1

and

e^(i * tau) = 1

Are equally beautiful

Anonymous said...

Well reasoned Anton.

IMHO,I dont find the controversy between pi and tau to be having much merit. Its a scalar multiplication after all and unless they have some really strong reason to use tau,its really a matter of convenience.