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Pi-Day -- Only the half truth

2011-03-14

Happy Pi-Day - But....

Pi is one of those mathematical constants that almost everyone has heard of, and though it has a slew of mathematical properties is it really this almighty constant with tons of mathematical properties of interest or are we just all orthodox and refuse to think any differently than the Greeks who defined this lasting constant, or better yet in the world of sci-fi would the aliens laugh at how feeble we are to idolize an inefficient constant. Bob Palis says it is the second case and we need to do away with pi for a better constant....wait for it.... tau = 2*pi

What is he saying? Well if you do a bit of trig you will see that pi is only half of the unit-circle while 2pi is the full unit-circle. In essence the constant we all love so much is merely half of the constant that is actually used (hence 2pi as a better choice).

Further if you look at mathematical formulas regarding pi they always have a factor of 2 in them to account for the fact that pi is only half of the circle and the full value of 2pi is needed. Here are some examples:

sin(x+2pi) = sin(x)
e^(2pi * i) = 1
n! approx sqrt(2pi n) n^n e^(-n)
h-bar = h/(2pi)
c_n = 1/(2p) int_0^(2pi) f(x) e^(inx) dx
int_-inf^+inf e^(-x^2/2) = 2pi

Mathematics is full of useful formulas in which pi appears and in almost all cases it is actually a factor of 2pi that appears (the length around the unit circle). So the argument presented in the article I linked is to do away with the orthodox value of pi we have been brainwashed into using because we are all sheep to the authorities of the past where we only consider half the unit-circle, or move into a new age in which we prefer the whole unit circle as opposed, as a full circle is the nature of life. The new constant of interest should be

2pi = 6.28318530.......

Thus we should be celebrating this pi-day on June 28th. Out with the old convention and in with the more enlightened number!!

The link: http://www.math.utah.edu/~palais/pi.pdf
CNN article: http://www.cnn.com/2011/TECH/innovation/03/14/pi.tau.math/index.html?eref=mrss_igoogle_cnn

Happy half-circle day, but I am in favor of switching to the modern value of having a full circle, no cups half-full or half-empty, we should move to a life of fullness and completeness!!

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