Omnimaga
General Discussion => Other Discussions => Math and Science => Topic started by: squidgetx on March 19, 2011, 05:17:18 pm
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http://www.youtube.com/watch?v=jG7vhMMXagQ&feature=player_embedded (http://www.youtube.com/watch?v=jG7vhMMXagQ&feature=player_embedded)
Watch O.o
(For some reason it won't embed properly with the [youtube] tag <_<)
Something not mentioned in the video. Take a look at what happens to our circumference formula.
C=τr
And to our area formula
A=∫C dr=∫τr dr
=1/2τr2
Now how beautiful is that? Falls right in line with our
Gravitational Acceleration Function: y=1/2gt2
Hooke's Law: U=1/2kx2
Kinetic Energy Function: 1/2mv2
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Now it works.
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Lol, they just changed it to reference diameter rather than radius. :P
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Tau references radius, pi references diameter
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I do agree with it though. :/
I dislike that pi = 180
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I'm not sure why everyone makes an issue of Tau being better than Pi. It's not really important, since Tau is a constant multiple of Pi. That's like saying that 6 is better than 3 because 2*3 = 6. It's not really that big of a difference, except in that
{x|(x Mod Tau) = 0}⊆ {x|(x Mod Pi) = 0}
EDIT: ( {x|(x Mod Tau) = 0}⊆{x|(x Mod Pi) = 0} ) ^ ( {X∈{x|(x Mod Pi) = 0}|X∉{x|(x Mod Tau)}}≠∅)
It's starting to look like Haskell now...
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I'm not sure why everyone makes an issue of Pi being better than Tau. It's not really important, since Pi is a constant multiple of Tau. That's like saying that 3 is better than 6 because 6*.5 = 3
Not to troll or anything, but it works both ways :P
Anyway, I think that it really is more important. Practically EVERY mathematical formula using pi uses 2pi, not just pi. And conceptually, it's way more fundamental. 360 degrees = 1 tau, not 2pi. One half tau = one half a circle. See?
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What I was getting at is that the difference is so minor that there's no reason to change convention. Plus, A = r2π is nicer than A=(Tau/2)r2
List of places where Tau would be just as bad as or worse than Pi:
Euler's identity: Eiπ=-1
Heisenberg uncertainty principle: Δx Δp = h/4π
Coulomb's law: F = |q1 q2|/(4πε0r2)
∫-∞∞ e-x2 = √(π)
Standard Cauchy distribution: (π(1+x2))-1
More coming...
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New Euler's identity: eτi=1. WHAT NOW. Or eτi=1+0. Whatever.
You didn't watch the video, did you? As for A=1/2 τ r^2, see the first post. And all those 4π's just change to 2τ's, it's not any more or less awkward. Also, I have 1111 posts. Therefore, your argument is invalid (j/k lol ;))
Edit at HOMER-16: No, the point is that we should always go with tau over pi. Name me ONE equation where pi is better and more mathematically convenient than tau.
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So, use Pi for some equations, and Tau for others depending on which works better.
Edit: Ninja'd
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Euler's identity: eτi=1. WHAT NOW. Or eτi=1+0. Whatever.
Um, Check it (http://www.wolframalpha.com/input/?i=e^%28pi*i%29)
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Heisenberg uncertainty principle: Δx Δp = h/4π
I think most physicists would agree that the more natural constant is ħ = h/2π. (There's that 2π again.)
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I said e^tau i = 1 (http://www.wolframalpha.com/input/?i=e^%282*pi*i%29)
Damn, now I don't have 1111 posts :(
Integral over all space in polar coordinates:
∫0τ∫0∞f(r,θ)r d rdθ
Normal distribution:
(1/√τσ)e−(x−μ)^2/2σ^2
Fourier transform:
f(x)=∫-∞∞F(k)eiτkxdk
F(k)=∫-∞∞f(x)e−iτkxdx
Cauchy’s integral formula:
f(a)=1/iτ∮γf(z)/(z−a) dz
nth roots of unity:
eiτ/n
The Riemann zeta function for positive even integers:
ζ(2n)=∑k=1∞1/k2n=Bnτ2n/[2(2n)!] n=1,2,3,…
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Heisenberg uncertainty principle: Δx Δp = h/4π
I think most physicists would agree that the more natural constant is ħ = h/2π. (There's that 2π again.)
Well, I can't argue with the reduced Planck's constant.
I said e^tau i = 1 (http://www.wolframalpha.com/input/?i=e^%282*pi*i%29)
Damn, now I don't have 1111 posts :(
Muahahahahaha, you took the bait to destroy your evil power >:D
j/k :P
What I'm saying is that I have no problem with either Tau or Pi. But saying that we should be teaching students one or the other is kind of stupid since neither one really simplifies anything. I mean, if I can take an equation with a couple of variables and operations, then blow it up into a hundred operation expression through "simplification," then using a factor of 2 or 1/2 doesn't seem like a bad thing to deal with.
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More useful than pi or not, I'll have to try to use Tau in my equations more often :P
Coupled with my occasional use of (http://i201.photobucket.com/albums/aa229/keithjohansen/samekh.png) as my constant for indefinite integrals (as opposed to C or K), I'll have VERY Star Driver mathematics now :D
Well, technically the Phoenician 'Tau' is an X not a t, so I'm _already_ doing very Star Driver math but whatever heh
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All right, I can concede that in higher math, the use of tau doesn't greatly impact anything (although it still does). The point though, is that pi is fundamentally incorrect as the so-called circle constant. Furthermore, the use of tau would significantly change teaching. Trigonometry and radians would become so, so much easier to grasp. For example: sin 2t. Well, that's 2 revolutions of a circle, which means we're back where we started. Hence, 0. Logically sound: it's much easier for a student to grasp that t=1 revolution than 2pi=1 revolution
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Plus in those kinds of equations it makes the math appear so much cleaner, thus, making it easier to work with.
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I can't believe it ... they're right! :o
It also applies to Buffon's needle (http://mste.illinois.edu/reese/buffon/buffon.html): it's not 2/π; it's 1/τ, or τ-1! Tau makes the world so much simpler!
Too bad it's already used to represent torque.
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And to that argument, I say, what about e? No one seems to have issues with the fact that e represents both Euler's number and the charge of an electron ;)
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And to that argument, I say, what about e? No one seems to have issues with the fact that e represents both Euler's number and the charge of an electron ;)
e (the number) is italicized, e (an electron) is not ;)