The Tau Manifesto

For the discussion of math. Duh.

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Re: The Tau Manifesto

Postby arbiteroftruth » Thu Sep 05, 2013 9:07 pm UTC

I think the main point behind tau is that it's worth doing precisely *because* it's irrelevant to real mathematicians. They can handle a variable substitution just fine, but all the anecdotal evidence I've seen indicates that tau is much easier for educational purposes. So if switching to tau helps one group of people, and is irrelevant to the other, the conclusion is to switch.

All the commentary about other places where the circle constant shows up is mainly about showing how those equations are still derived from the basic case of the circle, and in that case the derivation is potentially clarified or easier to follow when the association with the circle uses the more directly associated constant, tau. In particular, a broad range of categories relate back to actual circles in the following way.

The Gaussian integral is evaluated to sqrt(tau/2) by way of evaluating the 2-dimensional integral in polar coordinates, exploiting the function's circular symmetry in 2 dimensions.
From the Gaussian integral, we get all manner of probability applications, the values of the Gamma function at half-integers, and a non-recursive solution to the general problem of hyperspherical volume.
Through the Gamma function we can acquire the functional equation of the Riemann Zeta function.
From the Riemann Zeta function we get applications to number theory.

And so on. The point isn't to find the value that eliminates the most fractions in the most equations. The point is to relate things back to the simplest starting point possible.

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Re: The Tau Manifesto

Postby Derek » Thu Sep 05, 2013 10:01 pm UTC

Have I posted in this thread before? Not sure. Well, I'm in the Tau camp, for the record.

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Re: The Tau Manifesto

Postby PM 2Ring » Fri Sep 06, 2013 6:31 am UTC

I may have said this earlier in the thread; I can't be bothered re-reading the old posts. I agree that it's reasonable to claim that tau has various advantages over pi, but are these advantages great enough to warrant changing to tau now, when we've been using pi for so long? As others have said, it boils down to a factor of 2, and if coping with that is too hard then maybe mathematics is not for you. :) OTOH, if multiple trials clearly show the pedagogical advantages of tau over pi, then I'd have no objections to teaching kids tau. After all, the tau proponents don't seem to be pushing for the abolition of pi.

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Re: The Tau Manifesto

Postby kubit » Fri Sep 06, 2013 6:24 pm UTC

Just to put my two cents worth in... I'm fairly sure mathematics education has far more important problems these days than whether 2pi has its own symbol! Really, even though I agree that there is a point with tau being more intuitive in geometry it seems like major waste of time to argue over it...

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Re: The Tau Manifesto

Postby Cleverbeans » Fri Sep 06, 2013 11:33 pm UTC

kubit wrote:it seems like major waste of time to argue over it...

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Re: The Tau Manifesto

Postby elasto » Sat Sep 07, 2013 2:21 pm UTC

M= Man looking for an argument
R= Receptionist
Q= Abuser
A= Arguer (John Cleese)
C= Complainer (Eric Idle)
H= Head Hitter

M: Ah. I'd like to have an argument, please.
R: Certainly sir. Have you been here before?
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R: Fine. Well, I'll see who's free at the moment.
R: Mr. DeBakey's free, but he's a little bit conciliatory.
Ahh yes, Try Mr. Barnard; room 12.
M: Thank you.

(Walks down the hall. Opens door.)

M: Well, I was told outside that...
Q: Don't give me that, you snotty-faced heap of parrot droppings!
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(Walk down the corridor)

M: (Knock)
A: Come in.
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(short pause)
A: No it isn't.
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(pays money)
A: Thank you.
short pause
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(Walks down the stairs. Opens door.)

M: I want to complain.
C: You want to complain! Look at these shoes. I've only had them three weeks and the heels are worn right through.
M: No, I want to complain about...
C: If you complain nothing happens, you might as well not bother.
M: Oh!
C: Oh my back hurts, it's not a very fine day and I'm sick and tired of this office.

(Slams door. walks down corridor, opens next door.)

M: Hello, I want to... Ooooh!
H: No, no, no. Hold your head like this, then go Waaah. Try it again.
M: uuuwwhh!!
H: Better, Better, but Waah, Waah! Put your hand there.
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H: Why did you come in here then?
M: I wanted to complain.
H: Oh no, that's next door. It's being-hit-on-the-head lessons in here.
M: What a stupid concept.

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