Pi vs Tau

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Which should be taught: Pi vs Tau

π
30
52%
τ
28
48%
 
Total votes: 58

Fieari
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Pi vs Tau

Postby Fieari » Wed Oct 19, 2016 11:40 pm UTC

Sure, π and τ are easily substitutable for each other if you include a constant, but which should be taught in schools? Which is easier to learn? Which makes more sense? Which is more beautiful? Which is more philosophically sound? You know you have an opinion on the matter, so chime in!
Surely it is as ridiculous to consider sqrt(-1) "imaginary" because you can't use it to count pieces of chalk as to consider the number 200 imaginary because by itself it cannot express the location of one point with reference to another. -Isaac Asimov

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Flumble
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Re: Pi vs Tau

Postby Flumble » Thu Oct 20, 2016 12:17 pm UTC

Idealist, didactic and prescriptivist me all say τ. τ is the OTC... just like e, γ and φ. (I see i as part of complex number notation, not a constant.)
As Picard said: "There are TAU radians!"

Let's get a dozen arguments for both out of the way: The Tau Manifesto, Numberphile's Tau vs Pi Smackdown, and the rabbit hole follows naturally from there.

Like Phil says: τ may reduce confusion when dealing with angles and trigonometry for the first time, and that's very important because the concepts are hard enough by themselves. (And it should be clear why we need to stuff as many mathematical concepts into people's minds as possible.) It's hardly a big change in education, compared to all the "new math" stuff, and you can start by simply mentioning 2π=τ on the covers/in the footers of textbooks.
Those of us who are familiar with algebra can easily swap 2π for τ or π for τ/2 and vice versa.

So vote τ for a better tomorrow!
The revolution is just one τ away.

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Soupspoon
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Re: Pi vs Tau

Postby Soupspoon » Thu Oct 20, 2016 12:30 pm UTC

"Pi" (3.1415926isasfarasIgenerallygo) should clearly be given the "Tau" symbol "τ" and then 6.2831852ish the "π" symbol and 9.424687andonwards something like an inverted "ш".

S'obvious.

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Flumble
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Re: Pi vs Tau

Postby Flumble » Thu Oct 20, 2016 1:01 pm UTC

Soupspoon wrote:something like an inverted "ш".

m?

I see it differently: the ¯ signifies 1 rev/rad and the number of ι's signifies the denominator, so m = 2.0943951…. You could use the ¯'s as multipliers too: ῑ̄̄ = 12.5663706…, m̄̄ = τ = 6.2831852…, ι = 0, ā = τ/a and ¯ is undefined.

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Re: Pi vs Tau

Postby Derek » Mon Oct 24, 2016 12:55 am UTC

Soupspoon wrote:"Pi" (3.1415926isasfarasIgenerallygo) should clearly be given the "Tau" symbol "τ" and then 6.2831852ish the "π" symbol and 9.424687andonwards something like an inverted "ш".

S'obvious.

The earliest tau paper I know of (though the author called it a "turn") proposed a three-legged Pi as the symbol. The paper is Pi is Wrong, which my freshman calculus TA showed us for fun.

Fieari
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Re: Pi vs Tau

Postby Fieari » Wed Oct 26, 2016 12:03 am UTC

The fun thing about tau is that it can stand for "turn" in a way that pi doesn't really stand for anything (except the vague association that pies are round).
Surely it is as ridiculous to consider sqrt(-1) "imaginary" because you can't use it to count pieces of chalk as to consider the number 200 imaginary because by itself it cannot express the location of one point with reference to another. -Isaac Asimov

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Re: Pi vs Tau

Postby commodorejohn » Wed Oct 26, 2016 12:41 am UTC

Pi has two legs, therefore it's more stable. Clearly, the winner.
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Flumble
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Re: Pi vs Tau

Postby Flumble » Wed Oct 26, 2016 3:08 am UTC

Tau has curves*, therefore it's more attractive and wins.

Fieari wrote:The fun thing about tau is that it can stand for "turn" in a way that pi doesn't really stand for anything (except the vague association that pies are round).

But the π in pi stands for πerimeter. Moreover, a lot of languages don't have an easy word for revolution starting with a τ.

*in areas where the latin alphabet is the default. Π often loses its curves after the person gets familiar with one dash + two legs, whereas τ must keep its curved leg to tell it apart from T.

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Soupspoon
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Re: Pi vs Tau

Postby Soupspoon » Wed Oct 26, 2016 8:32 am UTC

If ╥≡π then what about ╤? ;)

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Re: Pi vs Tau

Postby Xanthir » Wed Nov 02, 2016 5:37 pm UTC

Flumble wrote:*in areas where the latin alphabet is the default. Π often loses its curves after the person gets familiar with one dash + two legs, whereas τ must keep its curved leg to tell it apart from T.

That's not relevant for it's use in mathematics, where we always use the lowercase letters. Lowercase τ doesn't look like any English letter unless you're *really* sloppy.

We only use Π to stand for "product", and that's got nothing to do with tau.
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Re: Pi vs Tau

Postby RCT Bob » Wed Feb 08, 2017 10:51 pm UTC

I definitely prefer pi. tau is already used for other variables in physics and engineering, primarily shear stress, as well as some time constants, while pi is pretty much never used for variables because pi is more generally implied as the constant. And I'm strictly of the opinion that duplicate symbol usage within the same application should be minimised as much as possible to prevent ambiguity.

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Re: Pi vs Tau

Postby Unlocked » Sun Mar 12, 2017 2:10 am UTC

I think that anyone who thinks that pi is better than tau in the context of trig should consider another variable for pi/2 as the superior constant. This pi/2 variable (m, as a placeholder for now) would make it such that every m radians would be equal to 90 degrees, which is an angle that lots of people are familiar with, probably more so than 180 degrees, at least for people who are first experiencing trigonometry.

Pi is that weird spot in the middle that's kind of annoying to use.

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Soupspoon
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Re: Pi vs Tau

Postby Soupspoon » Sun Mar 12, 2017 9:53 am UTC

Unlocked wrote:90 degrees, which is an angle that lots of people are familiar with, probably more so than 180 degrees

...I don't know about that. Any flat table has an infinity of 180° angles between any two arbitrary segments of its flat and obvious upper surface that you might care to mention, whereas some tables don't have any obvious 90° angles at all... ;)

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measure
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Re: Pi vs Tau

Postby measure » Tue Mar 14, 2017 10:58 pm UTC

Happy τ/2 day everyone! Pi is good because it provides a nerdy excuse to eat pie with your nerd friends, but when you go to calculate what volume of pie you've eaten, Tau all the way!

nichi
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Re: Pi vs Tau

Postby nichi » Thu Mar 16, 2017 12:59 pm UTC

Are we going to get all the old works translated, or just note to everyone being introduced to math that if they try to read anything before the year of the switch they should expect a symbol for tau/2? And during the interim it can go either way. Granted, I would hope anyone digging through old math would be able to handle this.

On the other hand, sure seeing a fraction of a revolution as a fraction of tau is easier, but as soon as you try to do anything computation you have uglier fractions. Not a big fan of integers greater than four.

wumpus
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Re: Pi vs Tau

Postby wumpus » Sat May 13, 2017 5:27 pm UTC

Do we really need to add a "2" to Euler's identity? You don't get to change Euler's identity simply because of pi*r**2. Switch to tau if and only if "2" is sufficiently fundamental as "1" "e" "j" "pi/tau" and "-".

Derek
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Re: Pi vs Tau

Postby Derek » Sun May 14, 2017 9:05 pm UTC

nichi wrote:Are we going to get all the old works translated, or just note to everyone being introduced to math that if they try to read anything before the year of the switch they should expect a symbol for tau/2? And during the interim it can go either way. Granted, I would hope anyone digging through old math would be able to handle this.

On the other hand, sure seeing a fraction of a revolution as a fraction of tau is easier, but as soon as you try to do anything computation you have uglier fractions. Not a big fan of integers greater than four.

The old works are already translated. Not just in the literal sense, that many of these works were written in Latin, Greek, German, etc., but also because modern mathematical notation didn't exist until the 19th century.

wumpus wrote:Do we really need to add a "2" to Euler's identity? You don't get to change Euler's identity simply because of pi*r**2. Switch to tau if and only if "2" is sufficiently fundamental as "1" "e" "j" "pi/tau" and "-".

No you don't add a 2 to Euler's identity. You simply write it in the more natural form:

exp(tau*i) = 1

or if you prefer,

exp(tau*i) - 1 = 0

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Re: Pi vs Tau

Postby chridd » Mon May 15, 2017 1:57 am UTC

e0 = 1
eiτ/4 = i
eiτ/2 = -1
e3iτ/4 = -i
e = 1

Perhaps some alien civilization or alternate universe uses κ = π/2 = τ/4 as a circle constant and is wondering why the pi-ists want to ruin the beauty of eκi = i. Do we really need to add a "1"? (Also, the series of identities above looks better with κ.)

Also ekiτ = 1 if k is an integer, and furthermore e(x + kτ)i = exi (i.e., τ is the period of f(x) = exi). Euler's identity doesn't have nearly as nice of a generalization (e(1 + 2k)πi = -1; ekπi = ±1 depending on if k is even or odd).
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Derek
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Re: Pi vs Tau

Postby Derek » Tue May 16, 2017 4:51 pm UTC

chridd wrote:Perhaps some alien civilization or alternate universe uses κ = π/2 = τ/4 as a circle constant and is wondering why the pi-ists want to ruin the beauty of eκi = i. Do we really need to add a "1"? (Also, the series of identities above looks better with κ.)

This has been suggested before. It's not an unreasonable idea, I think a quarter turn is more fundamental than a half turn, however I think a full turn is still the most fundamental of the circle constants.

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Re: Pi vs Tau

Postby eSOANEM » Wed Jun 21, 2017 12:26 am UTC

Sqrt(2π) is clearly the right choice. Just look at normal distributions, Fourier stuff (if you use the correct normalisation) and therefore QFT
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