Pi vs Tau
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Pi vs Tau
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
Re: Pi vs Tau
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.
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.
 Soupspoon
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Re: Pi vs Tau
"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.
S'obvious.
Re: Pi vs Tau
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.
Re: Pi vs Tau
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 threelegged Pi as the symbol. The paper is Pi is Wrong, which my freshman calculus TA showed us for fun.
Re: Pi vs Tau
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
Pi has two legs, therefore it's more stable. Clearly, the winner.
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Re: Pi vs Tau
Tau has curves*, therefore it's more attractive and wins.
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.
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.
 Soupspoon
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Re: Pi vs Tau
If ╥≡π then what about ╤?
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Re: Pi vs Tau
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
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.
Re: Pi vs Tau
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.
Pi is that weird spot in the middle that's kind of annoying to use.
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Re: Pi vs Tau
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...
Re: Pi vs Tau
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!
Re: Pi vs Tau
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.
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.
Re: Pi vs Tau
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 "".
Re: Pi vs Tau
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
e^{0} = 1
e^{iτ/4} = i
e^{iτ/2} = 1
e^{3iτ/4} = i
e^{iτ} = 1
Perhaps some alien civilization or alternate universe uses κ = π/2 = τ/4 as a circle constant and is wondering why the piists want to ruin the beauty of e^{κi} = i. Do we really need to add a "1"? (Also, the series of identities above looks better with κ.)
Also e^{kiτ} = 1 if k is an integer, and furthermore e^{(x + kτ)i} = e^{xi} (i.e., τ is the period of f(x) = e^{xi}). Euler's identity doesn't have nearly as nice of a generalization (e^{(1 + 2k)πi} = 1; e^{kπi} = ±1 depending on if k is even or odd).
e^{iτ/4} = i
e^{iτ/2} = 1
e^{3iτ/4} = i
e^{iτ} = 1
Perhaps some alien civilization or alternate universe uses κ = π/2 = τ/4 as a circle constant and is wondering why the piists want to ruin the beauty of e^{κi} = i. Do we really need to add a "1"? (Also, the series of identities above looks better with κ.)
Also e^{kiτ} = 1 if k is an integer, and furthermore e^{(x + kτ)i} = e^{xi} (i.e., τ is the period of f(x) = e^{xi}). Euler's identity doesn't have nearly as nice of a generalization (e^{(1 + 2k)πi} = 1; e^{kπi} = ±1 depending on if k is even or odd).
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Re: Pi vs Tau
chridd wrote:Perhaps some alien civilization or alternate universe uses κ = π/2 = τ/4 as a circle constant and is wondering why the piists want to ruin the beauty of e^{κi} = 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.
Re: Pi vs Tau
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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