Pi is wrong!

[uppi]

Pi is wrong...according to the proponents of Tau Day. And no, its not about legislating Pi to be three in accordance with the Bible, but a quite sensible proposal:

The Tau Manifesto is dedicated to the proposition that the proper response to “π is
wrong” is “No, really.” And the true circle constant deserves a proper name. As you may have guessed by now, The Tau Manifesto proposes that this name should be the Greek letter τ (tau):

τ≡ C/r =6.283185307179586…

Throughout the rest of this manifesto, we will see that the number τ is the correct
choice, and we will show through usage (Section 2 and Section 3) and by direct argumentation (Section 4) that the letter τ is a natural choice as well.

They argue, that Pi is the wrong choice for the circle constant and that the true circle constant should be what is currently known as 2π. After all, the fact that people have to use 2π all over the place (in sine and cosine functions, in Fourier transforms, in Gaussian distributions, in polar coordinates, ...) is a sign, that Pi might be a poor choice as a constant.

But because redefining conventions usually leads to a mess (I am looking at you, electric charge constant!), they propose to introduce a new constant τ, which equals exactly 2π. So a full circle would be τ radians, a half circle τ/2, a quarter circle τ/4 and so on.

And I really like this proposal, because implementing it would save me from having to use 2π over and over and over, especially when having to convert between frequencies and angular frequencies (which I have to do all the time).

And why this thread today? In the strange American way to write dates, today is 6/28, which matches the first three digits of τ, so today is Tau Day.

So what do you think of this proposal?

[Serutan]

Tau is pretty heavily used as it is in science. Not in favor of the proposal.

[uppi]

Originally Posted by Serutan

Tau is pretty heavily used as it is in science. Not in favor of the proposal.

In most cases, Tau is used as a replacement for t if there are more than one t in the equation. It would not be that hard to use another letter in these cases (and most letters have multiple meanings in physics anyway, even Pi).

[Earthling]

I actually hate, hate, hate using tau like that as a dummy variable in integration, gets frustrating the way the symbols look, so that's a strong reason I'd support this proposal.

However it would likely be rather problematic for people to adjust to and you'd still find situations with non-integer fractions or even powers and roots of pi and tau anyway. And we'd still have uppity mathematicians doing Fourier transforms backwards (calling the inverse the regular one and vice versa) and the like. On the fence here really.

[hoplitejoe]

Think of all the pi jokes that can be made, now try and think of a Tau one.
I think we have our answer

[EnglishCrusader]

I know someone who would disagree with this:

[LucyDuke]

Is 2π really such a burden?

[Earthling]

To put things in perspective, it's much less of a big deal than, say, the cgs mess with universal constants.

It is really ubiquitous though and kinda silly to have the 2π everywhere, which it really is, so replacing it with tau gets rid of an unecessary factor, and there may be some hypothetical benefit to teaching younger students that would help them learn geometry and trig, but there's also the disadvantages to changing everything up.

[deanej]

Originally Posted by LucyDuke

Is 2π really such a burden?

Mathematicians (and derivative disciplines such as physics and computer science) are inherently "lazy". Hence other peculiarities, such as the existence of natural log (otherwise known as log base e).

[uppi]

Originally Posted by LucyDuke

Is 2π really such a burden?

It is not so much a burden as an annoyance.

For example it is common in my field to give frequencies as Ω / 2π = ... MHz to avoid confusion with angular frequencies. However this is slightly ambiguous as the strict mathematical reading would be (Ω / 2) * π, which is not what is intended. One could avoid this by adding parentheses and write Ω / (2π), but this makes the expression even more unwieldy. Writing Ω / τ would save characters and eliminate this ambiguity.

[Defiant47]

Originally Posted by uppi

It is not so much a burden as an annoyance.

For example it is common in my field to give frequencies as Ω / 2π = ... MHz to avoid confusion with angular frequencies. However this is slightly ambiguous as the strict mathematical reading would be (Ω / 2) * π, which is not what is intended. One could avoid this by adding parentheses and write Ω / (2π), but this makes the expression even more unwieldy. Writing Ω / τ would save characters and eliminate this ambiguity.

I'm sorry, but 48/2(9+3) = 2. Always.

[madviking]

I think teaching-wise, tau is better than pi. Something about a circle being tau radians is more intuitive than a circle being two pi radians.

Added bonus - no more stupid math assignments on March 14th! June 28th is summer vacation!

[Perfection]

but pi r squared!

[ParadigmShifter]

It's not as bad as the gamma function,

gamma(n) = (n-1)!

What's all that about?

[classical_hero]

Originally Posted by uppi

Pi is wrong...according to the proponents of Tau Day. And no, its not about legislating Pi to be three in accordance with the Bible, but a quite sensible proposal:

The bible does not say that Pi=3. http://www.purplemath.com/modules/bibleval.htm

[contre]

Originally Posted by classical_hero

The bible does not say that Pi=3. http://www.purplemath.com/modules/bibleval.htm

I knew when I saw you were last respondent in this thread, this would be what you were posting about.

Getting around the fact you're making assumptions about things not written into the Bible (if I have to pidgin hole an answer in, I'd pick the measurements used on that page as well!), are you claiming that the Bible, the inerrant word of God, says Pi = 3.1395348837...?

[madviking]

Originally Posted by Perfection

but pi r squared!

Having .5 * tau * r^2 puts it in line with the scores of other half-square formulas (e.g. energy stored in a spring, energy stored in a capacitor, etc.)

[warpus]

Originally Posted by LucyDuke

Is 2π really such a burden?

Having taken way too much math at university I gotta admit tau would have made calculations and formulas simpler.. but only a bit.

It's not really a huge deal.

[mdwh]

I'd come across the issue before - I think they make a good point, and it probably would have been a more natural choice of a constant.

OTOH, I think making the change is more trouble than it's worth, and part of me feels that anyone insisting on using tau is in the same category as someone you meet talking about his "Mibibytes".

It's also not clear to me it's always better - obvious example being the area of a circle (and I'm not persuaded by section 3, yes some physical equations have a half in them, others don't, e.g. e=mc^2).

[Mise]

Originally Posted by uppi

It is not so much a burden as an annoyance.

For example it is common in my field to give frequencies as Ω / 2π = ... MHz to avoid confusion with angular frequencies. However this is slightly ambiguous as the strict mathematical reading would be (Ω / 2) * π, which is not what is intended. One could avoid this by adding parentheses and write Ω / (2π), but this makes the expression even more unwieldy. Writing Ω / τ would save characters and eliminate this ambiguity.

TBH, it would be easier to just make "2π" a symbol in its own right. I mean, I know when I see "2π", I just treat it as a single character in my head. Join up the "2" and the "π" and call it a new symbol pronouced "two-pi". Not every constant needs a Greek or Latin letter -- we can make our own!!