Pi is wrong; long live Tau!

[Golden Applesauce]

http://tauday.com/

I'd quote the manifesto, but it makes heavy use of math formatting that won't go over well to BBCode, so I'll try to summarize it.

Basically, the number pi is cute but isn't the right circle constant.  pi is only half of a circle; there are 2pi radians in a circle, sine and cosine have period 2pi, the circumference of a circle is 2pi*r, it's area is (1/2)*(2pi)*r^2, and e^[2pi*i] = 1.  2pi shows up basically everywhere in probability, quantum physics, geometry, etc.

The correct circle constant is 2pi, for which the author proposes using the symbol τ (tau), for a turn around the circle.

[Triple Zero]

I read about this and it makes a whole lot of sense.

I also read a debunking article (trying to show that pi is at least as fundamental and proliferous) and it made a whole lot less sense, seemingly grasping at straws.

Additionally, from personal experience, 99% of the time I have to import the constant pi into a computer program I'm writing, I exclusively use it in the form of 2pi, never just pi.

So, yeah.

There's no way we're going to rewrite centuries of math textbooks of course, but the idea seems pretty sound.

[Telarus]

Ran into this a little while ago myself. Fuck, it's hard to replace such an ingrained symbol. Then again, when was the last time you _wanted_ to compute circular geometry, over and over.


What I want to know is if it is easier to 'intuit' rough estimates once I integrate Tau into my math. Not for any on paper problems (except to get it to stick in my head), but IRL. So much of advanced martial arts runs off circularity and sphericity.

[Prelate Diogenes Shandor]

Isn't this all a bit like trying to prove that 1 is more fundamental than 2?

[BabylonHoruv]

pi is the area constant.

(pi)(r)^2

[Triple Zero]

Isn't this all a bit like trying to prove that 1 is more fundamental than 2?

More like how 1 is more fundamental than 0.5.

Did you even read the manifesto?

also see

pi is wrong
pi is (still) wrong (video)

pi is the area constant.

(pi)(r)^2

that is one of the straws the tau debunking article was grasping at.

let me find it again

http://www.thepimanifesto.com/

it sounds so much like how he wants to find reasons he doesn't have to reconsider pi.



Once again, it's not like it's going to be possible to make this change in the field of mathematics, pi's got way too much legacy for that. But at least it's an interesting thing to point out, and we can just acknowledge that this seems to be the case, in the very same way that we now acknowledge it was a mistake to assign the electron a negative charge (so that a lack of electrons implies positive charge), but there's of course no way we're going to risk the errors that'll come from reversing over a century's worth of plus/minus signs in physics textbooks

[Faust]

There should be separate constants for each, in fact there probably is in most cases.

For instance the reduced planc's constant (h/2pi) is used all over the gaff in Quantum mechanics, but you still have h when you need it for other situations.

[Cramulus]

this is pretty much an aesthetic choice, right? does using tau instead of pi change any calculations?

[Fractalbeard]

No, it really doesn't. The only true benefit is saving space and energy when writing.

Ok, maybe someone also finds it easier to conceptualize.

[Faust]

this is pretty much an aesthetic choice, right? does using tau instead of pi change any calculations?

Reduced complexity in equations. Less chances of error.

For instance the Schrodingers wave equation for the hydrogen atom in its general form is mostly symbols standing in for more complex elements and it is still fifteen or so elements long.

[Cuddlefish]

Before last semester, I wouldn't have cared about this, or seen it as relevent to my life, but after crunching calculations in my astronomy class (a feild which I plan on persuing) the use of Tau makes a lot of sense. Sure, it doesn't have any real bearing on how you do the math, but keeping things organized and in the simplest terms possible makes things all the more easy to deal with. Only problem: My calc doesn't have a "Tau" key...

[whenhellfreezes]

I think that both are useful. Also so long as you define your terms properly its really just a matter of language and semantics. Thus I could see each being used where it is conceptually useful to do so.

[Lord Cataplanga]

Before last semester, I wouldn't have cared about this, or seen it as relevent to my life, but after crunching calculations in my astronomy class (a feild which I plan on persuing) the use of Tau makes a lot of sense. Sure, it doesn't have any real bearing on how you do the math, but keeping things organized and in the simplest terms possible makes things all the more easy to deal with. Only problem: My calc doesn't have a "Tau" key...

My cheap calculator has a "memory" button, and enough memory to hold 8 variables. I use those to store the charge of an electron, the speed of light, or whatever constant I need at the moment, but one of those variables always holds the value 2pi.

[Freeky]

Math cheats.  End of story.

[Rumckle]

Before last semester, I wouldn't have cared about this, or seen it as relevent to my life, but after crunching calculations in my astronomy class (a feild which I plan on persuing) the use of Tau makes a lot of sense. Sure, it doesn't have any real bearing on how you do the math, but keeping things organized and in the simplest terms possible makes things all the more easy to deal with. Only problem: My calc doesn't have a "Tau" key...

My cheap calculator has a "memory" button, and enough memory to hold 8 variables. I use those to store the charge of an electron, the speed of light, or whatever constant I need at the moment, but one of those variables always holds the value 2pi.

Damn, that's a good idea, why didn't I think of that?