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.
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.
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.
Isn't this all a bit like trying to prove that 1 is more fundamental than 2?
pi is the area constant.
(pi)(r)^2
Quote from: Prelate Diogenes Shandor on July 25, 2011, 03:10:52 AM
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 (http://www.math.utah.edu/~palais/pi.html)
pi is (still) wrong (http://www.youtube.com/watch?v=jG7vhMMXagQ) (video)
Quote from: BabylonHoruv on July 25, 2011, 05:55:33 AM
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 :lol:
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.
this is pretty much an aesthetic choice, right? does using tau instead of pi change any calculations?
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.
Quote from: Cramulus on July 25, 2011, 02:24:54 PM
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.
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...
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.
Quote from: Cuddleshift on July 25, 2011, 06:30:14 PM
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.
Math cheats. End of story.
Quote from: Lord Cataplanga on July 27, 2011, 05:48:46 AM
Quote from: Cuddleshift on July 25, 2011, 06:30:14 PM
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?
They should come up with a name for "two times the radius".
Quote from: Jerry_Frankster on July 27, 2011, 06:08:50 PM
They should come up with a name for "two times the radius".
The diameter?
(http://i283.photobucket.com/albums/kk316/Jerry_Frankster/724370405-they_live_deal_w_It.gif)
Before I try reading this, let me ask, is it even possible for me to understand this if I am no good at math?
Quote from: Guybrush on August 03, 2011, 02:25:27 AM
Before I try reading this, let me ask, is it even possible for me to understand this if I am no good at math?
You mean highschool geometry?
I never learned about Tau in geometry.
Quote from: Jenkem and SPACE/TIME on August 03, 2011, 02:31:30 AM
I never learned about Tau in geometry.
From what I gather, Tau is suggested as a stand-in for 2pi, and is not currently taught as a variable at any level.
Quote from: COL Coyote on August 03, 2011, 02:30:21 AM
Quote from: Guybrush on August 03, 2011, 02:25:27 AM
Before I try reading this, let me ask, is it even possible for me to understand this if I am no good at math?
You mean highschool geometry?
Yeah, that.
I know what pi is,
and I recall 2pi coming up sometimes in formulae [that's a lie, I don't recall anything from high school geometry]. But skimming the article just now it doesn't look like anything I can comprehend. Why do we need tau when it is the same as 2pi? What's wrong with just using 2pi?
Is this basically an aesthetic thing?
Quote from: Guybrush on August 03, 2011, 02:38:19 AM
Quote from: COL Coyote on August 03, 2011, 02:30:21 AM
Quote from: Guybrush on August 03, 2011, 02:25:27 AM
Before I try reading this, let me ask, is it even possible for me to understand this if I am no good at math?
You mean highschool geometry?
Yeah, that.
I know what pi is, and I recall 2pi coming up sometimes in formulae [that's a lie, I don't recall anything from high school geometry]. But skimming the article just now it doesn't look like anything I can comprehend. Why do we need tau when it is the same as 2pi? What's wrong with just using 2pi?
Is this basically an aesthetic thing?
Numbers get lost very easily.
What does that mean?
Quote from: Guybrush on August 03, 2011, 02:47:05 AM
What does that mean?
It means exactly what he said.
If you're trying to solve a long ass equation with variables up the yin yang, it's really easy to forget about a variable somewhere and get it all fucked up.
Quote from: Guybrush on August 03, 2011, 02:47:05 AM
What does that mean?
You could: do the operations wrong, mix up numbers, forget a number.
Non-number variables and constants tend to be a lot less prone to running away.
Quote from: Jenkem and SPACE/TIME on August 03, 2011, 02:48:30 AM
Quote from: Guybrush on August 03, 2011, 02:47:05 AM
What does that mean?
It means exactly what he said.
If you're trying to solve a long ass equation with variables up the yin yang, it's really easy to forget about a variable somewhere and get it all fucked up.
Right, I get you.
Quote from: Jenkem and SPACE/TIME on August 03, 2011, 02:50:29 AM
Quote from: Guybrush on August 03, 2011, 02:49:46 AM
Quote from: Jenkem and SPACE/TIME on August 03, 2011, 02:48:30 AM
Quote from: Guybrush on August 03, 2011, 02:47:05 AM
What does that mean?
It means exactly what he said.
Could you explain it in a way that makes sense?
See edit.
I did:)
I understand better. It's not so much aesthetic as it is practical, to prevent human error when dealing with two signs instead of one. Is that the gist?
Quote from: Faust on July 25, 2011, 04:05:13 PM
Quote from: Cramulus on July 25, 2011, 02:24:54 PM
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.
I've been guilty of dropping factors all over quantum and probability homeworks/tests. 1/sq(2pi) tends to get rewritten as 1/sq(pi) a lot when I do it.
Quote from: Guybrush on August 03, 2011, 02:51:26 AM
Quote from: Jenkem and SPACE/TIME on August 03, 2011, 02:50:29 AM
Quote from: Guybrush on August 03, 2011, 02:49:46 AM
Quote from: Jenkem and SPACE/TIME on August 03, 2011, 02:48:30 AM
Quote from: Guybrush on August 03, 2011, 02:47:05 AM
What does that mean?
It means exactly what he said.
Could you explain it in a way that makes sense?
See edit.
I did:)
I understand better. It's not so much aesthetic as it is practical, to prevent human error when dealing with two signs instead of one. Is that the gist?
Yah.
Well, I like it. Makes sense to me.
I'm kind of surprisxsed tau doesn't already stand for something, though. I'd have figured the entire greek alphabet had been taken by now.
It stands for various things, in fact pretty much every letter has more than one meaning depending on the context (not to mention differences between capital and lower case). Pi also has a few meanings (though less than tau and also times when pi does stand for something it is less likely to be in an equation that requires 3.14 or 2*3.14).
http://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering#.CE.A4.CF.84_.28Tau.29
So, for practical purposes, tau = 6.28?
Quote from: BabylonHoruv on July 25, 2011, 05:55:33 AM
pi is the area constant.
(pi)(r)^2
And area is a hell of a lot more relevant than circumfrence!