Tau versus Pi

[Baby Astronaut]

Here's an article that backs up what ydoaPs said.

 

Kevin Houston, a mathematician at the University of Leeds in the U.K. who has made a YouTube video to explain all the advantages of tau over pi, said the most compelling argument for tau is that it is a much more natural number to use in the fields of math involving circles, like geometry, trigonometry and even advanced calculus.

 

"When measuring angles, mathematicians don't use degrees, they use radians," Houston enthusiastically told Life's Little Mysteries. "There are 2pi radians in a circle. This means one quarter of a circle corresponds to half of pi. That is, one quarter corresponds to a half. That's crazy. Similarly, three quarters of a circle is three halves of pi. Three quarters corresponds to three halves!"

 

"Let's now use tau," he continued. "One quarter of a circle is one quarter of tau. One quarter corresponds to one quarter! Isn't that sensible and easy to remember? Similarly, three quarters of a circle is three quarters of tau." Making tau equal to the full angular turn through a circle, he said, is "so easy and would prevent math, physics and engineering students from making silly errors."

.....

Indeed, other tau advocates have said they've noticed a significant improvement in the ability of students to learn math, especially geometry and trigonometry where factors of 2pi show up the most, when the students learn with tau rather than pi.

 

Though 2pi appears much more often in calculations than does pi by itself (in fact, mathematicians often accidentally drop or ad that extra factor of 2 in their calculations), "there is no need for pi to be eradicated," Houston said. "You might say I'm not anti-pi, I'm pro-tau. Hence, anyone could use pi when they had a calculation involving half of tau."

Edited June 30, 2011 by Baby Astronaut

[ewmon]

It seems to me that π was used originally because the diameter of an object was easiest to measure, along with its circumference, thus the calculation of 3.14159... (π).

 

The value of 2π does seem to occur much more frequently than π, so the use of τ might be in order. The difficulties I see is that τ is not as distinctive and, thus, not as easily recognizable as π (and π actually looks like two τ's stuck together, so there'll be some confusion about which one is twice the other).

 

So, call me old-fashioned, but I think we should stick with π. I mean, for cryin' out loud, look what the revisionists have done to Pluto. (And what'll they say next, that Donald isn't really a duck?!)

Edited June 30, 2011 by ewmon

[baxtrom]

Then by choosing prinhciple axes we can make [math]\tau[/math] go away. So [math]\pi[/math] is universal, but [math]\tau[/math] is just an artifact of the local coordinate system.

 

 

Yet the effective stress in pure shear is [math]2 \tau[/math] according to Henri Tresca. Since in engineering we use [math]2 \tau[/math] so often I think we should use a new symbol to avoid confusion. Perhaps [math]\pi[/math]?

[ajb]

Of course one should also note that the symbol [math]\pi[/math] is not just used for the "circle constant". Other uses I am aware of are

 

1. Projection of a fibre bundle [math]\pi:E \rightarrow M[/math].
   
2. Canonical momenta of a scalar field: [math]\pi = \partial_{t}\phi[/math].
   
3. The n-th homotopy group: [math]\pi_{n}[/math].
   
4. shorthand for Pi mesons:[math]\pi^{0}, \pi^{+},\pi^{-}[/math].
   

 

I have also used it in a manner similar to 2. as a "momenta" i.e. the (odd) fibre coordinates of a cotangent bundle over a (super)manifold. I am sure there are lots of other uses.

 

So, I would not worry about [math]\tau[/math] being used already, the context should make the meaning clear, to experts anyway.

Edited June 30, 2011 by ajb

[John Cuthber]

"It seems to me that π was used originally because the diameter of an object was easiest to measure, along with its circumference,"

Sure, it's perfectly easy to measure them both, but you can't use the same unit of length because pi is irrational the two measurements are incommensurate.

The same thing happens with tau.

Edited June 30, 2011 by John Cuthber

[DrRocket]

"It seems to me that π was used originally because the diameter of an object was easiest to measure, along with its circumference,"

Sure, it's perfectly easy to measure them both, but you can't use the same unit of length because pi is irrational the two measurements are incommensurate.

The same thing happens with tau.

 

Everyone in industry is familiar with the "pi-tape" which lets you measure the diameter or radius by measuring the circumference.

 

Training technicians to use a "tau-tape" would be costly and pointless, not to mention the need to change the name of the corporation that makes the gage.

 

So, I would not worry about [math]\tau[/math] being used already, the context should make the meaning clear, to experts anyway.

 

 

 

Not to mention the fact that most experts can multiply by 2.

[baric]

Everyone in industry is familiar with the "pi-tape" which lets you measure the diameter or radius by measuring the circumference.

 

Training technicians to use a "tau-tape" would be costly and pointless, not to mention the need to change the name of the corporation that makes the gage.

 

of course you are kidding! No corporation in its right mind would pass up the opportunity to resell an upgraded item to its entire customer base over a short period of time. If the conversion to tau was an actual possibility, "pi-tape" manufacturers would all be racing to be the first to sell the new tau-tapes.

 

 

edit: derp... I just looked at the product on the link.. there would be no change, lol.

Edited June 30, 2011 by baric

[Hal.]

Is this actually an argument in science , not about whether it is obviously the best thing to do or obviously not , rather ' who ' decides what the standard correct interpretations will be ? So , who wants tau as 2*pi , IUPAC , AMS , Girl Guides of New Zealand ?

Edited July 1, 2011 by Hal.

[DrRocket]

Is this actually an argument in science , not about whether it is obviously the best thing to do or obviously not , rather ' who ' decides what the standard correct interpretations will be ? So , who wants tau as 2*pi , IUPAC , AMS , Girl Guides of New Zealand ?

 

 

Good idea. Let's arrange for a convention with the Girl Guides of New Zealand, and the Swedish Bikini Team to discuss this issue. Don't forget the beer. I will be happy to represent the AMS, of which I am and have been a member for a long time. IUPAC doesn't get a vote, since this is not a question of chemical nomenclature. I intend to question the GGNZ and SBT at length, uncover the bare essentials and get to the bottom of the issue (and the bottom of the keg).

[mississippichem]

IUPAC doesn't get a vote, since this is not a question of chemical nomenclature.

 

Though I'm sure they will try. The IUPAC seems to always have too much to say about everything.

[ajb]

Is this actually an argument in science , not about whether it is obviously the best thing to do or obviously not , rather ' who ' decides what the standard correct interpretations will be ?

 

For notation and conventions, particularly with newly discovered things, someone will write an influential paper or a book and people will start to follow these. Trying to be consistent across a subject helps make work easier to read and understand. This aids the general dissemination. However, there are always different notation and conventions out there.

 

[math]\tau[/math] or [math]\pi[/math] is really "tongue-in-cheek". At most it could only ever be a conventional issue and nothing of any real significance.

 

 

So , who wants tau as 2*pi , IUPAC , AMS , Girl Guides of New Zealand ?

 

I am not sure that anyone does. But I second DrRockets proposal for an international conference to settle the issue. I also suggest that Hugh Hefner be contacted and asked to send a delegation to the conference.

 

Not to mention the fact that most experts can multiply by 2.

 

 

[TonyMcC]

There is one thing I discern through the general banter. Some people hold the view that mathematics would have been better served if the ratio circumference/radius had been adopted as a useful constant instead of circumference/diameter. Nobody seems to be saying that it is a good job that circumference/diameter was chosen rather than circumference/radius. From this I deduce that in historical times, for reasons appropriate to those times, an unfortunate choice was made. The best that can be said about pi is that it is so firmly entrenched that correcting this ancient poor choice just isn't worth the inconvenience this would cause.

By the way, if the Swedish Bikini Team accept an invitation to the proposed conference can I come as a neutral observer? I'll happily bring some beer!

[baxtrom]

There is one thing I discern through the general banter. Some people hold the view that mathematics would have been better served if the ratio circumference/radius had been adopted as a useful constant instead of circumference/diameter. Nobody seems to be saying that it is a good job that circumference/diameter was chosen rather than circumference/radius. From this I deduce that in historical times, for reasons appropriate to those times, an unfortunate choice was made. The best that can be said about pi is that it is so firmly entrenched that correcting this ancient poor choice just isn't worth the inconvenience this would cause.

By the way, if the Swedish Bikini Team accept an invitation to the proposed conference can I come as a neutral observer? I'll happily bring some beer!

 

The obvious advantage of using the diameter is that it is easier to measure than the radius. Pi was defined independently in different ancient cultures so the diameter seems to be a more natural definition of the size of a circle. Regarding the Swedish bikini team I believe they are only interested in circumferences and don't give a crap about diameters and radii.

[TonyMcC]

The obvious advantage of using the diameter is that it is easier to measure than the radius. Pi was defined independently in different ancient cultures so the diameter seems to be a more natural definition of the size of a circle. Regarding the Swedish bikini team I believe they are only interested in circumferences and don't give a crap about diameters and radii.

 

Can I change your first sentence slightly so that it is more in agreement with my thoughts and yet doesn't change its meaning? "The obvious advantage of using the diameter WAS that it WAS easier to measure than the radius". This could be a reasonable explanation of how the "unfortunate choice" was made.

[rktpro]

They say that tau makes it easy to measure angles of circle in radians. I don't really get it. Actually, above my schooling level!

Also, is tau really constant. I mean in Physics, it's variable. Isn't it?

[DrRocket]

They say that tau makes it easy to measure angles of circle in radians. I don't really get it. Actually, above my schooling level!

Also, is tau really constant. I mean in Physics, it's variable. Isn't it?

 

It is really constant. If you want to trce the definition back rigorously to the fundamental Zermelo Fraenkel axioms you can do that and bypass circles and geometry (it is still there if you dig hard enough). This can be easily done:

 

The series [math] \displaystyle \sum_{n=0}^ \infty \frac {(iz)^n}{n!}[/math] can be shown (see e.g. Real and Complex Analysis by Rudin) to define an entire periodic function and [math] \pi [/math] is defined to be one-half of the period. You are free to define [math] \tau = 2 \pi [/math] if you like.

 

The point is that this rigorous definition does not explicitly rely on geometry or trigonometry, so there is no question that pi is just a (constant) number.

Edited July 2, 2011 by DrRocket

[rktpro]

DrRocket,

In the formula of resistivity= m/ne^2*tau

Tau is average relaxation time here. And it is variable.

[ajb]

Also, is tau really constant. I mean in Physics, it's variable. Isn't it?

 

DrRocket,

In the formula of resistivity= m/ne^2*tau

Tau is average relaxation time here. And it is variable.

 

 

[math]\tau[/math] denoting the average relaxation time is a variable, i.e. does not have some fixed value (in some system of units). However [math]\tau = 2 \pi[/math] is not a variable.

 

[math]\tau[/math] would be used as a symbol for whatever you like, it then depends on the context if it is variable or not.

 

(I wonder if you are just pulling our leg here.)

[TonyMcC]

The confusion arises because both pi and tau are used as symbols for different things. If you google- Greek letters mathematics science engineering - you will easily find a comprehensive list.

[rktpro]

[math]\tau[/math] denoting the average relaxation time is a variable, i.e. does not have some fixed value (in some system of units). However [math]\tau = 2 \pi[/math] is not a variable.

 

[math]\tau[/math] would be used as a symbol for whatever you like, it then depends on the context if it is variable or not.

 

(I wonder if you are just pulling our leg here.)

 

No. I have respect for you both. I am just a kid of 15 and you are great minds. I am just like your student, sir.