τ as a circle constant

[Endercreeper01]

There is a website named tauday.com and it was mad by a guy who thinks τ should be the circle constant. I agree with him, but what do you guys think?

[ajb]

[math]2 \pi[/math] does seem to be quite a natural thing to consider...

[studiot]

 

mad by a guy

 

mad indeed.

 

Take a rod, tube, pipe or other object of circular cross section.

 

Tell me how to measure its radius?

 

The practical world out there works in diameters because that is what a pair of calipers measures.

[imatfaal]

If we were starting from scratch then perhaps - but we are not. And Studiot's point is very well made; maybe its a pure and applied sort of thing

[md65536]

Take a rod, tube, pipe or other object of circular cross section.

 

Tell me how to measure its radius?

 

The practical world out there works in diameters because that is what a pair of calipers measures.

It's not about diameter vs radius. Pi occurs in plenty of formulas that don't use diameter. Many of them use radius, and nobody advocates using diameter instead of radius in all formulas simply "because the world works in diameters", or because diameter is easier for the plumbers. Edited August 29, 2013 by md65536

[studiot]

 

It's not about diameter vs radius. Pi occurs in plenty of formulas that don't use diameter. Many of them use radius, and nobody advocates using diameter instead of radius in all formulas simply "because the world works in diameters", or because diameter is easier for the plumbers.

 

 

So what do you use pi for?

 

As a matter of interest is 2pi an even number and is pi even or odd?

Edited August 29, 2013 by studiot

[md65536]

So what do you use pi for?

 

As a matter of interest is 2pi an even number and is pi even or odd?

It's irrational not an integer, the question doesn't make sense.

 

I use it for the usual stuff... Riemann zeta functions and Gaussian integrals etc.

 

Ok truthfully: the last time I remember using pi was dealing with angles between vectors, in radians. Of which there are 2pi = tau per revolution. (Or, the maximum normalized angle is pi, so it's not like using one of pi or tau is always better than the other.)

Edited August 29, 2013 by md65536

[studiot]

Is your interest in doubling the value of the constant (pi is transcendental, not irrational) aestetic, perhaps because there are 2pi radians in a circle?

[imatfaal]

eulers identity would look lot less cool with tau over two.

 

And at the risk of turning a pretty silly thread even more pedantic pi is irrational - all real transcendentals are irrational

[Endercreeper01]

eulers identity would look lot less cool with tau over two.

If you solve the equation, e^iτ=1

 

a pretty silly thread

How is this silly?

 

Is your interest in doubling the value of the constant

Yes

 

mad indeed.

 

Take a rod, tube, pipe or other object of circular cross section.

 

Tell me how to measure its radius?

 

The practical world out there works in diameters because that is what a pair of calipers measures.

So What if we can only measure the diamater directly? The radius shows up in almost all of our equations for circles.

If we were starting from scratch then perhaps - but we are not.

We can still slowly bring in tau

[studiot]

Circles are only two dimensional.

 

We live in a three dimensional world.

 

There may be 2pi radians in a two dimensional circle but how many steradians are there in a sphere?

[Endercreeper01]

Circles are only two dimensional.

 

We live in a three dimensional world.

 

There may be 2pi radians in a two dimensional circle but how many steradians are there in a sphere?

There are 2tau steradians in a sphere, and 2tau should be the sphere constant.

[studiot]

So there is no gain in doubling pi, you still have the factor of 2 around.

 

What about all the electrodynamic equations that contain some multiple of pi somewhere?

[md65536]

So there is no gain in doubling pi, you still have the factor of 2 around.

 

What about all the electrodynamic equations that contain some multiple of pi somewhere?

And pi = tua/2 still has a factor of 1/2 around.

 

Try reading this before assuming the idea is worthless: http://www.math.utah.edu/~palais/pi.pdf

There are several examples of how tau is a more natural fit in various equations. Do you have a counter example where using 2pi would obscure how and why the constant fits into the equation? Is there an example where the occurrence of pi makes intuitive sense but a version using 2pi would not?

 

Sometimes the factor of 1/2 makes the occurrence of pi clearer. For example, A = pi r^2, or 1/2 tau r^2. The one with pi seems simpler, however it hides the factor of 1/2 that naturally comes up when deriving the area with integration, similar to how a factor of 1/2 makes intuitive sense in a formula for triangle area.

 

 

The only convincing argument against tau that I've seen here is that the use of pi is an established convention and it would be too much trouble to change that all (and to make an electron's charge called "positive", and any other such misleading conventions). And I agree with that.

 

I think that most people who don't really deal with pi much just think of it as a weird constant that just happens to have a strange value. Perhaps it would make more intuitive sense to people if everything was based on tau instead (meaning "one turn" as used in the pdf above). OR perhaps that intuitive sense only comes by really considering the meaning of tau vs. pi, and would be missed if one or the other is simply used without consideration of why.

[Endercreeper01]

So there is no gain in doubling pi, you still have the factor of 2 around.

 

What about all the electrodynamic equations that contain some multiple of pi somewhere?

Im talking about with circles then tau should be the circle constant and 2tau should be the sphere constant

And pi = tua/2 still has a factor of 1/2 around.

 

Try reading this before assuming the idea is worthless: http://www.math.utah.edu/~palais/pi.pdf

There are several examples of how tau is a more natural fit in various equations. Do you have a counter example where using 2pi would obscure how and why the constant fits into the equation? Is there an example where the occurrence of pi makes intuitive sense but a version using 2pi would not?

 

Sometimes the factor of 1/2 makes the occurrence of pi clearer. For example, A = pi r^2, or 1/2 tau r^2. The one with pi seems simpler, however it hides the factor of 1/2 that naturally comes up when deriving the area with integration, similar to how a factor of 1/2 makes intuitive sense in a formula for triangle area.

 

 

The only convincing argument against tau that I've seen here is that the use of pi is an established convention and it would be too much trouble to change that all (and to make an electron's charge called "positive", and any other such misleading conventions). And I agree with that.

 

I think that most people who don't really deal with pi much just think of it as a weird constant that just happens to have a strange value. Perhaps it would make more intuitive sense to people if everything was based on tau instead (meaning "one turn" as used in the pdf above). OR perhaps that intuitive sense only comes by really considering the meaning of tau vs. pi, and would be missed if one or the other is simply used without consideration of why.

I agree with what you said, but we can just slowly bring tau in.

[HalfWit]

I'm a tau-ist. One-quarter of the way around the unit circle is ... pi/2. I have to stop and think about that every single time.

 

It would be more natural to say that one-quarter of the way around is tau/4. One less mental translation to have to make every single time. You'd save a lot of cpu cycles in your head.

 

I have a theory on how this came about. In ancient times, math was developed to keep track of the crops. Farmers needed to know how big their field was. So diameters were important.

 

In our modern, abstract world, what's important is the unit circle in the plane. So much math and technology comes from the study of functions on the unit circle. From advanced abstract math to the digital signaling that underlies all our communications, the unit circle is where it all starts. It's the radius that's important, not the diameter.

 

As in so many aspects of modern life, we are stuck with a system designed for a world we no longer live in.

Edited September 1, 2013 by HalfWit

[ADreamIveDreamt]

I love invisible circles. I also love appie pie.

[Bignose]

As in so many aspects of modern life, we are stuck with a system designed for a world we no longer live in.

Sheesh, this seems awfully melodramatic for a constant. I just don't see how renaming one constant = 2 times some other constant will make us more 'modern'.

 

I guess I feel that it shouldn't be that hard to think around an arbitrary constant that's been generally agreed upon.

 

If you look around you, they are everywhere.

 

Why do we buy eggs in dozens? Why Liters? or Gallons? Why are 2x4s really 1 1/2" by 3 1/2"? And so on. It is just an arbitrary constant that everyone agreed upon so that everyone knew what was being said. It really isn't anything more than that, to me.

[md65536]

Why do we buy eggs in dozens? Why Liters? or Gallons? Why are 2x4s really 1 1/2" by 3 1/2"? And so on. It is just an arbitrary constant that everyone agreed upon so that everyone knew what was being said. It really isn't anything more than that, to me.

I don't really know enough about pi to care as much as others (and I think it would be a waste to use two Greek letters for essentially the same constant), but...

 

Imagine if you bought eggs in packages of 24 half-eggs and you'll see that counting eggs in units of "1 egg" makes the most sense. If a unit circle had a diameter of 1 then I'd probably think that pi makes more sense than tau.

[studiot]

If all you really want is to denote turns (circles), then why 2pi?

 

Why not much more simply 1 turn, 2 turns 3.378 turns...............?

 

But wait, engineers already do that , and have a symbol for it - usually n or N.

 

So what rpm does the dial on your dash show?

 

Or what is the transformer turns ratio ?

 

And then, of course, you could decimalise it.

 

But wait again, europeans already do that, they call them grads.

Edited September 1, 2013 by studiot

[md65536]

If all you really want is to denote turns (circles), then why 2pi?

 

Why not much more simply 1 turn, 2 turns 3.378 turns...............?

Because pi (or tau) is a ratio, whose value has meaning. You lose the meaning by choosing a value of 1 for the constant.

[studiot]

Since you have highlighted my caveat, you presumably read it.

 

A non integer ratio or any other number makes less sense than unity as the basis for counting turns.

[Endercreeper01]

If all you really want is to denote turns (circles), then why 2pi?

 

Why not much more simply 1 turn, 2 turns 3.378 turns...............?

 

But wait, engineers already do that , and have a symbol for it - usually n or N.

 

So what rpm does the dial on your dash show?

 

Or what is the transformer turns ratio ?

 

And then, of course, you could decimalise it.

 

But wait again, europeans already do that, they call them grads.

Not just turns, we are saying it is more natural to use tau

[studiot]

 

Not just turns

 

Are you trying to replace the perfectly servicable number 1 with tau?

[md65536]

Since you have highlighted my caveat, you presumably read it.

 

A non integer ratio or any other number makes less sense than unity as the basis for counting turns.

You must understand though that these constants represent the relationship between "turns" or angles or circumference etc, and radius or diameter.

 

As you argue for turns in units of 1, with radius in units of 1 the relationship is tau. But you also argue that the world works in diameters, and with diameter of 1 the relationship is pi. However, a unit circle remains defined with a radius of 1 and a diameter of 2, and as you say "any other number makes less sense than unity." So there is a discord between the choice of radius as the unit measurement, and pi as the constant.

 

It seems to me that all along you've been trying to show that the entire discussion is pointless by bringing up examples of pointless arguments (like whether pi is even or odd and whether tau is more aesthetically pleasing in that regard), while ignoring the actual arguments supporting tau.