τ as a circle constant

[mearo]

We are arguing if pi or tau is the better circle constant

 

Well then that is a 100% aesthetic argument you guys are having. Neither one is going to make math better. The math is the same, the only difference is ease of use or beauty.

It's then not surprising these arguments still go on without any resolution.

Because the idea that a resultion is needed in the first place is just a fabrication brought on by all the hype surrounding pi and tau.

 

I still hold the position I put forth in my previous post. Use which ever one you find suits you best in any particular situation. You don't have to pick one, this isn't a battle. Maybe you'll find tau suits you better in the majority of cases... maybe even always.. Ok, so use tau then. It's not going to cause any confusion if we have two circle constants and people use different ones, and using tau instead of pi isn't going to give you any deeper insight into anything.

 

 

The guy at www.tauday.org does make some good points...

 

The title of the site say "pi is wrong". That's a pretty stupid thing to start off with.

Edited September 16, 2013 by mearo

[Euler's Identity]

It doesn't really matter all that much, When working with unit circles and angles I find Tau is easier to work with and more intuitive, but if you want the circumfrence of a circle you can use pi. I prefer pi when I'm converting degrees and radians, after which I can easily translate to Tau if I was translating to radians. The mental translation is quite simple.

[imatfaal]

!

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[Amaton]

 

Well then that is a 100% aesthetic argument you guys are having. Neither one is going to make math better. The math is the same, the only difference is ease of use or beauty.

 

True. This discussion isn't really exclusive to mathematical aesthetic. What do you say about pedagogy? Public school students in the US begin learning trigonometry and radian geometry in high school (freshman year at the earliest AFAIK). There has always been some initial confusion with learning radians in multiples of pi, having to wrap one's head around pesky factors that seem almost extraneous. For most students in accelerated curricula, this almost never turns out to be problematic later on, but it is a slight pedagogical issue nonetheless. Do I think it merits a complete overhaul of which constant to use? Certainly not -- but it's still something to consider.

 

 

The title of the site say "pi is wrong". That's a pretty stupid thing to start off with.

 

It's more of a literary device than a serious, objective statement. The author did not intend anything "stupid" by saying that and indeed elaborates on it.

Edited September 16, 2013 by Amaton

[Euler's Identity]

 

True. This discussion isn't really exclusive to mathematical aesthetic. What do you say about pedagogy? Public school students in the US begin learning trigonometry and radian geometry in high school (freshman year at the earliest AFAIK). There has always been some initial confusion with learning radians in multiples of pi, having to wrap one's head around pesky factors that seem almost extraneous. For most students in accelerated curricula, this almost never turns out to be problematic later on, but it is a slight pedagogical issue nonetheless. Does it merit a complete overhaul of which constant to use. Certainly not -- but it's still something to consider.

 

 

True. Messing around with radians in multiples of Pi was SOMEWHAT annoying but I got familiar with it and got over it very quickly (I am 15), but as I said Tau is more intuitive on the unit circle.

[John Cuthber]

Since nobody seems able to agree whether we should use pi or 2pi (or, if you prefer, tau or half tau), I propose as a compromise we use the symbol Ѯ to represent 1.5 pi.

It's part of the early cyrillic alphabet and annoyingly difficult to write.

I would have suggested this but that would be silly because the noodles are not round.

 

http://en.wikipedia.org/wiki/Biangbiang_noodles

[Euler's Identity]

 

I suggest this actually, smoother strokes!

[Amaton]

 

I suggest this actually, smoother strokes!

 

Repainting the Mona Lisa seems a bit easier...

 

Okay, how about the harmonic mean of [math]\pi[/math] and [math]\tau[/math]? Love and peace, right guise?

[Euler's Identity]

 

Repainting the Mona Lisa seems a bit easier...

 

Okay, how about the harmonic mean of [math]\pi[/math] and [math]\tau[/math]? Love and peace, right guise?

 

Yeah that would be extremely intuitive haha, some weird fraction being the radian measurement for 90 degrees lol

[Amaton]

 

Yeah that would be extremely intuitive haha, some weird fraction being the radian measurement for 90 degrees lol

 

Maybe not so bad. [math]H(\pi,\tau)=\dfrac{2}{\frac{1}{\pi}+\frac{1}{\tau}}=\frac{4}{3}\pi=\frac{2}{3}\tau[/math].

 

Ah! Let's denote this constant [math]\eta[/math]. The volume of the space enclosed by a sphere is [math]V=\eta r^3[/math]. Now where's my Nobel Prize?

[Euler's Identity]

 

Maybe not so bad. [math]H(\pi,\tau)=\dfrac{2}{\frac{1}{\pi}+\frac{1}{\tau}}=\frac{4}{3}\pi=\frac{2}{3}\tau[/math].

 

Ah! Let's denote this constant [math]\eta[/math]. The volume of the space enclosed by a sphere is [math]V=\eta r^3[/math]. Now where's my Nobel Prize?

 

Certainly would be helpful in other areas of mathematical computation, I'd use it when it was helpful, and otherwise use pi or tau when that's helpful.

[Endercreeper01]

 

Certainly would be helpful in other areas of mathematical computation, I'd use it when it was helpful, and otherwise use pi or tau when that's helpful.

I agree

 

Maybe not so bad. [math]H(\pi,\tau)=\dfrac{2}{\frac{1}{\pi}+\frac{1}{\tau}}=\frac{4}{3}\pi=\frac{2}{3}\tau[/math].

 

Ah! Let's denote this constant [math]\eta[/math]. The volume of the space enclosed by a sphere is [math]V=\eta r^3[/math]. Now where's my Nobel Prize?

That constant would be the sphere constant