Author Topic: Tau versus Pi  (Read 1698 times)

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Offline eejmensenikbenhet

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Tau versus Pi
« on: May 15, 2013, 07:55:02 pm »
I'm somewhat sure that you, math loving people, have heard of the debate among mathematicians and math enthusiasts concerning τ and π.
So... Time to extract your opinions, give me your arguments. I myself think that τ would make for an excellent circle constant.
It really is a simple question, thus I'll keep this post short:
   τ    or   π   ?
« Last Edit: May 16, 2013, 06:24:40 am by eejmensenikbenhet »

Offline hemmond

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Re: Tau versus Pi
« Reply #1 on: May 16, 2013, 10:12:01 am »
I really like pi. :) If you look on area of circle (pi*r^2) will have to be (tau/2)*r^2 and imo I don't know many math formulas where you use 2*pi... usualy only pi or some powers of pi...
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Offline eejmensenikbenhet

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Re: Tau versus Pi
« Reply #2 on: May 16, 2013, 12:31:14 pm »
The area of a circle, good old Archimedes gave us a way to calculate it. I'll explain how the formula you mention was created.
Archimedes proved that the area of a circle is the same as the area of a triangle with a height equal to the radius of the circle and a base equal to the circumference. If we then apply the formula to calculate this triangle's area, we get:
      A = ½ · b · h = ½ · C · r
1.   A = ½Cr
Since the circumference is actually the radius times 2π, we get this:
      A = ½ · 2 · π · r · r = π · r2
2.   A = πr2
This formula is hiding the roots of the formula, now, if you were to use τ instead we would get the following:
      A = ½ · τ · r · r = ½ · τ · r2
3.   A = ½τr2

While you may have gotten used to the looks of formula 2, formula 3 doesn't look too weird when compared to some other quadratic formulas:
Kinetic energy:   Ekin = ½mv2
Distance fallen:   y = ½gt2

Edit: forgot to mention this: as you see, 2π does appear more often then you think, even the formula you mentioned was formed using 2π. It is present but most of the time it is obscured.
« Last Edit: May 16, 2013, 12:39:31 pm by eejmensenikbenhet »

Offline Taronyu Leleioae

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Re: Tau versus Pi
« Reply #3 on: May 16, 2013, 12:39:18 pm »
My vote is pi...


While one could adapt a change for circles, it wouldn't stop there...

In physics, quite a few of my equations using circular formulas were all with pi.

There is nothing wrong with Tau, but you aren't changing just one equation, you are impacting what was learned through many equations.

Offline hemmond

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Re: Tau versus Pi
« Reply #4 on: May 16, 2013, 02:16:03 pm »
Okay, you've got the point, but honestly π · r2 is easier to remember than ½ · τ · r2 :)

And also, when you use tau, you have to reprogram a lot of scientific calculators with pi. :) They have button for pi, but not for tau. :) And to insert equation with pi to calculator is easier than inserting it with tau and every tau replace with 2*pi... :D
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Offline eejmensenikbenhet

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Re: Tau versus Pi
« Reply #5 on: May 16, 2013, 02:21:16 pm »
And also, when you use tau, you have to reprogram a lot of scientific calculators with pi. :) They have button for pi, but not for tau. :) And to insert equation with pi to calculator is easier than inserting it with tau and every tau replace with 2*pi... :D
Auch, that one hurt... It was rather the point of this topic to get some arguments from both sides and this one is terrifyingly good. Thanks!

Offline hemmond

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Re: Tau versus Pi
« Reply #6 on: May 16, 2013, 02:32:29 pm »
And also, when you use tau, you have to reprogram a lot of scientific calculators with pi. :) They have button for pi, but not for tau. :) And to insert equation with pi to calculator is easier than inserting it with tau and every tau replace with 2*pi... :D
Auch, that one hurt... It was rather the point of this topic to get some arguments from both sides and this one is terrifyingly good. Thanks!

Yeah... Pi was popular sooner than tau... Also QWERTY/Z are standards and if you want something different, you're gonna have troubles. :)

But on the other hand, when you're doing maths on paper, tau is easier to write. :D Tau have one leg less than pi. :D :D :D
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Offline `Eylan Ayfalulukanä

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Re: Tau versus Pi
« Reply #7 on: May 16, 2013, 03:12:54 pm »
I will go with pi. I have pi memorized to about 55 places, give or take a few. (I need to work on that, after seeing 'The Life of Pi' ;) )

But tau gets used in a lot of places I run into. For instance, the electronic reactance formulas: Xl = 2piFL and Xc = 1/2piFC, two of the most important equations in electronics outside of Ohm's law. (F is frequency in Hz, C is capacitance in Farads, L is inductance in Henrys, Xl is inductive reactance in Ohms, Xc is capacitive reactance in Ohms) Closely related is the formula for resonant frequency F = 1/2pfSQRT(LC) Tau, as it were, shows up in a lot of electric formula because it has something to do with the complete cycle of a sine wave, which traverses through 360 degrees, or 2pi radians. 2piF in electronics is often refered to as lower case Omega, and is given in radians/second.

Then in quantum physics, is Planck's constant, the basic size of a quantum of energy. It is constant usually given as h. But like Tau, there is a shorthand for a frequently used derived valur of Planck's constant that actually involves tau. The 'reduced Planck's constant' is given as h-bar (an H with a little line drawn across the ascender), and the formyla is h-bar = h/2pi or h/tau.

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Offline eejmensenikbenhet

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Re: Tau versus Pi
« Reply #8 on: June 28, 2013, 12:50:17 pm »
Happy τ-day everybody!

 

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