General Discussion > Mathematics and Statistics

Tau versus Pi

**eejmensenikbenhet**:

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 ?

**hemmond**:

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...

**eejmensenikbenhet**:

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.

**Taronyu Leleioae**:

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.

**hemmond**:

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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