Should mathematicians abandon pi?

As for Euler's formula, using Tau/2 would:

(1) possibly feel more natural, since Tau would be associated with a whole circle, so Tau/2 might more easily be associated with the half-circle through which the number 1 rotates.

(2) allow you get the first prime number into the formula, in addition to the other iconic things already there.

Using Tau would help with early childhood teaching. I suspect a lot of adults don't understand Pi today, because they never understood it in school. Starting a lesson by showing a kid a hexagon divided into six equilateral triangles, then drawing a circle around it and adding some discussion should make the learning very easy for just about any kid.

Tau is a good idea, but Pi is so engrained it would be hard to change. Tell you what, if you mathematicians can convince astrophysicists to let Pluto back into the family of planets, I'll support the change from Pi to Tau :-)

I agree with Leo Moorman.

Let b = half side length of square and q = "square constant".

Then the square perimeter is

Sp = 2*q*(q*b)

and square area is

Sa = (q*b)^2

If we want to calculate the circle circumference and area in a similar way

then the circle constant must be equal to √pi

Let r = half diameter (radius) of circle and c = circle constant c = √pi

Then the circle circumference is

Cp = 2*c*(c*r)

and circle area is

Ca = (c*r)^2

e^{i\tau/2} = -1

This is not sensible, It is much simpler to adopt the constant 7*pi = 22, called 'tudux'. Close enough for government work.

I can see it now. Europe and Asia will accept the logic of this argument. Gradually- every nation on Earth will follow suit.

Meanwhile - the US will refuse. just as they did when Carter tried to take us to the metric system.

Tau is a trending affectation. It's a new hat for the Kentucky Derby: flashy, new, and useful for less than a day. Establishing it would snarl mathematics unnecessarily.

Pi is in pizza. Where is tau?

But Feynman's favorite formula was e^i*pi =-1 which he said captured all that is important in math in one equation.

Kudos to those who want to redefine the fundamental constant pi. The issue is not merely historical context, or notation, but what constant is truly most fundamental in mathematics and physics.

At age 12, when studying probability, I was shocked to see the square root of pi appear in the normalization factor of the Gaussian distribution. Even more striking was that its proof requires extending the problem into two dimensions, where cylindrical symmetry naturally introduces pi. This suggested to me that √pi is more fundamental than pi itself, despite pi’s simpler geometric definition.

Later, learning about the Gamma function reinforced this idea. We have Gamma(1)=1, but Gamma(1/2)=√pi. Again, the square root of pi on its own appears intimately connected to the number 1, suggesting that √pi is the deeper constant.

The formulas for n-dimensional volume and surface area provide another indication:

V_n=\frac{\pi^{n/2}}{\Gamma(n/2+1)}r^n

and

S_{n-1}=\frac{2\pi^{n/2}}{\Gamma(n/2)}r^{n-1}

The recurring universal quantity here is really √pi. If this constant were instead defined directly as a fundamental constant “c,” where:

c=\sqrt\pi

then the formulas become cleaner:

V_n=\frac{c^n}{\Gamma(n/2+1)}r^n

and

S_{n-1}=\frac{2c^n}{\Gamma(n/2)}r^{n-1}

No awkward square roots remain for either across arbitrary dimensions (not just the two-dimensional cases).

The strongest argument that √pi is more fundamental than pi is that it can be defined entirely analytically, without first invoking the geometry of a circle. Using it, the familiar formulas for circumference and area in two dimensions simply become:

C=2c^2r

and

A=c^2r^2

That reinterpretation may initially feel less intuitive, but that is a minor issue compared to identifying which constant is truly fundamental across many formula.

The numerical value of √pi is 1.77245385091…

Why not use both?

Tune: 175 Piece's of Pi

https://suno.com/s/zjjEi4P2PODeddkk

I have published on ResearchGate a paper (as 'reprint' though it has been aired privately) titled 'Pi walks the Planck', that could support the view that 2*pi or its multiples appear in equations of physical significance, but if you put 2*pi in Euler's formula it loses the necessary identification of a quarter rotation with the square root of -1.