Some mathematicians believe pi should be replaced by tau as the mathematical constant of a circle. What do you think? Is tau a better circle constant? Or would tau bring more disadvantages than advantages?
Some mathematicians believe pi should be replaced by tau as the mathematical constant of a circle. What do you think? Is tau a better circle constant?
Or would tau bring more disadvantages than advantages? 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. 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 :-)then the circle constant must be equal to √piI can see it now. Europe and Asia will accept the logic of this argument. Gradually- every nation on Earth will follow suit. 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. 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, but Gamma=√pi. Again, the square root of pi on its own appears intimately connected to the number 1, suggesting that √pi is the deeper constant.
S_{n-1}=\frac{2\pi^{n/2}}{\Gamma}r^{n-1} The recurring universal quantity here is really √pi. If this constant were instead defined directly as a fundamental constant “c,” where:No awkward square roots remain for either across arbitrary dimensions . 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:That reinterpretation may initially feel less intuitive, but that is a minor issue compared to identifying which constant is truly fundamental across many formula. I have published on ResearchGate a paper 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.
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