# Tau – A Mathematical Constant

**What is Tau?**

The constant is numerically equal to** 2*pi (2 times pi)**, and with value approximately** 6.28**. The ratio equates to 2*C/D. Where C is circumference and D is diameter of circle.

**Applications of Tau **

- There are
**many expressions**that actually require**“2*pi” calculation**, having tau being equal to that simplifies them to great extent, for e.g**Cicumference of circle = 2*pi*r = tau*r**. - Concept of tau can be useful in
**angular measurements**like angles in radians, representing as a complete “one-turn” and cos,sine functions in trigonometry have period of tau. - These concepts can be useful for
**teaching geometry**as would reduce the confusion of using “pi” and “2*pi” at many applications and would help get rid of factor of 2. - Tau
**simplifies euler’s identity**by eradicating the factor of 2. - It is
**useful at many places where “2*pi” are used**such as fourier transforms, cauchy integral formula’s etc.

**Criticism against Tau**

- Since it
**contradicts with the symbols of torque, shear stress and time**, this symbol has been a lot of criticism. - We already had a ratio of “C/D” equal to pi, having another circle ratio with factor of two will create confusion in choice.
- There exist
**formulas which look more elegant as expression of “pi”**rather than tau, for example, area of circle = pi*r*r = (tau*r*r)/2, introducing an extra factor of “1/2”.

**Coding Prospects**

Since Programming has always been trying to match up with mathematical advancements, symbol of tau has been introduced as a constant in recent python 3.6 under the math module. Below is the illustration of it.

`# Python code to demonstrate the working ` `# of tau ` ` ` `import` `math ` ` ` `# Printing the value of tau using 2*pi ` `print` `(` `"The value of tau (using 2*pi) is : "` `,end` `=` `"") ` `print` `(math.pi` `*` `2` `) ` ` ` `# Printing the value of tau using in-built tau function ` `print` `(` `"The value of tau (using in-built tau) is : "` `,end` `=` `"") ` `print` `(math.tau); ` |

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Output:

The value of tau (using 2*pi) is : 6.283185307179586 The value of tau (using in-built tau) is : 6.283185307179586

**Note :** This code won’t work on Geeksforgeeks IDE as Python 3.6 is not supported.

**Reference : **http://math.wikia.com/wiki/Tau_(constant)

This article is contributed by **Manjeet Singh**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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