# 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); `

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)

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