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# Tau – A Mathematical Constant

• Last Updated : 27 Jan, 2023

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 Circumference 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.

## C++

 `#include ``#include ` `int` `main()``{``  ``// C++ has no inbuilt tau but has inbuilt pi in cmath library``  ``// std::cout << M_PI; // this prints the value of pi``  ``// but no tau, so we can use the formula 2*pi to calculate it``  ``std::cout << ``"The value of tau (using 2*pi) is: "` `<< M_PI * 2 << std::endl;``  ``return` `0;``}``// This code contributed by Ajax`

## Java

 `/*package whatever //do not write package name here */``import` `java.io.*;``import` `java.util.*;``class` `GFG {``  ``public` `static` `void` `main(String[] args)``  ``{``    ``// java has no inbuilt tau but has inbuilt pi in math library``    ``// System.out.println(""+Math.PI); this print value``    ``// of pi``    ``// but no tau thus for using it we can use formula``    ``// for that``    ``System.out.println(``      ``"The value of tau (using 2*pi) is :  "``      ``+ Math.PI * ``2``);``  ``}``}`

## Python3

 `# 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: 6.28319
```

Time Complexity: O(1)
Auxiliary Space: O(1)
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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