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Tau – A Mathematical Constant

• Last Updated : 18 Mar, 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);`

C#

 `using` `System;`   `class` `GFG {` `    ``public` `static` `void` `Main()` `    ``{` `        ``// C# has no inbuilt tau but has inbuilt pi` `        ``// in Math library` `        ``// Console.WriteLine(Math.PI); this print` `        ``// value of pi` `        ``// but no tau thus for using it we can use` `        ``// formula for that` `        ``Console.WriteLine(``"The value of tau "` `+` `                          ``"(using 2*pi) is :  {0}"``,` `                          ``Math.PI * 2);` `    ``}` `}`   `// This code is contributed by surajrasr7277`

Javascript

 `// JavaScript has no inbuilt tau but has inbuilt pi in Math library` `// console.log(Math.PI); // this prints the value of pi` `// but no tau, so we can use the formula 2*pi to calculate it` `console.log(``"The value of tau (using 2*pi) is: "` `+ (Math.PI * 2));`

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