Tau A Mathematical Constant (original) (raw)

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 2pi to calculate it std::cout << "The value of tau (using 2pi) 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 2pi) is : ",end="") print (math.pi2)

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 2pi to calculate it console.log("The value of tau (using 2pi) 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 : https://math.fandom.com/wiki/Tau\_(constant)