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);


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)

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

This article is attributed to GeeksforGeeks.org

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