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”.
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.
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)
This article is contributed by Manjeet Singh. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Kaprekar Constant
- Find Index of given fibonacci number in constant time
- Check if two arrays are permutations of each other using Mathematical Operation
- Percentage increase in the cylinder if the height is increased by given percentage but radius remains constant
- Find the value of N XOR'ed to itself K times
- Game Theory (Normal-form Game) | Set 4 (Dominance Property-Pure Strategy)
- Goldbach's Weak Conjecture for Odd numbers
- Game Theory (Normal-form Game) | Set 5 (Dominance Property-Mixed Strategy)
- Find all the possible remainders when N is divided by all positive integers from 1 to N+1
- Count of primes below N which can be expressed as the sum of two primes
- Find the centroid of a non-self-intersecting closed Polygon
- Find N in the given matrix that follows a pattern
- Minimum cells to be flipped to get a 2*2 submatrix with equal elements
- Print all palindrome dates between the given years