Kata

The aim of the kata is to try to show how difficult it can be to calculate decimals of an irrational number with a certain precision. We have chosen to get a few decimals of the number "pi" using the following infinite series (Leibniz 1646–1716):

PI / 4 = 1 - 1/3 + 1/5 - 1/7 + ... which gives an approximation of PI / 4.

http://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

To have a measure of the difficulty we will count how many iterations are needed to calculate PI with a given precision of epsilon.

There are several ways to determine the precision of the calculus but to keep things easy we will calculate PI within epsilon of your language Math::PI constant.

In other words, given as input a precision of epsilon we will stop the iterative process when the absolute value of the difference between our calculation using the Leibniz series and the Math::PI constant of your language is less than epsilon.

Your function returns an array or a string or a tuple depending on the language (See sample tests) with

• your number of iterations
• your approximation of PI with 10 decimals

Example :

Given epsilon = 0.001 your function gets an approximation of 3.140592653839794 for PI at the end of 1000 iterations : since you are within epsilon of Math::PI you return

iter_pi(0.001) --> [1000, 3.1405926538]

Notes :

Unfortunately, this series converges too slowly to be useful, as it takes over 300 terms to obtain a 2 decimal place precision. To obtain 100 decimal places of PI, it was calculated that one would need to use at least 10^50 terms of this expansion!

About PI : http://www.geom.uiuc.edu/~huberty/math5337/groupe/expresspi.html