What is the fastest way to get the value of π?

Question

I\'m looking for the fastest way to obtain the value of π, as a personal challenge. More specifically, I\'m using ways that don\'t involve using #define constan

Answer 1

Here's a general description of a technique for calculating pi that I learnt in high school.

I only share this because I think it is simple enough that anyone can remember it, indefinitely, plus it teaches you the concept of "Monte-Carlo" methods -- which are statistical methods of arriving at answers that don't immediately appear to be deducible through random processes.

Draw a square, and inscribe a quadrant (one quarter of a semi-circle) inside that square (a quadrant with radius equal to the side of the square, so it fills as much of the square as possible)

Now throw a dart at the square, and record where it lands -- that is, choose a random point anywhere inside the square. Of course, it landed inside the square, but is it inside the semi-circle? Record this fact.

Repeat this process many times -- and you will find there is a ratio of the number of points inside the semi-circle versus the total number thrown, call this ratio x.

Since the area of the square is r times r, you can deduce that the area of the semi circle is x times r times r (that is, x times r squared). Hence x times 4 will give you pi.

This is not a quick method to use. But it's a nice example of a Monte Carlo method. And if you look around, you may find that many problems otherwise outside your computational skills can be solved by such methods.