compute pi by Monte-Carlo method.

mc-pi.rb

=begin 
Find pi by the Monte-Carlo method.

area of a circle = pi r^2
area of a square = (2r)^2 = 4 r^2

Perform random uniform sampling between -1 and 1.
The proportion of points in the unit circle is:

p = (pi r^2) / (4r^2)

So pi = 4.0 * p
=end


N = 1000000

n_circle = 0
n_total = 0

N.times do
  x = rand * 2 - 1
  y = rand * 2 - 1

  # equation of the unit circle
  if x ** 2 + y ** 2 < 1
    n_circle += 1
  end
  
  n_total += 1
end

puts "pi = #{4.0 * n_circle / n_total}"