Created
July 30, 2012 13:02
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compute pi by Monte-Carlo method.
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=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}" |
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