Question

The area of a circle is defined as r^2. Estimate to 3 decimal places using a monte carlo method.

Answer 1

def pi_estimation(r=5)

inside =0.0

outside = 0.0

total = 0.0

rnd = Random.new

for i in 1 ... 10000

x = rnd.rand(-1*inside..inside)

y = rnd.rand(-1*inside..inside)

measure = distance(x, y)

if measure > inside

outside += 1

else

inside += 1

end

end

total = outside + inside

return (4 * (inside / total)).to_f()

end

def distance(x1, y1, x=0, y=0)

x_diff = x1 - x

y_diff = y1 - y

x_diff *= x_diff

y_diff *= y_diff

return Math.sqrt(x_diff + y_diff)

end

puts '%.2f' % pi_estimation()