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# Numerical integration to calculate value of pi
from pylab import *

r = 1.0                      # radius of circle
dx = .05                     # integration delta x
x = arange(0, r+dx, dx)      # array ox x-coordinates
y = sqrt(r**2 - x**2)        # equation of circle, r^2 = x^2 + y^2
plot(x,y, 'x-')
show()

N = len(y)
A = 0.0
for k in range(N-1):                 # N-1 trapezoids
at = (y[k] + y[k+1])* dx/2   # area of one trapezoid
A += at                                              # add up the areas

print A*4, pi                # compare area of circle calculated and pi*r^2