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a0589da | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | import numpy as np
import matplotlib.pyplot as plt
# Constants
num_samples = 1000000 # Number of random samples
radius = 1.0 # Radius of the circle
# Generate random points in the unit square [0, 1] x [0, 1]
x = np.random.uniform(-radius, radius, num_samples)
y = np.random.uniform(-radius, radius, num_samples)
# Count how many points fall inside the quarter circle
inside_circle = np.sum(x**2 + y**2 <= radius**2)
# Estimate pi using the ratio of points inside the circle to total points
pi_estimate = (inside_circle / num_samples) * 4
print(f"Estimated value of pi with {num_samples} samples: {pi_estimate}")
# Optional: Visualize the points
def plot_simulation(x, y):
plt.figure(figsize=(8, 8))
plt.scatter(x[x**2 + y**2 <= radius**2], y[x**2 + y**2 <= radius**2], color='blue', s=1) # Points inside the circle
plt.scatter(x[x**2 + y**2 > radius**2], y[x**2 + y**2 > radius**2], color='red', s=1) # Points outside the circle
plt.xlim(-1.5, 1.5)
plt.ylim(-1.5, 1.5)
plt.title('Monte Carlo Simulation of Pi')
plt.gca().set_aspect('equal', adjustable='box')
plt.axhline(0, color='black', lw=0.5)
plt.axvline(0, color='black', lw=0.5)
plt.grid()
plt.show()
# Uncomment the line below to visualize the simulation
# plot_simulation(x, y)
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