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Math/monte_carlo_pi.py

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+import random
+import matplotlib.pyplot as plt
+
+
+def monte_carlo_pi(num_points):
+    inside_circle = 0
+    for _ in range(num_points):
+        x, y = random.uniform(-1, 1), random.uniform(-1, 1)
+        if x**2 + y**2 <= 1:
+            inside_circle += 1
+    return 4 * inside_circle / num_points
+
+
+def visualize_monte_carlo(num_points):
+    inside_x, inside_y = [], []
+    outside_x, outside_y = [], []
+    for _ in range(num_points):
+        x, y = random.uniform(-1, 1), random.uniform(-1, 1)
+        if x**2 + y**2 <= 1:
+            inside_x.append(x)
+            inside_y.append(y)
+        else:
+            outside_x.append(x)
+            outside_y.append(y)
+    plt.figure(figsize=(6, 6))
+    plt.scatter(inside_x, inside_y, color="blue", s=1, label="Inside Circle")
+    plt.scatter(outside_x, outside_y, color="red", s=1, label="Outside Circle")
+    plt.xlabel("X")
+    plt.ylabel("Y")
+    plt.legend(loc="upper right")
+    plt.title(f"Monte Carlo Pi Approximation with {num_points} Points")
+    plt.show()
+
+
+num_points = int(input("Enter the number of points to use for the approximation: "))
+pi_estimate = monte_carlo_pi(num_points)
+print(f"Approximation of Pi with {num_points} points: {pi_estimate}")
+# Uncomment below to visualize
+# visualize_monte_carlo(num_points)