Create estimate_pi.py

Author: Amogh Singhal

estimate_pi.py

@@ -0,0 +1,45 @@
+import numpy as np
+from math import pi as PI
+
+def estimate_pi(sims=100):
+    """
+    takes the number of simulations as input to estimate pi
+    """
+    
+    # counter to hold points lying inside the circle
+    in_circle = 0
+    
+    for s in range(0,sims):
+        
+        x = np.random.rand()
+        y = np.random.rand()
+        
+        if (x**2 + y**2) <= 1:
+            in_circle += 1
+        
+    # The ratio of pts. inside the circle and the total pts. will be same as the ratio
+    # of the area of circle to the area of the square, inside which the circle is inscribed
+    # Area of circle = PI * R * R
+    # Area of square = (2R) * (2R)
+    
+    pi_estimated = 4.0 * in_circle / sims
+    
+    print("Simulations ran: ", sims)
+    print("Estimated pi", pi_estimated)
+    print("Error", PI - pi_estimated)
+
+estimate_pi(sims=100)    
+print()
+estimate_pi(sims=1000)
+print()
+estimate_pi(sims=10000)    
+print()
+estimate_pi(sims=100000)
+print()
+estimate_pi(sims=1000000)    
+print()
+estimate_pi(sims=10000000)
+print()
+estimate_pi(sims=100000000)    
+print()
+estimate_pi(sims=1000000000)