Commit 7f9aed8

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Amogh Singhal

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Create estimate_pi.py

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	`1`	`+import numpy as np`
	`2`	`+from math import pi as PI`
	`3`	`+`
	`4`	`+def estimate_pi(sims=100):`
	`5`	`+ """`
	`6`	`+ takes the number of simulations as input to estimate pi`
	`7`	`+ """`
	`8`	`+`
	`9`	`+ # counter to hold points lying inside the circle`
	`10`	`+ in_circle = 0`
	`11`	`+`
	`12`	`+ for s in range(0,sims):`
	`13`	`+`
	`14`	`+ x = np.random.rand()`
	`15`	`+ y = np.random.rand()`
	`16`	`+`
	`17`	`+ if (x2 + y2) <= 1:`
	`18`	`+ in_circle += 1`
	`19`	`+`
	`20`	`+ # The ratio of pts. inside the circle and the total pts. will be same as the ratio`
	`21`	`+ # of the area of circle to the area of the square, inside which the circle is inscribed`
	`22`	`+ # Area of circle = PI * R * R`
	`23`	`+ # Area of square = (2R) * (2R)`
	`24`	`+`
	`25`	`+ pi_estimated = 4.0 * in_circle / sims`
	`26`	`+`
	`27`	`+ print("Simulations ran: ", sims)`
	`28`	`+ print("Estimated pi", pi_estimated)`
	`29`	`+ print("Error", PI - pi_estimated)`
	`30`	`+`
	`31`	`+estimate_pi(sims=100)`
	`32`	`+print()`
	`33`	`+estimate_pi(sims=1000)`
	`34`	`+print()`
	`35`	`+estimate_pi(sims=10000)`
	`36`	`+print()`
	`37`	`+estimate_pi(sims=100000)`
	`38`	`+print()`
	`39`	`+estimate_pi(sims=1000000)`
	`40`	`+print()`
	`41`	`+estimate_pi(sims=10000000)`
	`42`	`+print()`
	`43`	`+estimate_pi(sims=100000000)`
	`44`	`+print()`
	`45`	`+estimate_pi(sims=1000000000)`

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