added square_root.py

square_root.py

@@ -0,0 +1,56 @@
+import math
+import cmath
+
+
+# functions
+
+# returns the next estimate using Newton's Method
+def new_estimate(old_estimate,number_):
+    return old_estimate - (old_estimate**2 - number_)/(2 * old_estimate)
+
+# returns the number truncated to the requested number of decimals
+def truncate(number_,decimals=0):
+    return math.floor(abs(number_)*(10**decimals)) / (10**decimals)
+
+# returns true if estimates are equal to the specified decimal place
+def compare_estimates(estimate1,estimate2,decimals):
+    return truncate(estimate1,decimals) == truncate(estimate2,decimals)
+
+# prints the provided loop number and estimate
+def print_details(estimate,loop):
+    print("{}: {}".format(loop,estimate))
+
+# Prompt for number
+input_number = input("Enter a number > ")
+
+# Convert input_number to a float
+try:
+    number = float(input_number)
+except ValueError:
+    print ("You did not enter a number.")
+    exit()
+
+# Original Estimate
+current_estimate = number / 2
+if number < 0:
+    current_estimate += 1j * number / 2
+
+number_of_loops = 1
+print_details(current_estimate,0)
+
+# Algorithm
+while True:
+    # Calculate new estimate
+    next_estimate = new_estimate(current_estimate,number)
+    # Print current information
+    print_details(next_estimate,number_of_loops)
+    # Compare new estimate to old estimate
+    if compare_estimates(next_estimate,current_estimate,2):
+        # If hundredth's place hasn't changed, break
+        break
+    # Else repace old estimate with new estimate and repeat
+    current_estimate = next_estimate
+    number_of_loops += 1
+
+# Print Results
+print("The square root of {} is {}.".format(number,current_estimate))