####Square root algorithm as a function
##def sqrt(x, epsilon):
##    """Newton's Method to find square root
##       with precision epsilon (Heron's algorithm)"""
##    ans = 1
##    num_guesses = 0
##    while abs(x/ans - ans) > epsilon:
##        ans = (x/ans + ans)/2
##        num_guesses += 1
##    print("found square root in", num_guesses, "guesses")
##    return ans
##
##x = float(input("Enter a number:"))
##root = sqrt(x, 0.00001)
##print(root, "is close to the square root of", x)
##
##fourth_root = sqrt(root, 0.00001)
##print(fourth_root, "is close to the fourth root of", x)


#### Demonstration of nested function calls
##def sqrt(x, epsilon):
##    """Newton's Method to find square root
##       with precision epsilon (Heron's algorithm)"""
##    ans = 1
##    num_guesses = 0
##    while abs(x/ans - ans) > epsilon:
##        ans = (x/ans + ans)/2
##        num_guesses += 1
##    print("found square root in", num_guesses, "guesses")
##    return ans
##
##def distance_to_origin(x, y):
##    """find the distance from a point at (x, y) to the origin"""
##    ans = sqrt(x**2 + y**2, 0.00001)
##    return ans
##
##def geometric_mean(x, y):
##    """Returns the root of x*y"""
##    return sqrt(x*y, 0.00001)
##
##x = float(input("Enter a x-coordinate:"))
##y = float(input("Enter a y-coordinate:"))
##magnitude = distance_to_origin(x, y)
##print("The magnitude of your vector is", magnitude)
##geo_mean = geometric_mean( x, y)
##print("The geometric mean of x and y is", geo_mean)
### check to see if values have changed
##print("x is", x)
##print("y is", y)


#### Demonstrates that local variables and global variables
#### can have the same name.  This can be confusing!
##def add_one(x):
##    x = x + 1 # a parameter is always a local variable
##    y = x + 1 # assignment: this creates a local variable, y
##    print('In the function, x =', x)
##    print('In the function, y =', y)
##    return x
##
##x = 3
##y = 3
##result = add_one(x)
##print('the function returns', result)
##print('outside the function, x =', x)
##print('outside the function, y =', y)


####Demonstrates reading global variables from inside function
##def add_y(x):
##    x = x + y # there is no local y, so the global value is used
##    print('In the function, x =', x)
##    print('In the function, y =', y)
##    return x
##
##x = 3
##y = 5
##result = add_y(x)
##print('the function returns', result)
##print('outside the function, x =', x)
##print('outside the function, y =', y)