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-# Approximating square root
-
-## Goals
-
-* Encode and solve a recurrence relation from mathematics using iteration in Python to approximate a real-world, real valued function: `sqrt`.
-* Make a function within a function
-
-The end result is file `sqrt.py`.
-
-## Description
-
-To approximate square root, the idea is to pick an initial estimate, x0, and then iterate with better and better estimates, xi, using the recurrence relation:
-
-<center>
-<img src=figures/sqrt-recurrence.png width=120>
-</center>
-
-There’s a great deal on the web you can read to learn more about why this process works but it relies on the average (midpoint) of x and n/x getting us closer to the square root of n. The cool thing is that the iteration converges quickly.
-
-Our goal is to write a function that takes a single  number and returns it square root
-
-```python
-# Stop iterating when the new approximation is within
-# PRECISION of the old value.
-PRECISION = 0.00000001
-def sqrt(n):
-    "compute square root of n"
-    # print "Compute sqrt(%f)" % n 
-    x_0 = 1.0 # pick any old initial value
-    x_prev = x_0 
-    while True:
-        x_new = 0.5 * (x_prev + n/x_prev)
-        delta = abs(x_new - x_prev)
-        if delta < PRECISION:
-            print "sqrt(%f) = %f" % (n, x_new)
-            return x_new
-        # print x_new
-        x_prev = x_new 
-```
-
-And then to test it, we can use `numpy`:
-
-```python
-import math
-def test_sqrt():
-    def check(n):
-        assert np.isclose(sqrt(n), math.sqrt(n))
-    check(125348)
-    check(89.2342)
-    check(100)
-    check(1)
-    check(0)
-
-test_sqrt()
-```
-
-As you can see you can define a function within a function. It's not special in any way except that code outside of `test_sqrt()` cannot see function `check()`. On the other hand, `check()` **can** see the symbols outside of `test_sqrt()`, such as our `sqrt()`.
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