Approximating Square Roots w/ Newton's Method

(Expand description for Errata!) Computing the Square Root of a number is something that turns out to not be straight forward - School teaches us to do it out of memory, without considering the actual algorithm or steps to achieve it.

Today, we look at one algorithm to approximate the square root of a number - Newton's Method! We'll first look at the math behind the technique, before going on to code it in Python!

ERRATA: At 10:30, there is a mistake in the equation shown in the yellow box. The sign in the middle is "-" not "+". Thanks to Gil Shapira for pointing out the error!

= CODE DOWNLOAD =
To view and download the code written in this video, check out the following Bitbucket repository: https://bitbucket.org/nerdfirst/newto...

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= Contents =
00:00 Introduction
01:31 Contents Page
02:11 Explanation of the Math
→ 02:20 Forming the main function f(x)
→ 03:00 How to use the function representation
→ 03:23 Overview of what Newton's Method does
→ 04:10 Injecting our function into Newton's Method
→ 04:54 Drawing the Tangent Line
→ 06:58 Using the Tangent Line to find the next guess
→ 08:16 General Formulation of Newton's Method
→ 09:35 Applying the Method to Square Roots
→ 11:07 Conclusion / Summary

11:21 Writing The Code
→ 11:42 Starting the Function
→ 12:03 Discussion of Terminating Condition
→ 12:46 Making the First guess
→ 13:21 Difference variable for termination
→ 13:34 Building the main loop / applying Newton's Method
→ 14:23 Building terminating mechanism
→ 15:32 Brief Trace of completed algorithm
→ 16:18 First test
→ 17:04 Comparing with "ground truth"
→ 17:34 Changing Error value
→ 17:50 Adding a counter to see the number of iterations
→ 19:12 Discussion of verbose version of the code

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