Program 1 for Comp 150

This is a pair assignment worth 20 points.

The program should begin with a comment including your names, a brief description of what the program does and information on any help you received on the project.  If it is entirely your own work, say so.  If anyone helped either of you, identify them by name and describe how they helped.  

If you helped anyone else, separately identify them. 

Submit a single file to Blackboard, with the naming convention prog1_ID.py  where ID is the blackboard ID of the submitter.  For instance I would submit prog1_aharrin.py.

Remember to have each team member submit a log to Blackboard also.  Your grade will not be final until the log is passed in.  The log format is described in the Pairs Administration page:  The log should indicate your hours working on the homework and an assessment of your contribution and an assessment of your partner's contribution.  Please name the file 150log1ID.doc, where ID is your blackboard ID, and the 1 refers to Program 1, so if I were submitting a log for this assignment, it would be called 150log1aharrin.doc.

The Problem: 

This program will implement a well known technique for approximating the square root of a number.  In general, a positive number can be written as the product of two positive numbers in an infinite number of ways.  For example, 

36 = 1 * 36 = 2*18 = 3* 12 = 4* 3 = 5 * 7.2 = 6 * 6 = 10*3.6 = 16 * 2.25 etc.

If the factors are the same, then use have found the square root.  Notice that when one factor is larger than the square root, the other one is smaller.  So one way to proceed is to choose one factor of a number, calculate the other by dividing.  Generally they will be different.  Since we want to find two equal factors, the next choice for the first factor can be the average of the two we found.  Each time through this loop we get a better approximation.  You can start your first guess with 1.0 if you want.  (The decimal point is important to avoid integer arithmetic.)

For example, if we try 5 steps on the number 36, starting from the initial guess 1.0, then the next five approximations are
The above steps describe what happens internally in this example, not what is printed out, (except for the last number).

Your program should

• Ask the user for the number whose square root you are to find
• Ask the user for how many steps to execute in finding better approximations
• Do the approximation steps.  In the final version nothing should be printed inside the loop.
• Print the results at the end:  Your output should nicely label each of the following:
  
  • the number initially specified by the user,
  • the final approximate square root of this number calculated in your loop,
  • and the result using math.sqrt, which gives the root as close as the computer can calculate it.  (Remember to import math).

Note 1:  This is the best we can do with the amount of Python introduced so far.  It would make more sense to automatically repeat this process until the answers do not change, but we have not studied that kind of loop yet.

Note 2:  Math may not be your favorite thing, but at least it is better to have Python doing the calculations rather than you!   We are doing numerical things first because they are particularly easy to introduce.  As we introduce more of Python, we will go on to processing text and producing graphics, web pages, ....

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