Write a program that asks the user for a positive number and then outputs the approximated square root of the number. Use Newton's method to find the square root, with epsilon = 0.01. (Epsilon is the allowed error, plus or minus, when you square your calculated square root and compare it to your original number.)
After completing this assignment, you should understand:
- How variables work
- How
whileworks - The concept of successive approximation
After completing this assignment, you should be able to:
- Write a Python script
- Ask for input
- Print output
- A GitHub repo called approximate-square-root containing at least:
- This
README.mdfile - a file called
square_root.py
- This
Here is an example of the program running correctly:
$ python square_root.py
Enter a positive number: 4
The square root of 4 is 2.0.
$ python square_root.py
Enter a positive number: 20
The square root of 20 is 4.472137791286727.
Your program will be tested with the script test.sh. To run this script, run
brew install roundup first.
Newton's method of successive approximations says that whenever we have a guess
y for the value of the square root of a number x, we can get a better guess
(one closer to the actual square root) by averaging y with x/y. If we do
this over and over, we should be able to get a very accurate guess.
You have to write a script that asks the user for a positive number and then compute the square root with a maximum error of 0.01. You then print out your answer to the user.
In each iteration of your loop, print out the current number of iterations and the current guess.
Examine the input into your program and give an appropriate error message if a non-number or negative number is given.
Look up complex numbers in Python. Allow negative numbers as input into your program.
- Read more about the Babylonian/Newton's method of approximating square roots.
- Numeric types in Python.
This assignment is adapted from SICP by Abelson and Sussman.