Laboratory 3 Arithmetic, Loops Solution

Learning Objectives:

 
Develop simple Python programs that do input, produce output and do arithmetic using loops.

 
Develop simple Python programs that use for loops.




Directed Activities:

0. Download lab3.py. Demonstrate each of your solutions for the instructor.




 
Finding an average

Write a function, average(), that asks the user the number of grades to input. The function should then ask for each grade and output the average. The message to the user should be:

Enter your grade on HW1:

Enter your grade on HW2:

…




 
Fibonacci.

A Fibonacci sequence is a sequence of numbers where each successive number is the sum of the previous two. The classic Fibonacci sequence begins: 0, 1, 1, 2, 3, 5, 8, 13, …. Write a function, fibonacci() , that computes and outputs all of the Fibonacci numbers up to and including the nth number, where n is a value input by the user.




 
Compute a square root. (Adapted from the text, p. 78, Exercise 17)

Write a function newton() that approximates the square root of a number using Sir Isaac Newton's method. Ask the user what the number, x, is and how many times to improve the approximation. x / 2 is a good first approximation. Given an existing approximation,




approx = approx + x

approx













is a better approximation. Display the number and the final value of the approximation.




4. Draw a house

Write a function, buildHouse(), that uses the author’s graphic package to create a blue background with a white square house and a brown triangle roof. The house should be in the middle of the window. Use Rectangle class to build the house. Use Polygon to build the triangle.




5. Output a sequence

Write a function, sequence(), that asks the user for the number of terms in a series, then prints the following pattern for the appropriate number of terms.

 

1 3 3 5 5 7 7 9 9 …




6. Computing pi.

Write a function pi() that approximates the value of using the Wallis formula:

π 2 * 2 * 4 * 4 * 6 * 6 * 8

2 1 3 3 5 5 7 7







The program should prompt the user for n, the number of terms in the series, compute the product of the n terms, and output the resulting approximation of pi.




 
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