Description
1. Write a program that asks the user to input three numbers, and prints the
largest and smallest values. e.g. For input: 6.7, 74, 9 the output is: The
largest number input is 74 and the smallest 6.7
2. A leap year is a year (1582 and after) divisible by 4, unless it is a century year.
A century year is a leap year if it is divisible by 400.
Hence, 1900 is not a leap year, while 2000 is.
Write a program isLeapYear.py that takes a year as input and prints if the
year input is or is not a leap year.
input: 2020 output: 2020 is a leap year
input: 1900 output: 1900 is not a leap year
3. In the lecture notes, Henon’s algorithm for finding the square root was outlined.
It is reproduced below. Write a program to implement Henon’s algorithm to
find the square root of a number, that asks the user to input a number x to find
the square root of. Floats should not be compared exactly (think why) instead,
you should produce an answer correct to within 1.e-5 (this is close enough).
i.e. stop the loop when abs(g ∗ g − x) < 1.e − 5
Once the rogram is working, compute the square roots of xList = [10, 20, . . . 90].
Compare the values to the values obtained using math.sqrt(). Henon’s Algorithm to find the square root y of a number x:
(a) Start with a guess: g
(b) Test: Is g ∗ g close (enough) to x?
(c) If YES then DONE. Report: y = g
(d) Else update guess: gnew =
1
2
g +
x
g
(e) g = gnew
(f) goto 2.
4. The value of π is equal to the following infinite series:
π = 4 ·
1
1
−
1
3
+
1
5
−
1
7
+ . . .
(a) While we cannot compute the entire infinite series, we can get an approximation to the value by using the first n terms. Allow the user to input n.
Name you program piSeries.py Experiment with n = 10, 100, 1000, 10000.
1
(b) As you can see, the value gets closer to the actual value of π as the number
of terms increases. Make a copy of the program you made fro the exercise
above and save it as piTolerance.py. Modify the program so that you
keep adding terms such that the computation with n terms and the computation with n + 1 differs by less than 10e − 5 (1 part in 10000). Your
program should print out the estimate of π and the number of terms used
to obtain the value.
