Scientific Computing
Recall from your textbook that the Leibniz formula states that
The Wallis formula states that
Create a file leibniz-wallis.py
and save it to cs100/ch2
. Copy the archimedes(sides)
function definition from the previous activity to it.
Add and implement the functions which approximate Pi using the Leibniz and Wallis formulas. I suggest you call your Leibniz function for 200 and 500 terms, and the Wallis function for 4, 20, and 100 pairs. Here is a sketch of your program.
def leibniz(terms):
# your code goes here
approxPi = 0
return approxPi
def wallis(numPairs):
# your code goes here
approxPi = 1
return approxPi
print("Results for Leibniz formula:")
print(leibniz(200))
print(leibniz(500))
print("Results for Wallis formula:")
print(wallis(4))
print(wallis(20))
print(wallis(100))
Compare the approaches to compute Pi using Archimedes, Leibniz, and Wallis approximations. Which one is better for a comparable number of sides / terms / pairs ?
Type help('math')
in the Shell area. Use it (or the corresponding website) to determine how to print the constant Pi from the math library.
What other functions from the math library can you use? Try a few to experiment! đŸ§®
computeSummation(terms)
that will compute the summation up to so many terms. Test it by invoking your function. What does the value approach for very large terms? (Make sure you get a decimal result).Submit your file to Moodle.