Inverse Tangent Formulas for π

MATH 242 practice problems

Learning Goals: Gain proficiency with programming in Mathematica. Develop and implement an algorithm to solve a mathematical problem, and interpret your results.

Your task: Compare the number of correct digits of π produced by Ferguson’s formula and Størmer’s formula. (These formulas are found on page 28 in the text.)

Due: Monday, September 15, at 5pm. Try to complete this before class, but you can ask last-minute questions on Monday before turning it in. Upload your solution as a Mathematica notebook to the Inverse Tangent Formulas assignment on Moodle.

Grading: If you successfully make a plot and estimate the number of correct digits per term of the sum, you will earn a Satisfactory grade.

Need help? Review the notes from class (which are posed on the course web site), talk with your classmates, email Prof. Wright, or visit the help session.

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Problem 1: Ferguson’s formula

Convert Ferguson’s formula (see page 30 in the text) to a power series, and write a module for approximating π using this formula. Then compute the number of correct digits of π for various values of n, the number of terms that you add up.  Make a plot showing how the number of correct digits of π depends on n. How many correct digits of π are produced by each term of the sum?

Problem 2: Størmer's formula

Convert Størmer’s formula (see pages 30-31 in the text) to a power series, and write a module for approximating π using this formula. Then compute the number of correct digits of π for various values of n, the number of terms that you add up.  Make a plot showing how the number of correct digits of π depends on n. How many correct digits of π are produced by each term of the sum?