Inverse Tangent Formulas for π

Math 242 practice problems

Name: _________________

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 accuracy of approximations of π using Machin’s, Ferguson’s and Størmer’s formulas. (These formulas are found on page 28 in the text.)

To do this, first write Modules for approximating π using each formula. Each Modules should return the sum of n terms of the appropriate formula. Then compute the accuracy (that is, the number of correct digits of π) for each formula for various values of n.

Make one or more plots that compare the accuracy of the three methods. The horizontal axis of your plot should be the number of iterations, and the vertical axis should be the accuracy (similar to Figure 1.8 in the text).

Finally, write one or more sentences to summarize your observations.

Due: Friday, February 18, at 5:00pm. Upload your solution as a Mathematica notebook to the Inverse Tangent Formulas assignment (Moodle link).

Grading: If you successfully make one or more plots that compare the accuracy of the three methods, you will earn a Satisfactory grade.

Need help? Review the notes from class, which are posed on the course web site. If you still need help, email Prof. Wright.