Dart Board Method 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: Complete the two problems below involving the “dart board” method of approximating π.

Due: Monday, February 23 at 5:00pm. Upload your solution as a Mathematica notebook to the Dart Board Pi assignment on Moodle.

Grading: If you find reasonable answers to the questions below, supported by computational evidence, you will earn a Satisfactory grade for each problem.

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

Suppose you run the dart board algorithm to approximate π with 10,000 darts. What percentage of the time does your experiment return an approximation of pi that includes the correct digits 3.14?

Problem 2

Using the dart board algorithm, how many points are required to obtain an estimate of π that is within 0.01 of π at least 75% of the time? Provide computational evidence to support your answer.