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The Origins of Pi

CSEF · 2005 Mathematics & Software

Chase W. Raymond · Estancia High School, Costa Mesa

Overview

Objectives/Goals What are some of the different methods for calculating the irrational decimal place values of the constant, Pi (d)? Is any method more accurate or efficient than others? Methods/Materials Beaker Marble Yarn Graphing Calculator Ruler Toothpicks Procedure: Methods to be Analyzed: · Spherical Method · Buffon#s Needle Experiment · Monte Carlo Method (Quarter Circle) · Arctangent Infinite Series · Wallis# Formula · Newtonian Fluxions Calculate Percentage Error for the different methods and analyze which approaches the constant value of Pi (d) most rapidly and accurately. Results Wallis# Formula provided the most accurate calculation approaching the value of Pi (d). The real resultant from this data, however, is that no method or number can represent or calculate Pi#s (d) exact value, except Pi (d), itself. Conclusions/Discussion We, in the real world, must decide the amount of precision we are going to use on a given project (ie: the building of a bridge) in order to accept something as perfect 'enough' to accept its usage.

Summary statement

I looked at different methods of calculating Pi's decimal places and tested which approached Pi's true value fastest.

Competition history

  • CSEF 2005 Mathematics & Software · Entry S1214

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