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Computer Science Science Fair Project

Pi of Pieces Unlimited: A Continuation

Hard
Pi of Pieces Unlimited: A Continuation | Science Fair Projects | STEM Projects
Join us in this project to discover the upperbound recursive equation for Pi and the Pi Associates! We will use regular polygons circumscribed about a circle to approximate its circumference and show the equivalence of François Viete's and my Last year's lowerbound expression for Pi. We will also derive an Algebraic Polynomial of which one root is Pi itself.

Hypothesis

The hypothesis is that Pi can be derived from an Algebraic Polynomial.

Method & Materials

You will use regular circumscribed polygons about circle of radius 1 to derive an upperbound expression for Pi. You will start from a square and construct an 8-sided regular polygon, doubling the number of sides. This procedure can be repeated endlessly doubling the sides of the polygon with every step.
You will need regular polygons, a circle of radius 1, and a calculator.

Results

Through this project, we have discovered the upperbound recursive equation for Pi and the Pi Associates. We have also shown that François Viete's expression for Pi is equivalent to my last year's lowerbound expression for Pi.

Why do this project?

This science project is so interesting and unique because it involves discovering the mystery of Pi and the Pi Associates.

Also Consider

Experiment variations to consider include using different shapes of polygons and different radii of circles.

Full project details

You can find additional information and details for this science fair project here. Have fun exploring!
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