How Big Is Your Icosoikaihenagon?

Overview

Objectives/Goals The purpose of this project is to find out if there is a relation between the area of any regular polygon and it's height. Methods/Materials First, all the areas were calculated for the regular polygons with sides 5-21 and heights 1-15 for each of them. This was done using a website. Then I found the ratios for them which was area/height squared. Then, I graphed the deltas (pi/4 - constant) using Excel and it looked like an exponential decay (d=De^-kn). I tried to derive k (constant) which would satisfy all the deltas, but one individual k could not be identified. Results I found out that the area/ height squared for each polygon had it's own constant. The constant got closer to pi/4, or 0.78, as the number of sides increased. Then the k values were derived but every k value was different and the results were too inconsistent to make into a formula. Conclusions/Discussion It was not possible to find a formula for all the regular polygons, but it was possible to find a pattern for each individual polygon. There should be an equation since the line is such a perfect curve, but I couldn't find that equation.

Competition history

• CSEF 2011 Mathematics & Software · Entry J1411

Resources

• CSEF project summary ↗

Related projects

Closest projects by meaning, across every fair and year in the corpus.

Browse more like this

• All Computational Sciences projects
• CSEF Computational Sciences projects
• Every CSEF 2011 project