**AiS Challenge Team Intrim Report**

Team Number: 038

School Name: Melrose high

Area of Science: Math Project

Title: Can we get the sides of heptagon?

Project Purpose: The purpose of our project is to find a perfect seven-side polygon (a heptagon). We are doing this because it has not been done before only as an estimated chord length is used. We will also us the standard geometric construction technique(compass and straight edged) to construct the heptagon.

Problem Solution: Using a computer we are going to draw a circle and construct the 3 basic shapes (an equilateral triangle, a square, and a pentagon) in the circle. The coordinate points were these touch the circle will be entered into a data array. Using a mathematic algorithm to compute the geometric distance of each point in the array to all the others in the array. Then we will compare each of the point’s distances to the mathematical distance of each side of a heptagon to see if we can find out the points of the heptagon. If none of these distances work, we will shift our reference point and try this procedure again.

Progress to Date: We have researched the history of the heptagon and the polygon. We have also determined the procedure of how to find a heptagon using the standard geometric construction technique. We also plan to design a computer program to analyze the data that we have made.

Expected Results: We are going to find the chord of a heptagon at least 2 time of what is known now. We are going to find out ways to us the heptagon in a different way.

Sources:

· http://mathworld.wolfram.com/Heptagon.html

· Courant, R. and Robbins, H. "The Regular Heptagon." §3.3.4 in What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 138-139, 1996

· Bold, B. Famous Problems of Geometry and How to Solve Them. New York: Dover, pp. 59-60, 1982.

· Bankoff, L. and Garfunkel, J. "The Heptagonal Triangle." Math. Mag. 46, 7-19, 1973.

· Dixon, R. Mathographics. New York: Dover, pp. 35-40, 1991.