Page 33 - KVIS Book

MAT06I

Utilizing High-School Mathematics to Approximate the

Circumference of an Ellipse

Nitthan Thaowan
Kamnoetvidya Science Academy, Thailand
Supervisor: Atiratch Laoharenoo
Email: nitthan.t@kvis.ac.th

This research is aimed to approximate the circumference of an ellipse using as simple
functions available in high-school mathematics. Note that the exact circumference of
an ellipse is given in as an elliptic integral which is not elementary, that is, it is neither
a) sum, difference, product, or quotient, b) powers or roots, c) exponential functions or
ogarithms, d) trigonometric functions or their inverse functions, nor composition of
these function of a dummy variable or dummy variables. Because of these, despite of
lack of practical use, an approximation of the circumference of an ellipse might be
useful. Not only that that this research focuses on approximation of the function, but
also applying high-school mathematics, although not completely relying on it. Two
approaches are mainly used in this research: using regression analysis to fit some
desired functions, and coming up with original ideas. Accidental discoveries
occasionally make their appearances, but they are more like "bonuses" than the results
intended to find. In the end, the research shows that despite the lack of high level
tools, close approximations can be made.