Rapid estimation of π by weighing triangles, circles, and ellipses

Abstract

Abstract This article presents a simple, fast, and equally accurate technique for measuring the area of a circle and of an ellipse without using geometric formulas. This therefore, together with the known radius of the circle and the semi-major and semi-minor axes of the ellipse, allows for the calculation of π. The experiment is easy, thrilling, and fun to replicate as a math or physics classroom activity, for high school freshmen or sophomore, in celebration of the famous constant and irrational number. In addition, the graphical data reveal an empirical derivation of the area of the circle and of the ellipse which is academically-enriching, for the students most specially.