A Modern Spin on Archimedes’ Quadrature of the Parabola

Summary

In the 3rd century B.C.E., Archimedes wrote his treatise on the quadrature of the parabola, in which he laid out his solution to the problem of finding the area of a parabolic segment. Archimedes attacks the problem from two sides; first, he uses classical mechanics to derive an area formula, and then he uses pure geometry to prove his formula is correct. In this paper, we will present two modern approaches to this problem using calculus. The first approach can be presented to a calculus class that has learned about optimization methods and convergent geometric sequences, and the second can be presented after they have learned the Fundamental Theorem of Calculus.

Acknowledgment

The author wishes to thank Archimedes of Syracuse for his profound contributions to mathematics as a whole and for his Quadrature of the Parabola, which is my favorite problem from math antiquity.

Additional information

Notes on contributors

Jason Snyder

Jason Snyder ([email protected]) received his Ph.D. in Mathematics from the University of North Texas (UNT) in Denton, TX. After graduating, Dr. Snyder was an actuarial technician for four years, and he taught high school for three years. In 2016, he joined the full-time faculty at Collin College teaching in the Mathematics department. His greatest accomplishment is raising a family with his wife and four children.