This Is AuburnElectronic Theses and Dissertations

Isoperimetric Properties of the Circle




Holman, Kimberly

Type of Degree

Master's Thesis


Mathematics and Statistics


Jakob Steiner and Karl Weierstrass provided formal proofs of the isoperimetric property of the circle in the late 1830s. New mathematical tools, proof language, and concepts were needed to prove this rather obvious fact, that of all regions with a given perimeter the circle, and only the circle, has maximum area. We examine the historical context of the isoperimetric property, the proofs of Steiner and Weierstrass, and subsequent proofs using alternate methods. A comprehensive history and applications of the isoperimetric problem are presented. Several exercises are posed and solved using the isoperimetric property, relying heavily on methods used by Richard Demar in 1975.