Event Title
On the New Reading of Archimedes' Method, Proposition 14
Presentation Type
Oral and/or Visual Presentation
Presenter Major(s)
Mathematics, Classics
Mentor Information
David Austin
Department
Mathematics
Location
Kirkhof Center 2263
Start Date
11-4-2012 2:30 PM
Keywords
Mathematical Science
Abstract
Study over the past decade by the Archimedes Palimpsest Project of the Method of Mechanical Theorems, recovered in 1998, has produced evidence that the ancient Greek mathematician may have made informal use of actual infinity in his method of discovering geometric theorems. This runs contrary to the Greek tradition of rigorous proof which allows only for the use of potential infinity. We will examine the relevant argument, Proposition 14, compare it with other, more or less traditional, Greek infinitary arguments (such as his proof by exhaustion of the quadrature of the parabola), and consider the questions arising about the Greek attitude toward infinity. Greek geometry benefited from illustration and plenty will be provided.
On the New Reading of Archimedes' Method, Proposition 14
Kirkhof Center 2263
Study over the past decade by the Archimedes Palimpsest Project of the Method of Mechanical Theorems, recovered in 1998, has produced evidence that the ancient Greek mathematician may have made informal use of actual infinity in his method of discovering geometric theorems. This runs contrary to the Greek tradition of rigorous proof which allows only for the use of potential infinity. We will examine the relevant argument, Proposition 14, compare it with other, more or less traditional, Greek infinitary arguments (such as his proof by exhaustion of the quadrature of the parabola), and consider the questions arising about the Greek attitude toward infinity. Greek geometry benefited from illustration and plenty will be provided.