Speaker: Ilhan M. Izmirli, George Mason University

Title: Egyptian unit fractions

Abstract: In this paper we will first give a brief overview of Egyptian mathematics, in particular their arithmetic. We will then discuss one of the most captivating aspects of Egyptian arithmetic, their insistence on representing every fraction as a sum of unit fractions, which in this paper will be referred to as a unit representation. It is rather remarkable that the first existence theorem of these representations was actually given some millennia later by Fibonacci.

After dealing with some interesting special cases, we will give an existence proof of unit representations. We will also talk about the significance of unit fractions and the possible reasons as to their being the preferred mode of representation. We will conclude by stating some open problems.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491