The circle, so simple and yet complex, has fascinated mathematicians since the earliest civilizations. Archimedes, a well–known Greek mathematician born in 287 BCE, began to unravel part of the mystery involving π by applying iteration to the circle. Building on Euclid's postulates and theorems, Archimedes used iterations of inscribed and circumscribed regular polygons to find upper and lower bounds for the value of π. These bounds are close approximations of the value of π, and one is still used today: 22/7 differs from π only in the third place to the right of the decimal (see fig. 1).
Nicholas H. Wasserman, email@example.com, and Itir N. Arkan, firstname.lastname@example.org, are colleagues at Marymount School in New York City. Wasserman is a Ph.D. candidate at Teachers College, Columbia University, who is interested in mathematics teacher education and enjoys modeling mathematics with technology and incorporating reasoning and sense making in the classroom. Arkan has taught all levels of secondary school mathematics; her areas of interest include statistics, geometry, problem solving, and the implementation of technology in the classroom. Nick Wasserman; Itir Arkan