The Tortoise and Achilles: using Geometry Expressions to investigate the infinite - Softcover

Ottman, Larry

Softcover

ISBN 10: 1882564243 ISBN 13: 9781882564248

Publisher: Saltire Software, Incorporated, 2011

Synopsis

Calculus is the study of the infinite and since much of secondary mathematics is designed to prepare one for the study of calculus, wrestling with the ideas of the infinite, even if informally, is extremely important for a student's mathematical development. That is the purpose of this book. Among the first to discuss these ideas was the Greek philosopher / mathematician Zeno, and not long after him, Archimedes came the closest to "discovering" Calculus without the tools of modern mathematics. Though none of Zeno's actual writings survive, Aristotle recorded accounts of Zeno's thoughts on the infinite, time and space in what have come to be known as Zeno's Paradoxes. One of those specifically involves the idea of a race in which a slower runner is given a head start and investigates the possibilities of the faster runner "catching up". This has come to be known as "Achilles and the Tortoise". These characters are our hosts as we use Geometry Expressions to investigate Archimedes methods, ideas of the infinite, and Zeno's Paradoxes in an introduction to Calculus, without using Calculus.

Edition details

• Publisher: Saltire Software, Incorporated
• Publication date: 2011
• Language: English
• ISBN 10: 1882564243
• ISBN 13: 9781882564248
• Binding: Paperback
• Number of pages: 132