### The Tortoise and Achilles:

##### using Geometry Expressions to investigate the infinite

by: Larry Ottman

Physical book (delivered by mail) $24.95

PDF eBook (digital download) $9.99

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 the modern software, Geometry Expressions, to
investigate Archimedes methods, ideas of the infinite, and Zeno's Paradoxes in
an introduction to Calculus, without using Calculus.

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