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The art of the infinite : the pleasures of mathematics

Author: Robert Kaplan; Ellen Kaplan
Publisher: Oxford ; New York : Oxford University Press, ©2003.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Tracing a path from Pythagoras, whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret (the existence of irrational numbers); through Descartes and Leibniz; to the brilliant, haunted Georg Cantor, who proved the infinity can come in different sizes. The  Read more...
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Details

Genre/Form: Einführung
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Robert Kaplan; Ellen Kaplan
ISBN: 019514743X 9780195147438 9780195176063 0195176065
OCLC Number: 51962641
Description: ix, 324 pages : illustrations ; 25 cm
Contents: Acknowledgments --
Invitation --
Time and the mind --
How do we hold these truths? --
Designs on a locked chest --
Infinite and the indefinite --
Skipping stones --
Euclid alone --
Longing and the infinite --
Eagle of algebra --
Into the Highlands --
Infinite and the unknown --
Back of beyond --
Abyss.
Responsibility: Robert Kaplan and Ellen Kaplan ; illustrations by Ellen Kaplan.
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Abstract:

The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Tracing a path from Pythagoras, whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret (the existence of irrational numbers); through Descartes and Leibniz; to the brilliant, haunted Georg Cantor, who proved the infinity can come in different sizes. The Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics. The Kaplans guide us through the "Republic of Numbers," where we meet both its upstanding citizens and more shadowy dwellers; and we travel across the plane of geometry into the unlikely realm where parallel lines meet. Along the way, deft character studies of great mathematicians (and equally colorful lesser ones) illustrate the opposed yet intertwined modes of mathematical thinking: The intuitionist notion that we discover mathematical truth as it exists, and the formalist belief that math is true because we invent consistent rules for it. "Less than All," wrote William Blake, "cannot satisfy Man." The Art of the Infinite shows us some of the ways that Man has grappled with All, and reveals mathematics as one of the most exhilarating expressions of the human imagination.

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