
Beyond Geometry
John Tabak(Author)
Facts On File Inc (Publisher)
Published on 30. July 2011
Book
Hardback
237 pages
978-0-8160-7945-2 (ISBN)
Description
For millennia, Euclidean geometry, the geometry of the ancient Greeks, set the standard for rigor in mathematics--it was the only branch of mathematics that had been developed axiomatically, or based on a system of axioms. This form of geometry was the language of mathematics. But early in the 19th century, mathematicians developed geometries very different from Euclid's simply by choosing axioms different from those used by Euclid. These new geometries were internally consistent in the sense that mathematicians could find no theorems arising within these geometries that could be proven both true and false. Beyond Geometry describes how set-theoretic topology developed and why it now occupies a central place in mathematics. Describing axiomatic method as well as providing a definition of what a geometric property is, this new resource examines how early analysts incorporated geometric thinking into their development of the calculus. It also looks at the various mathematicians who struggled to develop a new conceptual framework for mathematics and examines one of the sub-disciplines of set-theoretic topology called dimension theory.<\p>
More details
Language
English
Place of publication
New York
United States
Target group
College/higher education
Illustrations
Illustrations
Dimensions
Height: 231 mm
Width: 154 mm
Thickness: 17 mm
Weight
592 gr
ISBN-13
978-0-8160-7945-2 (9780816079452)
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Schweitzer Classification
Person
John Tabak, Ph.D., performed graduate work at Suny at Stony Brook and received a degree in mathematics from Rensselaer Polytechnic Institute. He is the author of A Look at Earth and A Look at Neptune, two astronomy titles for middle school readers. He is presently writing a history of American sign language.