Wow! eBook
Beyond Geometry: A New Mathematics of Space and Form (History of Mathematics) (History of Mathematics (Facts on File))
Author(s): John Tabak (Author)
- Publisher: Facts on File
- Publication Date: 30 April 2011
- Language: English
- Print length: 237 pages
- ISBN-10: 0816079455
- ISBN-13: 9780816079452
Book 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>
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About the Author
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.
