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Old and New Unsolved Problems in Plane Geometry and Number Theory

Old and New Unsolved Problems in Plane Geometry and Number Theory

Victor Klee and Stan Wagon

Print ISBN: 978-0-88385-315-3
340 pp., Paperbound, 1991
List Price: $32.00
Member Price: $24.00
Series: Dolciani Mathematical Expositions

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Part of the broad appeal of mathematics is that there are simply stated questions that have not yet been answered. These questions are plentiful in the areas of plane geometry and number theory, and the purpose of this book is to discuss some unsolved problems in these fields.

The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. Each problem is placed in its historical and mathematical context and is presented in two parts. The first gives an elementary overview, discussing the history and both solved and unsolved variants of the problem. Part Two contains more details, including a few proofs of related results, a wider and deeper survey of what is known about the problem and its relatives, and a large collection of references.

The book will appeal to a range of mathematicians―teachers at all levels, students (both undergraduate and graduate) as well as researchers. It could be used as a text in a course about unsolved problems, and also in courses in geometry or number theory. High school teachers interested in learning about developments in modern mathematics and the status of famous problems such as those dealing the Riemann hypothesis, perfect and prime numbers, tilings of the plane, or illumination of polygons will find the book very useful.

Table of Contents

Preface
Chapter 1: Two Dimensional Geometry
Chapter 2: Number Theory
Chapter 3: Interesting Real Numbers
Hints and Solutions: Two-Dimensional Geometry
Hints and Solutions: Number Theory
Hints and Solutions: Interesting Real Numbers
Glossary
Index of Names
Subject Index
Addendum

About the Authors

Victor Klee was born in San Francisco in 1925. He received his B.A. from Pomona College in 1945, and his Ph.D. from the University of Virginia in 1949. He was Professor of Mathematics and Adjunct Professor of Computer Science at the University of Washington in Seattle. He served as President of the Mathematical Association of America (1971-1972), and was the recipient of the Association’s Award for Distinguished Service to Mathematics (1977). He wrote more than 200 research papers in several areas of mathematics. Victor Klee passed away in 2007.

Stan Wagon was born in Montreal in 1951. He received his B.S. from McGill University in 1971 and his Ph.D. from Dartmouth College in 1975. He taught at Smith College for 15 years, and now teaches at Macalester College in St. Paul, Minnesota. He has published 34 mathematical papers and several books, including: The Banach-Tarski Paradox, Mathematica in Action, and Animating Calculus.

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