Old and New Unsolved Problems in Plane Geometry and Number Theory, Volume 11Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the history and both the solved and unsolved variants of the problem. The second part 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. Both parts contain exercises, with solutions. The book is aimed at both teachers and students of mathematics who want to know more about famous unsolved problems. |
Contents
Introduction | 1 |
Illuminating a Polygon 311 7179 | 71 |
Universal Covers 2124 9194 | 91 |
Points on Lines 2935 103110 | 103 |
Painting the Plane 4549 120127 | 119 |
Approximation by Rational Sets 5457 132136 | 132 |
Fixed Points 6670 145150 | 145 |
Perfect Numbers | 213 |
The 3n + 1 Problem | 225 |
| 234 | |
TwoDimensional Geometry | 269 |
Number Theory | 300 |
1 | 301 |
Glossary | 315 |
| 331 | |
Other editions - View all
Old and New Unsolved Problems in Plane Geometry and Number Theory Victor Klee,Stan Wagon Limited preview - 1991 |
Old and New Unsolved Problems in Plane Geometry and Number Theory Victor Klee,Stan Wagon Limited preview - 2020 |
Common terms and phrases
algebraic algorithm angle answer to Problem billiard path bound boundary circle collinear colors computable congruent by dissection conjecture connecting lines contains convex body convex n-gon convex pentagons convex polygons convex set denote diameter digits disk distance edge-length edges equation equichordal points equidecomposable Erdős example Exercise exists Fermat's Fermat's last theorem Figure fixed-point property function geometry hence hints and solutions infinitely inscribed square integer interior intersection isohedral Jordan curve Jordan region known least length Mathematical Mersenne primes monohedral monohedral tiling n-gon noncollinear number theory ordinary lines p₁ path of period perfect numbers plane set polynomial positive integers positive number prime prototiles proved radius rational set rationally approximable real numbers real-time computable regular primes result Reuleaux triangle segment sequence Show simple closed curve smooth Suppose tiles the plane translation unit fractions unsolved problems vertex vertices