Old and new unsolved problems in plane geometry and number theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Washington, DC
Mathematical Assoc. of America
1991
|
| Series: | The Dolciani mathematical expositions
11 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 340 S. graph. Darst. |
| ISBN: | 0883853159 |
Staff View
MARC
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| 245 | 1 | 0 | |a Old and new unsolved problems in plane geometry and number theory |c Victor Klee ; Stan Wagon |
| 264 | 1 | |a Washington, DC |b Mathematical Assoc. of America |c 1991 | |
| 300 | |a XV, 340 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804122527805472768 |
|---|---|
| adam_text | CONTENTS
Preface xi
Chapter 1. TWo Dimensional Geometry
Introduction 1
1. Illuminating a Polygon 3 11, 71 79
Is each reflecting polygonal region illuminable?
2. Equichordal Points 12 15, 80 85
Can a plane convex body have two equichordal points?
3. Pushing Disks Together 16 20, 86 90
When congruent disks are pushed closer together, can the area of their
union increase?
4. Universal Covers 21 24, 91 94
If a convex body C contains a translate of each plane set of unit diameter,
how small can C s area be?
5. Forming Convex Polygons 25 28, 95 102
How many points are needed to guarantee a convex n gon?
6. Points on Lines 29 35,103 110
If n points are not collinear, must one of them lie on at least | n connect¬
ing lines?
7. Tiling the Plane 36 44,111 119
Is there a polygon that tiles the plane but cannot do so periodically?
8. Painting the Plane 45^9,120 127
What is the minimum number of colors for painting the plane so that no
two points at unit distance receive the same color?
9. Squaring the Circle 50 53,128 131
Can a circle be decomposed into finitely many sets that can be rearranged
to form a square?
10. Approximation by Rational Sets 54 57,132 136
Does the plane contain a dense rational set?
11. Inscribed Squares 58 65,137 144
Does every simple closed curve in the plane contain all four vertices of
some square?
12. Fixed Points 66 70,145 150
Does each nonseparating plane continuum have the fixed point prop¬
erty?
References 151
vii
Vjjj CONTENTS
Chapter 2. Number Theory
Introduction 167
13. Fermat s Last Theorem 168 172,199 202
Do there exist positive integers x, y, and z and an integer n 3 such that
xn+yn = znl
14. A Perfect Box 173 174, 203 205
Does there exist a box with integer sides such that the three face diagonals
and the main diagonal all have integer lengths?
15. Egyptian Fractions 175 177,206 208
Does the greedy algorithm always succeed in expressing a fraction with
odd denominator as a sum of unit fractions with odd denominator?
16. Perfect Numbers 178 181,209 214
Is there an odd perfect number? Are there infinitely many even perfect
numbers?
17. The Riemann Hypothesis 182 185, 215 220
Do the nontrivial zeros of the Riemann zeta function all have real part
I?
2 •
18. Prime Factorization 186 190,221 224
Is there a polynomial time algorithm for obtaining a number s prime fac¬
torization?
19. The 3n + 1 Problem 191 194, 225 229
Is every positive integer eventually taken to the value 1 by the 3n I 1
function?
20. Diophantine Equations and Computers 195 198, 230 233
Is there an algorithm to decide whether a polynomial with integer coeffi¬
cients has a rational root?
References 234
Chapter 3. Interesting Real Numbers
Introduction 239
21. Patterns in Pi 240 242, 251 254
Are the digits in the decimal expansion of 7r devoid of any pattern?
22. Connections between n and e 243, 255 257
Are 7T and e algebraically independent? Is their ratio rational?
23. Computing Algebraic Numbers 244 247, 258 260
If an irrational number is real time computable, is it necessarily transcen¬
dental? Is /2 real time computable?
24. Summing Reciprocals of Powers 248 250, 261 264
Isl + ^ + ^ + ^H irrational?
References 265
CONTENTS JX
Hints and Solutions: Two Dimensional Geometry 269
Hints and Solutions: Number Thoery 300
Hints and Solutions: Interesting Real Numbers 311
Glossary 315
Index of Names 325
Subject Index 331
|
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| author_sort | Klee, Victor 1925-2007 |
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| bvnumber | BV008145437 |
| classification_rvk | SK 380 |
| ctrlnum | (OCoLC)243765256 (DE-599)BVBBV008145437 |
| discipline | Mathematik |
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| id | DE-604.BV008145437 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:15:18Z |
| institution | BVB |
| isbn | 0883853159 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005374075 |
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| physical | XV, 340 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Mathematical Assoc. of America |
| record_format | marc |
| series | The Dolciani mathematical expositions |
| series2 | The Dolciani mathematical expositions |
| spelling | Klee, Victor 1925-2007 Verfasser (DE-588)119043815 aut Old and new unsolved problems in plane geometry and number theory Victor Klee ; Stan Wagon Washington, DC Mathematical Assoc. of America 1991 XV, 340 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Dolciani mathematical expositions 11 Geometrie (DE-588)4020236-7 gnd rswk-swf Planimetrie (DE-588)4046223-7 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Ungelöstes Problem (DE-588)4186869-9 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Geometrie (DE-588)4020236-7 s DE-604 Zahlentheorie (DE-588)4067277-3 s Ungelöstes Problem (DE-588)4186869-9 s Planimetrie (DE-588)4046223-7 s Wagon, Stan 1951- Verfasser (DE-588)172440114 aut The Dolciani mathematical expositions 11 (DE-604)BV001900740 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005374075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Klee, Victor 1925-2007 Wagon, Stan 1951- Old and new unsolved problems in plane geometry and number theory The Dolciani mathematical expositions Geometrie (DE-588)4020236-7 gnd Planimetrie (DE-588)4046223-7 gnd Zahlentheorie (DE-588)4067277-3 gnd Ungelöstes Problem (DE-588)4186869-9 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4046223-7 (DE-588)4067277-3 (DE-588)4186869-9 (DE-588)4143413-4 |
| title | Old and new unsolved problems in plane geometry and number theory |
| title_auth | Old and new unsolved problems in plane geometry and number theory |
| title_exact_search | Old and new unsolved problems in plane geometry and number theory |
| title_full | Old and new unsolved problems in plane geometry and number theory Victor Klee ; Stan Wagon |
| title_fullStr | Old and new unsolved problems in plane geometry and number theory Victor Klee ; Stan Wagon |
| title_full_unstemmed | Old and new unsolved problems in plane geometry and number theory Victor Klee ; Stan Wagon |
| title_short | Old and new unsolved problems in plane geometry and number theory |
| title_sort | old and new unsolved problems in plane geometry and number theory |
| topic | Geometrie (DE-588)4020236-7 gnd Planimetrie (DE-588)4046223-7 gnd Zahlentheorie (DE-588)4067277-3 gnd Ungelöstes Problem (DE-588)4186869-9 gnd |
| topic_facet | Geometrie Planimetrie Zahlentheorie Ungelöstes Problem Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005374075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001900740 |
| work_keys_str_mv | AT kleevictor oldandnewunsolvedproblemsinplanegeometryandnumbertheory AT wagonstan oldandnewunsolvedproblemsinplanegeometryandnumbertheory |