Numbers and shapes revisited: more problems for young mathematicians
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1995
|
| Schriftenreihe: | Oxford science publications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 308 S. graph. Darst. |
| ISBN: | 0198534604 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Part 1: Problems
Chapter I The Fibonacci sequence, generalized Fibonacci sequences,
and related topics 3
Introduction 3
1.1 A few puzzles on house painting 5
1.2 Some well known properties of the Fibonacci numbers 5
1.3 bonacci numbers and generalizations of the golden rectangle 6
1.4 From Fibonacci numbers of higher order to fractals 13
1.5 How to solve recurrence relations of the form
fn(a, b) = afn_, (a, b) + bfn^2{a, b) 17
Chapter II Patterns of dots and partitions of integers 20
Introduction 20
2.1 A puzzle on a heap of pebbles and other questions 23
2.2 Partitions of integers into distinct parts and corresponding
Ferrer graphs 26
2.3 The proof of Euler s formula 30
Chapter III Patterns, related to rational numbers; Periodic
decimal fractions, repunits, and visible lattice points 31
Introduction 31
3.1 Periodic decimal numbers; what is a repunit? 31
3.2 Exercises on decimal expansions 34
3.3 Fractions and lattice points 34
Chapter IV Reflected light rays and real numbers; a theorem of
Kronecker 37
Introduction 37
4.1 Problems on reflected light rays 37
4.2 Non periodic light ray paths; a theorem of Kronecker on
irrational numbers 40
4.3 Further applications of Kronecker s theorem 42
ix
x Contents
Chapter V The Chinese remainder theorem and invisible lattice
points 45
Introduction 45
5.1 Linear congruences and the Chinese remainder theorem 45
5.2 Applications of the Chinese remainder theorem 48
Chapter VI Two famous inequalities and some related problems 51
Introduction 51
6.1 A proof of Cauchy s theorem 51
6.2 A generalization of Cauchy s inequality and its applications 53
6.3 Special cases of the isoperimetric theorem 56
Chapter VII Mysteries of the third dimension: on cubes, pyramids,
and spheres 58
Introduction 58
7.1 Cubes, rhombic dodecahedra, and honeybee cells 58
7.2 Tetrahedra — compared with triangles 63
7.3 Are shapes of equal content equidecomposable? Hilbert s
third problem 66
7.4 Problems on spheres 69
Chapter VIII A glimpse of higher dimensional spaces: hypercubes,
lattice paths, and related number patterns 71
Introduction 71
8.1 On M dimensional real euclidean spaces 71
8.2 M dimensional hypercubes 76
8.3 Hypercubic lattice paths and corresponding number patterns 80
Chapter IX Do it with groups 88
Introduction 88
9.1 Examples and some basic properties of groups 89
9.2 How to use groups for the solution of some functional
equations 93
9.3 Groups and lattice points 96
9.4 Permutations in the study of the fifteen puzzle and Rubik s
cube 97
Contents xi
Chapter X From puzzles to research topics: selected problems of
combinatorics 103
Introduction 103
10.1 36 officers and Latin squares 103
10.2 Complete sets of mutually orthogonal Latin squares and finite
affine and projective planes 107
10.3 Problems on map colouring 112
10.4 Problems related to graphs; memory wheels and instant
insanity 115
Part 2 Solutions
Chapter I 125
Chapter II 151
Chapter III 165
Chapter IV 175
Chapter V 187
Chapter VI 193
Chapter VII 208
Chapter VIII 235
Chapter IX 255
Chapter X 273
References and suggestions for further reading 301
Index 305
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:48:37Z |
| institution | BVB |
| isbn | 0198534604 |
| language | English |
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| physical | XI, 308 S. graph. Darst. |
| publishDate | 1995 |
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| publishDateSort | 1995 |
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| spelling | Cofman, Judita 1936-2001 Verfasser (DE-588)12103173X aut Numbers and shapes revisited more problems for young mathematicians Judita Cofman Oxford Clarendon Press 1995 XI, 308 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford science publications Wiskunde gtt Mathematik Mathematics Problems, exercises, etc Problem solving Mathematik (DE-588)4037944-9 gnd rswk-swf Problemlösen (DE-588)4076358-4 gnd rswk-swf Problemlösen (DE-588)4076358-4 s Mathematik (DE-588)4037944-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006788576&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cofman, Judita 1936-2001 Numbers and shapes revisited more problems for young mathematicians Wiskunde gtt Mathematik Mathematics Problems, exercises, etc Problem solving Mathematik (DE-588)4037944-9 gnd Problemlösen (DE-588)4076358-4 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4076358-4 |
| title | Numbers and shapes revisited more problems for young mathematicians |
| title_auth | Numbers and shapes revisited more problems for young mathematicians |
| title_exact_search | Numbers and shapes revisited more problems for young mathematicians |
| title_full | Numbers and shapes revisited more problems for young mathematicians Judita Cofman |
| title_fullStr | Numbers and shapes revisited more problems for young mathematicians Judita Cofman |
| title_full_unstemmed | Numbers and shapes revisited more problems for young mathematicians Judita Cofman |
| title_short | Numbers and shapes revisited |
| title_sort | numbers and shapes revisited more problems for young mathematicians |
| title_sub | more problems for young mathematicians |
| topic | Wiskunde gtt Mathematik Mathematics Problems, exercises, etc Problem solving Mathematik (DE-588)4037944-9 gnd Problemlösen (DE-588)4076358-4 gnd |
| topic_facet | Wiskunde Mathematik Mathematics Problems, exercises, etc Problem solving Problemlösen |
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