Beautiful mathematics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Washington, DC
MAA, Mathematical Association of America
2011
|
| Series: | Spectrum series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 177 S. graph. Darst. 25 cm |
| ISBN: | 0883855763 9780883855768 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804149078170271744 |
|---|---|
| adam_text | Titel: Beautiful mathematics
Autor: Erickson, Martin J
Jahr: 2011
Contents
Preface ix
1 Imaginative Words 1
1.1 Lemniscate.................................. 1
1.2 Centillion................................... 3
1.3 Golden Ratio................................. 3
1.4 Borromean Rings............................... 5
1.5 Sieve of Eratosthenes............................. 5
1.6 Transversal of Primes............................. 6
1.7 Waterfall of Primes.............................. 7
1.8 Squares, Triangular Numbers, and Cubes .................. 7
1.9 Determinant.................................. 8
1.10 Complex Plane................................ 8
2 Intriguing Images 13
2.1 Square Pyramidal Square Number...................... 13
2.2 Binary Trees ................................. 15
2.3 Bulging Hyperspheres ............................ 16
2.4 Projective Plane................................ 16
2.5 Two-Colored Graph.............................. 17
2.6 Hypercube................................... 18
2.7 Full Adder................................... 19
2.8 Sierpiñski s Triangle.............................. 20
2.9 Squaring Map................................. 21
2.10 Riemann Sphere................................ 22
3 Captivating Formulas 25
3.1 Arithmetical Wonders............................. 25
3.2 Heron s Formula and Heronian Triangles .................. 25
3.3 Sine, Cosine, and Exponential Function Expansions............. 28
3.4 Tangent and Secant Function Expansions .................. 29
3.5 Series for Pi.................................. 30
3.6 Product for Pi................................. 31
3.7 Fibonacci Numbers and Pi.......................... 32
3.8 VolumeofaBall............................... 32
3.9 Euler s Integral Formula........................... 34
3.10 Euler s Polyhedral Formula.......................... 35
xii Contents
3.11 The Smallest Taxicab Number........................ 36
3.12 Infinity and Infinity Squared......................... 37
3.13 Complex Functions.............................. 38
3.14 The Zeta Function and Bernoulli Numbers.................. 40
3.15 The Riemann Zeta Function......................... 41
3.16 The Jacobi Identity.............................. 42
3.17 Entropy.................................... 43
3.18 Rook Paths.................................. 44
4 Delightful Theorems 49
4.1 A Square inside Every Triangle........................ 49
4.2 Morley s Theorem .............................. 50
4.3 The Euler Line................................ 52
4.4 Monge s Theorem............................... 54
4.5 Power Means................................. 54
4.6 Regular Heptagon............................... 58
4.7 Isometries of the Plane............................ 59
4.8 Symmetries of Regular Convex Polyhedra.................. 61
4.9 Polynomial Symmetries............................ 63
4.10 Kings and Serfs................................ 65
4.11 The Erdôs-Szekeres Theorem......................... 66
4.12 Minkowski s Theorem............................ 67
4.13 Lagrange s Theorem............................. 69
4.14 Van der Waerden s Theorem......................... 72
4.15 Latin Squares and Projective Planes..................... 76
4.16 The Lemniscate Revisited .......................... 79
5 Pleasing Proofs 83
5.1 The Pythagorean Theorem.......................... 83
5.2 The Erdôs-Mordell Inequality......................... 84
5.3 Triangles with Given Area and Perimeter .................. 85
5.4 A Property of the Directrix of a Parabola................... 86
5.5 A Classic Integral............................... 87
5.6 Integer Partitions............................... 88
5.7 Integer Triangles............................... 89
5.8 Triangle Destruction ............................. 92
5.9 Squares in Arithmetic Progression...................... 94
5.10 Random Hemispheres............................. 95
5.11 Odd Binomial Coefficients.......................... 95
5.12 Frobenius Postage Stamp Problem...................... 96
5.13 Perrin s Sequence............................... 99
5.14 On the Number of Partial Orders....................... 99
5.15 Perfect Error-Correcting Codes........................ 101
5.16 Binomial Coefficient Magic ......................... 104
5.17 A Group of Operations............................ 106
Contents xiii
6 Elegant Solutions 109
6.1 A Tetrahedron and Four Spheres....................... 109
6.2 Alphabet Cubes................................ 110
6.3 A Triangle in an Ellipse............................ 110
6.4 About the Roots of a Cubic.......................... Ill
6.5 Distance on Planet X............................. 113
6.6 ATiltedCircle ................................ 114
6.7 The Millionth Fibonacci Number....................... 116
6.8 The End of a Conjecture........................... 117
6.9 A Zero-Sum Game.............................. 117
6.10 An Expected Maximum............................ 119
6.11 Walks on a Graph............................... 120
6.12 Rotations of a Grid.............................. 123
6.13 Stamp Rolls.................................. 125
6.14 Making a Million............................... 128
6.15 Coloring a Projective Plane.......................... 129
7 Creative Problems 131
7.1 Two-Dimensional Gobbling Algorithm....................131
7.2 Nonattacking Queens Game .........................132
7.3 Lucas Numbers Mod m............................132
7.4 Exact Colorings of Graphs..........................133
7.5 Queen Paths..................................134
7.6 Transversal Achievement Game.......................136
7.7 Binary Matrix Game.............................136
A Harmonious Foundations 139
A.l Sets...................................... 139
A.2 Relations................................... 141
A.3 Functions................................... 141
A.4 Groups .................................... 142
A.5 Fields..................................... 145
A.6 Vector Spaces................................. 146
B Eye-Opening Explorations 151
B.l Problems ...................................151
B.2 Solutions...................................155
Bibliography 165
Index 169
About the Author 177
|
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| ctrlnum | (OCoLC)778784418 (DE-599)BSZ361777280 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040119354 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:17:18Z |
| institution | BVB |
| isbn | 0883855763 9780883855768 |
| language | English |
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| physical | XIII, 177 S. graph. Darst. 25 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | MAA, Mathematical Association of America |
| record_format | marc |
| series2 | Spectrum series |
| spelling | Erickson, Martin J. 1963-2013 Verfasser (DE-588)139664181 aut Beautiful mathematics Martin Erickson Washington, DC MAA, Mathematical Association of America 2011 XIII, 177 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Spectrum series Mathematik Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematics / Popular works 1\p (DE-588)4144384-6 Beispielsammlung gnd-content Mathematik (DE-588)4037944-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-61444-509-8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024975499&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Erickson, Martin J. 1963-2013 Beautiful mathematics Mathematik Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4144384-6 |
| title | Beautiful mathematics |
| title_auth | Beautiful mathematics |
| title_exact_search | Beautiful mathematics |
| title_full | Beautiful mathematics Martin Erickson |
| title_fullStr | Beautiful mathematics Martin Erickson |
| title_full_unstemmed | Beautiful mathematics Martin Erickson |
| title_short | Beautiful mathematics |
| title_sort | beautiful mathematics |
| topic | Mathematik Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematik Beispielsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024975499&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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