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Beautiful mathematics:

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Bibliographische Detailangaben
Beteilige Person:	Erickson, Martin J. 1963-2013 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Washington, DC MAA, Mathematical Association of America 2011
Schriftenreihe:	Spectrum series
Schlagwörter:	Mathematik Mathematics / Popular works Beispielsammlung
Links:	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
Umfang:	XIII, 177 S. graph. Darst. 25 cm
ISBN:	0883855763 9780883855768

Internformat

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Datensatz im Suchindex

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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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author	Erickson, Martin J. 1963-2013
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dewey-tens	510 - Mathematics
discipline	Mathematik
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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
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