 | Rozhkovskaya N. M is for Math, Museum, and Manhattan, Kansas. - Novosibirsk: Tamara Rozhkovskaya Publisher, 2017. - 200 p., [5] l. col. ill.: ill. - Bibliogr.: p.179-184. - Ind. of names: p.195-196. - Sub. ind.: p.197-199.
ШИФР ОТДЕЛЕНИЯ ГПНТБ СО РАН B1-R87
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Short Guide to the Book ......................................... 9
What is This Book About? ........................................ 9
Where to See the Art Objects Discussed in the Book? ............. 9
Audience ........................................................ 9
Navigation ..................................................... 10
Acknowledgments ................................................ 11
Chapter l. Three Letters M ..................................... 13
1.1 M is for Manhattan ........................................ 13
1.1.1 In the heart of the country ........................ 13
1.1.2 How Manhattan was founded .......................... 14
1.1.3 The long road to a college town .................... 14
1.2 M is for Museum ........................................... 16
History of the Marianna Kistler Beach Museum of Art
by Kathrine Schlageck ..................................... 17
1.3 M is for Mathematics ...................................... 18
1.4 How It Worked for Us: Math and Art Workshops at the
Beach Museum of Art ....................................... 21
Chapter 2. Regular Polyhedra ................................... 25
2.1 About the Artwork [Kansas Meatball] ....................... 25
2.2 Polyhedra ................................................. 26
2.3 About the Artist [Alan Shields] ........................... 27
2.4 Other Examples in Art ..................................... 28
2.4.1 Polyhedra .......................................... 28
2.4.2 Geodesic domes ..................................... 29
2.5 Why Are There only Five Platonic Solids? .................. 30
2.6 Euler Characteristic. Magic of the Number 2 ............... 33
2.7 Dual Polyhedra ............................................ 34
2.8 Math Problems ............................................. 34
2.9 Art Projects .............................................. 35
2.9.1 Paper plate icosahedron ............................ 36
2.9.2 Toothpick icosahedron .............................. 39
2.10 Answers ................................................... 39
Chapter 3. Combinatorics and Probability ....................... 41
3.1 About the Artwork [21 with Cube] .......................... 41
3.2 What is a Die? ............................................ 42
3.3 Probability Theory. It All Started with a Game ............ 42
3.4 About the Artist [Jesus Manuel Montes] .................... 44
3.5 Card Games and Games of Chance in Art ..................... 45
3.6 Randomness as Art Technique ............................... 46
3.7 Math Problems ............................................. 47
3.8 Probability Experiments in Class .......................... 51
3.9 Art Projects .............................................. 53
3.9.1 Decorated die ...................................... 53
3.9.2 Random Person ...................................... 54
3.10 Answers ................................................... 57
Chapter 4. Symmetry ............................................ 61
4.1 What is Symmetry? ......................................... 61
4.2 Frieze Patterns ........................................... 64
4.3 Symmetries of Frieze Patterns ............................. 69
4.4 Seven Types of Frieze Patterns ............................ 70
4.5 About the Artists ......................................... 71
4.5.1 Jack Chevalier ..................................... 71
4.5.2 Pueblo communities ................................. 72
4.6 Math Problems ............................................. 74
4.7 Art Projects .............................................. 74
4.7.1 Paper People ....................................... 74
4.7.2 Decorate a vase .................................... 74
4.8 Answers ................................................... 74
Chapter 5. Circles ............................................. 75
5.1 Clay Painting with Circles ................................ 75
5.2 About the Artist [Orval F. Hempler] ....................... 76
5.3 Other Examples in Art ..................................... 77
5.4 Wonderful Circles around Us ............................... 77
5.5 Circles and Right Angles .................................. 79
5.6 More Problems about Circles ............................... 83
5.7 Art Projects .............................................. 84
5.8 Answers ................................................... 85
Chapter 6. Fibonacci Sequence .................................. 89
6.1 About the Artwork [Pyrrho Techniko] ....................... 89
6.2 Pattern of the Table ...................................... 90
6.3 Fibonacci Numbers ......................................... 91
6.4 Golden Ratio as a Limit of Fibonacci Sequence ............. 92
6.5 About the Artist [John L. Vogt] ........................... 92
6.6 Some Words of Caution from M. Gardner, G. Markowsky,
C. Falbo, U. Eco, et al. .................................. 94
6.7 Phyllotaxis and Examples of the Golden Ratio and
Fibonacci Numbers in Modern Art ........................... 97
6.7.1 Pinecones .......................................... 98
6.7.2 Modulor ............................................ 98
6.7.3 Other examples .................................... 100
6.8 Geometric Construction of Golden Ratio ................... 101
6.9 Problems on Properties of Fibonacci Numbers .............. 102
6.10 Playing with Sequences ................................... 104
6.11 Answers .................................................. 105
Chapter 7. Geometrical Optics ................................. 109
7.1 About the Artwork [Konza Prism] .......................... 110
7.2 Travel of Light .......................................... 110
7.3 Artist's Choices ......................................... 112
7.4 About the Artist [Roger Lane Routson] .................... 113
7.5 Other Examples in Art .................................... 113
7.6 Snell's Law .............................................. 113
7.7 The Reflection Principle and Billiards ................... 117
7.8 Refraction Experiment .................................... 120
7.9 Art Project [Rainbow Paper Collage] ...................... 120
7.10 Answers .................................................. 122
Chapter 8. Linear Perspective ................................. 127
8.1 Space Presentation ....................................... 127
8.2 Main Features of Linear Perspective ...................... 128
8.3 Picture Plane and Ground Plane ........................... 129
8.4 Horizon Line ............................................. 130
8.5 Vanishing Points ......................................... 132
8.6 The Number of Vanishing Points ........................... 136
8.6.1 No vanishing points: front view ................... 136
8.6.2 One-point perspective ............................. 137
8.6.3 Two-point perspective ............................. 137
8.6.4 Multi-point perspective ........................... 138
8.7 Do Artists Rigorously Follow Mathematical Rules of
Linear Perspective? ...................................... 139
8.7.1 Anderson Hall ..................................... 140
8.7.2 Spring and Mercer ................................. 140
8.8 Why Linear Perspective Rules Are not Always Followed
by Artists ............................................... 141
8.9 About the Artists ........................................ 143
8.9.1 Charles Merrick Capps ............................. 143
8.9.2 Stevan Dohanos .................................... 144
8.9.3 Norma Bassett Hall ................................ 144
8.9.4 George M. Kren .................................... 144
8.9.5 Roy Langford ...................................... 145
8.9.6 Carol Pylant ...................................... 145
8.9.7 Larry W. Schwarm .................................. 147
8.9.8 Shirley Smith ..................................... 147
8.10 Problems on Linear Perspective ........................... 148
8.11 Answers .................................................. 152
Chapter 9. Star Polygons ...................................... 155
9.1 About the Artwork [Lead Crystal Vase] .................... 155
9.2 Definition of Star Polygons .............................. 155
9.3 Star Polygons with Different Step Lengths ................ 157
9.4 The Greatest Common Divisors ............................. 157
9.5 About the Artists [Riickl Crystal] ....................... 158
9.6 Art Projects ............................................. 159
9.6.1 Decorated plate ................................... 159
9.6.2 Vase drawing ...................................... 159
9.6.3 String star polygon ............................... 160
9.7 Proof of Proposition 9.1 ................................. 162
9.8 Answers .................................................. 164
Chapter 10. Topology .......................................... 165
10.1 About the Artwork [Klein Bottle] ......................... 165
10.2 Nonorientable Surface .................................... 165
Klein bottle = 2 x Möbius band ........................... 168
10.3 About the Artist [Mitsugi Ohno] .......................... 168
10.4 Other Examples in Art .................................... 169
10.5 Topological Projects ..................................... 170
10.5.1 Let us cut ........................................ 170
10.5.2 Klein bottles and tori from pipe cleaners ......... 170
10.6 Topology ................................................. 172
10.7 Problems ................................................. 173
10.8 Tracing Designs .......................................... 174
10.9 Knots .................................................... 176
10.10 Answers ................................................. 177
References .................................................... 179
Artwork Index ................................................. 185
Image Index ................................................... 189
Name Index .................................................... 195
Subject Index ................................................. 197
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| The book is devoted to the natural bonds connecting art and mathematics illustrated by artworks from the collection of the Marianna Kistler Beach Museum of Art at Manhattan, Kansas. The mathematical concepts discussed in the book include properties of polyhedra, combinatorics of dice throwing, symmetry, geometry of circles, Fibonacci sequence, geometric optics, linear perspective, star polygons, and non-orientable surfaces. In many cases, the mathematical insight contributes to a better understanding of the artwork and the artist's methods and intentions. Each chapter contains a study of an art object from the museum's collection followed by a mathematical discussion, a list of mathematical problems, biographical notes on the artists, and creative projects. The material is based on the workshops taught by the author at the math enrichment program Math Circle Seminar at Kansas State University.
The book is addressed to a broad spectrum of readers interested in relations between art and mathematics, including the general public, professional mathematicians, professional artists, math and art educators, parents, and school students.
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