Architecture and Mathematics in Ancient Egypt

Corinna Rossi

Cambridge University Press | 2007 | 300 páginas | pdf | 4,8 Mb

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Corinna Rossi explores the use of numbers and geometrical figures by the Ancient Egyptians in their architectural projects and buildings. Whereas previous architectural studies have searched for "universal rules" to explain the entire history of Egyptian architecture, Rossi reconciles the approaches of architectural historians and archaeologists by testing architectural theories. This book is essential reading for all scholars of Ancient Egypt and the architecture of ancient cultures. 

Contents
List of illustrations page viii
List of tables xiii
Preface xiv
Acknowledgments xvii
List of abbreviations xix
Part I Proportions in ancient Egyptian architecture
Introduction to Part I: Harmony and proportions in architecture 2
1 In search of ‘the rule’ for ancient Egyptian architecture 7
Triangles and other figures 7
Three triangles for ancient Egypt 7
Viollet-le-Duc, Babin and the primeval pyramid 11
Choisy and the introduction of the Golden Section 16
The Golden Section 23
The origin and definitions of the Golden Section 23
The Golden Section and ancient Egyptian art and architecture 28
The theory of Alexander Badawy 32
2 Mathematics and architecture in ancient Egypt 57
Ancient Egyptian mathematics 57
The mathematical sources and their language 57
On , and other anachronisms 60
Intention, coincidence or tendency? 68
Triangles and architecture 68
Psychological experiments and involuntary trends 78
Cases from ancient Egypt 80
Conclusion to Part I: Ancient mathematics and practical operations 87
Part II Ancient Egyptian sources: construction and representation of space
Introduction to Part II: Tradition and variations in ancient Egyptian art and architecture 92
3 Documents on the planning and building process 96
Architectural drawings 96
Representations of buildings and working drawings 96
Drawings with written dimensions: the problem of the scale 101
Full-size geometrical sketches of architectural details 113
The use of square grids and the idea of a module 122
Architectural models 128
Votive objects 128
Working models 135
Projects and works in the Nineteenth and Twentieth Dynasty royal tombs 139
Documents on the works 139
Recording the progress: from the project to the survey 142
4 Foundation rituals 148
Foundation ceremonies 148
The ritual sequence 148
Cords and geometry 154
Building Texts 161
The dimensions of the primeval temples 161
The dimensions of the temples at Edfu and Dendera 166
Conclusion to Part II: From the plan to the building 174
Part III The geometry of pyramids
Introduction to Part III: Combining the knowledge 178
5 Symbolic shape and constructional problems 180
The form 180
Pyramidal form and solar cult 180
Benben and benbenet 182
As high as possible 184
The technique 185
Seked, side-length, diagonals and corners 185
Methods for obtaining the slope 188
Dimensions and proportions 196
6 The proportions of pyramids 200
Analysing true pyramids 200
Numerological theories 200
Lauer’s simple ratios 202
A list of true pyramids 204
Available data 204
Pyramidia as alternative sources 205
7 Pyramids and triangles 212
Geometrical models 212
Approximation and seked 212
Equilateral and b = h triangles 214
Seked 512
palms, generally called 14
11 triangle 215
Pythagorean triplets 216
The evolution of the form 221
Old Kingdom pyramids 221
Middle Kingdom pyramids 228
New Kingdom and Late Period pyramids 231
Conclusion to Part III: Interpreting the slope of pyramids 236
An overview 239
Appendix List of Old and Middle Kingdom true pyramids 242
Bibliography 255
Index 271

Nexus Network Journal: Leonardo da Vinci: Architecture and Mathematics

Sylvie Duvernoy 

Nexus Network Journal, vol. 10, number 1

Birkhäuser | 2008 | 200 páginas | pdf | 24 Mb

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Leonardo da Vinci was well aware of the fundamental importance of mathematics for architecture. This book examines Leonardo’s knowledge of theoretical mathematics, explores how he used concepts of geometry in his designs for architectural projects, and reports on a real-life construction project using Leonardo’s principles. Authors include Sylvie Duvernoy, Kim Williams, Rinus Roelofs, Biagio Di Carlo, Mark Reynolds, João Pedro Xavier, Vesna Petresin, Christopher Glass, and Jane Burry.

CONTENTS

Letter from the Guest Editor

5 SYLVIE DUVERNOY. An Introduction to Leonardo’s Lattices Leonardo da Vinci: Architecture and Mathematics

13 KIM WILLIAMS. Transcription and Translation of Codex Atlanticus, fol. 899 v

17 RINUS ROELOFS. Two- and Three-Dimensional Constructions Based on Leonardo Grids

27 BIAGIO DI CARLO. The Wooden Roofs of Leonardo and New Structural Research

39 SYLVIE DUVERNOY. Leonardo and Theoretical Mathematics

51 MARK REYNOLDS. The Octagon in Leonardo’s Drawings

77 JOÃO PEDRO XAVIER. Leonardo’s Representational Technique for Centrally- Planned Temples

101 VESNA PETRESIN ROBERT. Perception of Order and Ambiguity in Leonardo’s Design Concepts

129 CHRISTOPHER GLASS. Leonardo’s Successors Geometer’s Angle

149 RACHEL FLETCHER. Dynamic Root Rectangles Part Two: Root-Two Rectangles and Design Applications Didactics

179 JANE BURRY and ANDREW MAHER. The Other Mathematical Bridge

Book Reviews

195 MICHAEL OSTWALD. A Theory of General Ethics: Human Relationships, Nature and the Built Environment by Warwick Fox

199 SARAH CLOUGH EDWARDS. Inigo Jones and the Classical Tradition by Christy Anderson

203 SYLVIE DUVERNOY. Architecture and Mathematics in Ancient Egypt by Corinna Rossi

Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education

Patsy Wang-Iverson, Robert J. Lang e Mark YIM

A K Peters/CRC Press | 2011 | 632 páginas | rar - pdf |11,65 Mb

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Origami⁵ continues in the excellent tradition of its four previous incarnations, documenting work presented at an extraordinary series of meetings that explored the connections between origami, mathematics, science, technology, education, and other academic fields.

The fifth such meeting, 5OSME (July 13–17, 2010, Singapore Management University) followed the precedent previous meetings to explore the interdisciplinary connections between origami and the real world. This book begins with a section on origami history, art, and design. It is followed by sections on origami in education and origami science, engineering, and technology, and culminates with a section on origami mathematics—the pairing that inspired the original meeting.

Within this one volume, you will find a broad selection of historical information, artists’ descriptions of their processes, various perspectives and approaches to the use of origami in education, mathematical tools for origami design, applications of folding in engineering and technology, as well as original and cutting-edge research on the mathematical underpinnings of origami.

Contents

Preface xvii

I Origami History, Art, and Design 1

History of Origami in the East and the West before Interfusion 3

Koshiro Hatori

Deictic Properties of Origami Technical Terms and Translatability: Cross-Linguistic Differences between English and Japanese 13

Koichi Tateishi

Betsy Ross Revisited: General Fold and One-Cut Regular and Star Polygons 29

Arnold Tubis and Crystal Elaine Mills

Reconstructing David Huffman’s Legacy in Curved-Crease Folding 39

Erik D. Demaine, Martin L. Demaine, and Duks Koschitz

Simulation of Nonzero Gaussian Curvature in Origami by Curved-Crease Couplets 53

Cheng Chit Leong

Compression and Rotational Limitations of Curved Corrugations 69

Christine E. Edison

Polygon Symmetry Systems 81

Andrew Hudson

New Collaboration on Modular Origami and LED 89

Miyuki Kawamura and Hiroyuki Moriwaki

Using the Snapology Technique to Teach Convex Polyhedra 99

Faye Goldman

A Systematic Approach to Twirl Design 111

Krystyna Burczyk and Wojciech Burczyk

Oribotics: The Future Unfolds 127

Matthew Gardiner

II Origami in Education 139

Origametria and the van Hiele Theory of Teaching Geometry 141

Miri Golan

Student Teachers Introduce Origami in Kindergarten and Primary Schools: Froebel Revisited 151

Maria Llu¨ısa Fiol, Neus Dasquens, and Montserrat Prat

Narratives of Success: Teaching Origami in Low-Income Urban Communities 165

Christine E. Edison

Origami and Spatial Thinking of College-Age Students 173

Norma Boakes

Close Observation and Reverse Engineering of Origami Models 189

James Morrow and Charlene Morrow

Origami and Learning Mathematics 205

Sue Pope and Tung Ken Lam

Hands-On Geometry with Origami 219

Michael J. Winckler, Kathrin D. Wolf, and Hans Georg Bock

My Favorite Origamics Lessons on the Volume of Solids 233

Shi-Pui Kwan

III Origami Science, Engineering, and Technology 251

Rigid-Foldable Thick Origami 253

Tomohiro Tachi

Folding a Patterned Cylinder by Rigid Origami 265

Kunfeng Wang and Yan Chen

The Origami Crash Box 277

Jiayao Ma and Zhong You

Origami Folding: A Structural Engineering Approach 291

Mark Schenk and Simon D. Guest

Designing Technical Tessellations 305

Yves Klett and Klaus Drechsler

A Simulator for Origami-Inspired Self-Reconfigurable Robots 323

Steven Gray, Nathan J. Zeichner, Mark Yim, and Vijay Kumar

A CAD System for Diagramming Origami with Prediction of Folding Processes 335

Naoya Tsuruta, Jun Mitani, Yoshihiro Kanamori, and Yukio Fukui

Development of an Intuitive Algorithm for Diagramming and 3D Animated Tutorial for Folding Crease Patterns 347

Hugo Akitaya, Matheus Ribeiro, Carla Koike, and Jose Ralha

Hands-Free Microscale Origami 371

Noy Bassik, George M. Stern, Alla Brafman, Nana Y. Atuobi, and David H. Gracias

Foldable Parylene Origami Sheets Covered with Cells: Toward Applications in Bio-Implantable Devices 385

Kaori Kuribayashi-Shigetomi and Shoji Takeuchi

IV Mathematics of Origami 393

Introduction to the Study of Tape Knots 395

Jun Maekawa

Universal Hinge Patterns for Folding Orthogonal Shapes 405

Nadia M. Benbernou, Erik D. Demaine, Martin L. Demaine, and Aviv Ovadya

A General Method of Drawing Biplanar Crease Patterns 421

Herng Yi Cheng

A Design Method for Axisymmetric Curved Origami with Triangular Prism Protrusions 437

Jun Mitani

Folding Any Orthogonal Maze 449

Erik D. Demaine, Martin L. Demaine, and Jason S. Ku

Every Spider Web Has a Simple Flat Twist Tessellation 455

Robert J. Lang and Alex Bateman

Flat-Unfoldability and Woven Origami Tessellations 475

Robert J. Lang

Degenerative Coordinates in 22.5◦ Grid System 489

Tomohiro Tachi and Erik D. Demaine

Two Folding Constructions 499

Robert Orndorff

Variations on a Theorem of Haga 507

Emma Frigerio

Precise Division of Rectangular Paper into an Odd Number of Equal Parts without Tools: An Origamics Exercise 519

Kazuo Haga

The Speed of Origami Constructions Versus Other Construction Tools 531

Eul`alia Tramuns

A Note on Operations of Spherical Origami Construction 543

Toshikazu Kawasaki

Origami Alignments and Constructions in the Hyperbolic Plane 553

Roger C. Alperin

A Combinatorial Definition of 1D Flat-Folding 575

Hidefumi Kawasaki

Stamp Foldings with a Given Mountain-Valley Assignment 585

Ryuhei Uehara

Flat Vertex Fold Sequences 599

Thomas C. Hull and Eric Chang

Circle Packing for Origami Design Is Hard 609

Erik D. Demaine, S´andor P. Fekete, and Robert J. Lang

Contributors 627

Outros livros das atas das conferências:

Origami 4 : Fourth International Meeting of Origami Science, Mathematics, and Education por Robert J Lang; Origami USA.; Idioma: Inglês   Editora: Natick, Mass. : A K Peters, ©2009.

Origami³ : Third International Meeting of Origami Science, Math, and Education por Thomas Hull; Idioma: Inglês   Editora: Natick, MA : A K Peters, ©2002.

Galileo's Muse: Renaissance Mathematics and the Arts

Mark A. Peterson

Harvard University Press | 2011 | páginas | rar - pdf | 829 kb

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Mark Peterson makes an extraordinary claim in this fascinating book focused around the life and thought of Galileo: it was the mathematics of Renaissance arts, not Renaissance sciences, that became modern science. "Galileo's Muse" argues that painters, poets, musicians, and architects brought about a scientific revolution that eluded the philosopher-scientists of the day, steeped as they were in a medieval cosmos and its underlying philosophy. According to Peterson, the recovery of classical science owes much to the Renaissance artists who first turned to Greek sources for inspiration and instruction. Chapters devoted to their insights into mathematics, ranging from perspective in painting to tuning in music, are interspersed with chapters about Galileo's own life and work. Himself an artist turned scientist and an avid student of Hellenistic culture, Galileo pulled together the many threads of his artistic and classical education in designing unprecedented experiments to unlock the secrets of nature. In the last chapter, Peterson draws our attention to the Oratio de Mathematicae laudibus of 1627, delivered by one of Galileo's students. This document, Peterson argues, was penned in part by Galileo himself, as an expression of his understanding of the universality of mathematics in art and nature. It is 'entirely Galilean in so many details that even if it is derivative, it must represent his thought', Peterson writes. An intellectual adventure, "Galileo's Muse" offers surprising ideas that will capture the imagination of anyone - scientist, mathematician, history buff, lover of literature, or artist - who cares about the humanistic roots of modern science.

Contents
Prologue 1
1. Galileo, Humanist 3
2. The Classical Legacy 33
Poetry 67
3. The Plan of Heaven 69
4. The Vision of God 81
Painting 95
5. The Power of the Lines 99
6. The Skin of the Lion 125
Music 149
7. The Orphic Mystery 153
8. Kepler and the Music of the Spheres 174
Architecture 197
9. Figure and Form 203
10. The Dimensions of Hell 214
11. Mathematics Old and New 237
12. Transforming Mathematics 255
13. The Oration272
Epilogue 292
Notes 299
Acknowledgments 321
Index 323

Making Mathematics with Needlework: Ten Papers and Ten Projects

 Sarah-Marie Belcastro e Carolyn Yackel 

A K Peters/CRC Press | 2007 | 202 páginas | rar - pdf | 25,3 Mb

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Mathematical craftwork has become extremely popular, and mathematicians and crafters alike are fascinated by the relationship between their crafts. The focus of this book, written for mathematicians, needleworkers, and teachers of mathematics, is on the relationship between mathematics and the fiber arts (including knitting, crocheting, cross-stitch, and quilting). Each chapter starts with an overview of the mathematics and the needlework at a level understandable to both mathematicians and needleworkers, followed by more technical sections discussing the mathematics, how to introduce the mathematics in the classroom through needlework, and how to make the needlework project, including patterns and instructions.

Contents
Quilted mobius band
Picking up stitches and Diophantine equations
The Sierpinski variations: self-similar crochet
Ony two knit stitches can create a torus
Symmetry patterns in cross-stitch
Socks with Algebraic structure
Fortunatus's purse
(K)not cables, braids
The graph theory of blackwork embroidery
Stop those pants!

Livro relacionado: 

Crocheting adventures with hyperbolic planes por Daina Taimin̦a Idioma: Inglês   Editora: Wellesley, MA : A.K. Peters, ©2009.

Math and the Mona Lisa: The Art and Science of Leonardo da Vinci

Atalay Bülent
Smithsonian | 2004 | 352 páginas | rar - epub | 6,1 Mb

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PDF | 4,8 Mb - link

Math and the Mona Lisa sees the transcendant unity of art and science in almost every aspect of Leonardo's life and work. Atalay seeks the consilience of science and art—painting, architecture, sculpture, music, mathematics, physics, biology, astronomy, and engineering—and the unity of the two cultures. He delves deeply into the underlyingmathematics and aesthetics of science and art, paying special attention to the mathematical sequence called the Fibonacci series and to the related notion of the "golden ratio" or "divine proportion"—the keys to understanding the unity of art and nature. 32 b/w and 16 color illustrations.

Contents
  1    Leonardo Fiorentino: A Life Well Spent
  2    The Confluence of Science and Art
  3    Painting by Numbers
  4    The Nature of Science
  5    The Nature of Art
  6    The Art of Nature
  7    The Science of Art
  8    The Eye of the Beholder and the Eye of the Beheld
  9    Leonardo, Part-Time Artist
10    The Manuscripts of the Consummate Scientist
11    Unifying the Physics of Heaven and Earth
12    The Greatest Collective Piece of Art of the Twentieth Century
13    Bridging the Cultural Divide
Bibliographical Essay

Using Children’s Literature to Teach Problem Solving in Math: Addressing the Common Core in K–2

Jeanne White

Routledge | 2013 | 111 páginas | rar - pdf | 516 kb

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Learn how to use children’s literature to engage students in mathematical problem solving. Teaching with children’s literature helps build a positive math environment, encourages students to think abstractly, shows students the real-world purposes of math, builds content-area literacy, and appeals to students with different learning styles and preferences. This practical book provides specific children’s book ideas and standards-based lessons that you can use to bring math alive in your own classroom.

Special Features:

• Step-by-step ideas for using children’s literature to teach lessons based on the Common Core Standards for Mathematical Content in kindergarten, first, and second grade

• Scripting, modeling, and discussion prompts for each lesson

• Information on alignment to the Standards for Mathematical Practice and how to put them into student-friendly language

• Reference to a wide variety of specific children’s literature that can provide a context for young children learning to engage in the standards

• Differentiated activities for students who are early, developing, and advanced problem solvers

Contents
About the Author ix
Acknowledgments xi
Introduction: Using Children’s Literature to Teach
Problem Solving in Math 1
Types of Problem Solvers 2
Creating a Problem-Solving Community 3
1 Make Sense and Persevere 5
Early Problem Solvers 6
Seven Blind Mice—Decomposing Numbers 6
Developing Problem Solvers 10
MATH-Terpieces: The Art of Problem Solving—Using 2 and 3 Addends to Find a Sum 10
Advanced Problem Solvers 12
Splash!—Representing Addition and Subtraction Problems 12
2 Reason Abstractly 15
Early Problem Solvers 16
Ten Flashing Fireflies—Exploring the Commutative Property of Addition 16
Rooster’s Off to See the World—Exploring the Associative Property of Addition 17
Developing Problem Solvers 19
Each Orange Had 8 Slices—Demonstrating Fluency for Addition 19
Advanced Problem Solvers 21
How Many Mice?—Representing and Solving Problems With Addition and Subtraction 21
3 Construct Arguments 23
Early Problem Solvers 24
How Many Seeds in a Pumpkin?—Skip-Counting and Comparing Three-Digit Numbers 24
Developing Problem Solvers 27
Mall Mania—Adding Two-Digit Numbers Using Various Strategies 27
Advanced Problem Solvers 29
Spaghetti and Meatballs for All!—Creating Composite Shapes 29
4 Create a Model 33
Early Problem Solvers 33
The Doorbell Rang—Representing Addition in Various Ways 33
Developing Problem Solvers 38
Bigger, Better, Best!—Using Addition With Rectangular Arrays 38
Advanced Problem Solvers 42
Alexander, Who Used to be Rich Last Sunday—Solving Word Problems With Money 42
5 Use Mathematical Tools 47
Early Problem Solvers 48
Earth Day-Hooray!—Using Place Value to Add and Subtract 48
Developing Problem Solvers 52
Mummy Math—Recognizing Attributes of 3D Objects 52
Advanced Problem Solvers 54
Measuring Penny—Measuring in Standard and Nonstandard Units 54
6 Attend to Precision 59
Early Problem Solvers 59
If You Were a Quadrilateral—Identifying Quadrilaterals 59
Developing Problem Solvers 62
Lemonade for Sale—Representing and Interpreting Data 62
Advanced Problem Solvers 65
Measuring Penny—Relating Addition and Subtraction to Length 65
7 Look for Structure 69
Early Problem Solvers 69
The Button Box—Identifying Attributes for Sorting 69
Developing Problem Solvers 73
Patterns in Peru—Describing Relative Positions 73
Advanced Problem Solvers 76
The Greedy Triangle—Exploring Attributes of Shapes 76
8 Apply Repeated Reasoning 81
Early Problem Solvers 82
Bunches of Buttons: Counting by Tens—Counting to 100 by Tens 82
Developing Problem Solvers 85
How Big is a Foot?—Iterating Length Units 85
Advanced Problem Solvers 87
The King’s Commissioners—Representing Tens and Ones 87
Next Steps 91
Appendix: Common Addition and Subtraction Situations 93
References 95

Wizards, aliens, and starships : physics and math in fantasy and science fiction

Charles L. Adler

Princeton University Press | 2014 | 392 páginas | rar - epub | 2,05 Mb

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Wizards, Aliens, and Starships will speak to anyone wanting to know about the correct--and incorrect--science of science fiction and fantasy.

From teleportation and space elevators to alien contact and interstellar travel, science fiction and fantasy writers have come up with some brilliant and innovative ideas. Yet how plausible are these ideas--for instance, could Mr. Weasley's flying car in the Harry Potter books really exist? Which concepts might actually happen, and which ones wouldn't work at all? Wizards, Aliens, and Starships delves into the most extraordinary details in science fiction and fantasy--such as time warps, shape changing, rocket launches, and illumination by floating candle--and shows readers the physics and math behind the phenomena.

With simple mathematical models, and in most cases using no more than high school algebra, Charles Adler ranges across a plethora of remarkable imaginings, from the works of Ursula K. Le Guin to Star Trek and Avatar, to explore what might become reality. Adler explains why fantasy in the Harry Potter and Dresden Files novels cannot adhere strictly to scientific laws, and when magic might make scientific sense in the muggle world. He examines space travel and wonders why it isn't cheaper and more common today. Adler also discusses exoplanets and how the search for alien life has shifted from radio communications to space-based telescopes. He concludes by investigating the future survival of humanity and other intelligent races. Throughout, he cites an abundance of science fiction and fantasy authors, and includes concise descriptions of stories as well as an appendix on Newton's laws of motion.

CONTENTS

1 PLAYING THE GAME 1

1.1 The Purpose of the Book 1

1.2 The Assumptions I Make 3

1.3 Organization 4

1.4 The Mathematics and Physics You Need 5

1.5 Energy and Power 6

I POTTER PHYSICS 11

2 HARRY POTTER AND THE GREAT CONSERVATION LAWS 13

2.1 The Taxonomy of Fantasy 13

2.2 Transfiguration and the Conservation of Mass 14

2.3 Disapparition and the Conservation of Momentum 16

2.4 Reparo and the Second Law of Thermodynamics 21

3 WHY HOGWARTS IS SO DARK 27

3.1 Magic versus Technology 27

3.2 Illumination 28

4 FANTASTIC BEASTS AND HOW TO DISPROVE THEM 38

4.1 Hic sunt Dracones 38

4.2 How to Build a Giant 39

4.3 Kleiber’s Law, Part 1: Mermaids 45

4.4 Kleiber’s Law, Part 2: Owls, Dragons, Hippogriffs, and Other Flying Beasts 49

II SPACE TRAVEL 57

5 WHY COMPUTERS GET BETTER AND CARS CAN’T (MUCH) 59

5.1 The Future of Transportation 59

5.2 The Reality of Space Travel 61

5.3 The Energetics of Computation 63

5.4 The Energetics of the Regular and the Flying Car 64

5.5 Suborbital Flights 68

6 VACATIONS IN SPACE 71

6.1 The Future in Science Fiction: Cheap, Easy Space Travel? 71

6.2 Orbital Mechanics 74

6.3 Halfway to Anywhere: The Energetics of Spaceflight 74

6.4 Financing Space Travel 82

7 SPACE COLONIES 86

7.1 Habitats in Space 86

7.2 O’Neill Colonies 87

7.3 Matters of Gravity 89

7.4 Artificial “Gravity” on a Space Station 93

7.5 The Lagrange Points 103

7.6 Off-Earth Ecology and Energy Issues 106

7.7 The Sticker Price 112

8 THE SPACE ELEVATOR 115

8.1 Ascending into Orbit 115

8.2 The Physics of Geosynchronous Orbits 116

8.3 What Is a Space Elevator, and Why Would We Want One? 118

8.4 Why Buildings Stand Up—or Fall Down 119

8.5 Stresses and Strains: Carbon Nanotubes 122

8.6 Energy, “Climbers,” Lasers, and Propulsion 123

8.7 How Likely Is It? 125

8.8 The Unapproximated Elevator 127

9 MANNED INTERPLANETARY TRAVEL 130

9.1 It’s Not an Ocean Voyage or a Plane Ride 130

9.2 Kepler’s Three Laws 131

9.3 The Hohmann Transfer Orbit 134

9.4 Delta v and All That 136

9.5 Getting Back 137

9.6 Gravitational Slingshots and Chaotic Orbits 138

9.7 Costs 142

10 ADVANCED PROPULSION SYSTEMS 145

10.1 Getting There Quickly 145

10.2 Why Chemical Propulsion Won’t Work 146

10.3 The Most Famous Formula in Physics 147

10.4 Advanced Propulsion Ideas 148

10.5 Old “Bang-Bang”: The Orion Drive 153

10.6 Prospects for Interplanetary Travel 155

11 SPECULATIVE PROPULSION SYSTEMS 157

11.1 More Speculative Propulsion Systems 157

11.2 Mass Ratios for Matter-Antimatter Propulsion Systems 168

11.3 Radiation Problems 173

12 INTERSTELLAR TRAVEL AND RELATIVITY 176

12.1 Time Enough for Anything 176

12.2 Was Einstein Right? 178

12.3 Some Subtleties 182

12.4 Constant Acceleration in Relativity 184

13 FASTER-THAN-LIGHT TRAVEL AND TIME TRAVEL 188

13.1 The Realistic Answer 188

13.2 The Unrealistic Answer 188

13.3 Why FTL Means Time Travel 190

13.4 The General Theory 193

13.5 Gravitational Time Dilation and Black Holes 195

13.6 Wormholes and Exotic Matter 198

13.7 The Grandfather Paradox and Other Oddities 205

III WORLDS AND ALIENS 215

14 DESIGNING A HABITABLE PLANET 217

14.1 Adler’s Mantra 218

14.2 Type of Star 221

14.3 Planetary Distance from Its Star 226

14.4 The Greenhouse Effect 229

14.5 Orbital Eccentricity 232

14.6 Planetary Size and Atmospheric Retention 233

14.7 The Anna Karenina Principle and Habitable Planets 237

14.8 Imponderables 239

15 THE SCIENTIFIC SEARCH FOR SPOCK 242

15.1 Exoplanets and Exoplants 242

15.2 Doppler Technique 246

15.3 Transits and the Kepler Mission 249

15.4 The Spectral Signatures of Life 250

15.5 Alien Photosynthesis 251

16 THE MATHEMATICS OF TALKING WITH ALIENS 255

16.1 Three Views of Alien Intelligences 255

16.2 Motivation for Alien Contact 259

16.3 Drake-Equation Models and the Mathematics of Alien Contact 267

IV YEAR GOOGOL 273

17 THE SHORT-TERM SURVIVAL OF HUMANITY 275

17.1 This Is the Way the World Will End 275

17.2 The Short-Term: Man-Made Catastrophes 275

18 WORLD-BUILDING 292

18.1 Terraforming 292

18.2 Characteristics of Mars 294

18.3 Temperature and the Martian Atmosphere 295

18.4 Atmospheric Oxygen 299

18.5 Economics 301

19 DYSON SPHERES AND RINGWORLDS 303

19.1 Dyson’s Sphere 303

19.2 The Dyson Net 305

19.3 Niven’s Ringworld 311

19.4 The Ringworld, GPS, and Ehrenfest’s Paradox 318

19.5 The Ringworld Is Unstable! 320

19.6 Getting There from Here—and Do We Need To? 324

20 ADVANCED CIVILIZATIONS AND THE KARDASHEV SCALE 326

20.1 The Kardashev Scale 326

20.2 Our Type 0.7 Civilization 327

20.3 Type I Civilizations 329

20.4 Moving Upward 331

20.5 Type II Civilizations 332

20.6 Type III Civilizations 334

21 A GOOGOL YEARS 336

21.1 The Future of the Future 336

21.2 The “Short Term”: Up to 500 Million Years or so 336

21.3 The “Medium Term”: Up to about 1013 Years 338

21.4 The “Long Term”: Up to a Googol Years 341

21.5 Black Hole–Powered Civilizations 344

21.6 Protons Decay—or Do They? 346

21.7 A Googol Years—All the Black Holes Evaporate 346

21.8 Our Last Bow 349

Acknowledgments 351

Appendix: Newton’s Three Laws of Motion 353

Bibliography 359

Index 371

Celestial Sleuth: Using Astronomy to Solve Mysteries in Art, History and Literature

Donald W. Olson

Springer | 2014 | 368 páginas | rar - pdf | 18,2 Mb

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For a general audience interested in solving mysteries in art, history, and literature using the methods of science, 'forensic astronomy' is a thrilling new field of exploration. Astronomical calculations are the basis of the studies, which have the advantage of bringing to readers both evocative images and a better understanding of the skies. 

Weather facts, volcano studies, topography, tides, historical letters and diaries, famous paintings, military records, and the friendly assistance of experts in related fields add variety, depth, and interest to the work. The chosen topics are selected for their wide public recognition and intrigue, involving artists such as Vincent van Gogh, Claude Monet, Edvard Munch, and Ansel Adams; historical events such as the Battle of Marathon, the death of Julius Caesar, the American Revolution, and World War II; and literary authors such as Chaucer, Shakespeare, Joyce, and Mary Shelley. This book sets out to answer these mysteries indicated with the means and expertise of astronomy, opening the door to a richer experience of human culture and its relationship with nature.
Each subject is carefully analyzed. As an example using the study of sky paintings by Vincent van Gogh, the analytical method would include:
- computer calculations of historical skies above France in the 19th century
- finding and quoting the clues found in translations of original letters by Van Gogh
- making site visits to France to determine the precise locations when Van Gogh set up his easel and what celestial objects are depicted.
For each historical event influenced by astronomy, there would be a different kind of mystery to be solved. As an example:
- How can the phase of the Moon and time of moonrise help to explain a turning point of the American Civil War - the fatal wounding of Stonewall Jackson at Chancellorsville in 1863?
For each literary reference to astronomy, it was determined which celestial objects were being described and making an argument that the author is describing an actual event. For example, what was the date of the moonlit scene when Mary Shelley first had the idea for her novel “Frankenstein?”

These and more fun riddles will enchant and delight the fan of art and astronomy.

Contents

Preface vii

Foreword ix

Acknowledgments xiii

Part I Astronomy in Art

1 Monet and Turner, Masters of Sea and Sky 3

2 Vincent van Gogh and Starry Skies Over France 35

3 Edvard Munch: Mysterious Skies in Norway 67

4 Yosemite Moonrises and Moonbows 113

Part II Astronomy in History

5 Moons and Tides in the Battle of Marathon,

Paul Revere’s Midnight Ride, and the Sinking of the Titanic 147

6 Lincoln, the Civil War Era, and American Almanacs 199

7 Th e Moon and Tides in World War II 237

Part III Astronomy in Literature

8 Literary Skies Before 1800 277

9 Literary Skies Aft er 1800 317

Index 351

The Game of Probability: Literature and Calculation From Pascal to Kleist

Rudiger Campe e Ellwood Wiggins

Stanford University Press | 2013 | 504 páginas | rar - pdf | 2,3 Mb

link (password: matav)

There exist literary histories of probability and scientific histories of probability, but it has generally been thought that the two did not meet. Campe begs to differ. Mathematical probability, he argues, took over the role of the old probability of poets, orators, and logicians, albeit in scientific terms. Indeed, mathematical probability would not even have been possible without the other probability, whose roots lay in classical antiquity.
The Game of Probability revisits the seventeenth and eighteenth-century "probabilistic revolution," providing a history of the relations between mathematical and rhetorical techniques, between the scientific and the aesthetic. This was a revolution that overthrew the "order of things," notably the way that science and art positioned themselves with respect to reality, and its participants included a wide variety of people from as many walks of life. Campe devotes chapters to them in turn. Focusing on the interpretation of games of chance as the model for probability and on the reinterpretation of aesthetic form as verisimilitude (a critical question for theoreticians of that new literary genre, the novel), the scope alone of Campe's book argues for probability's crucial role in the constitution of modernity.

Contents
Introduction 1
part i. games for example: modeling probability
1 Theology and the Law: Dice in the Air 15
2 Numbers and Calculation in Context: The Game of Decision—Pascal 37
3 Writing the Calculation of Chances: Justice and Fair Game—Christiaan Huygens 73
4 Probability, a Postscript to the Theory of Chance: Logic and Contractual Law—Arnauld, Leibniz, Pufendorf 97
5 Probability Applied: Ancient Topoi and the Theory of Games of Chance—Jacob Bernoulli 118
6 Continued Proclamations: The Law of logica probabilium—Leibniz 147
7 Defoe’s Robinson Crusoe, or, The Improbability of Survival 172
part ii. verisimilitude spelled out: the appearance of truth
8 Numbers and Tables in Narration: Jurists and Clergymen and Their Bureaucratic Hobbies 195
9 Novels and Tables: Defoe’s A Journal of the Plague Year and Schnabel’s Die Insel Felsenburg 220
10 The Theory of Probability and the Form of the Novel: Daniel Bernoulli on Utility Value, the Anthropology of Risk, and Gellert’s Epistolary Fiction 248
11 “Improbable Probability”: The Theory of the Novel and Its Trope—Fielding’s Tom Jones and Wieland’s Agathon 273
12 The Appearance of Truth: Logic, Aesthetics, and Experimentation—Lambert 305
13 “Probable” or “Plausible”: Mathematical Formula Versus Philosophical Discourse—Kant 338
14 Kleist’s “Improbable Veracities,” or, A Romantic Ending 369
Conclusion 391
Notes 399
Bibliography 465

The Unimaginable Mathematics of Borges' Library of Babel

William Goldbloom Bloch 

Oxford University Press | 2011 | 213 páginas | pdf | 1 Mb

link
link1

Written in the vein of Douglas R. Hofstadter's Pulitzer Prize-winning Gödel, Escher, Bach, this original and imaginative book sheds light on one of Borges' most complex, richly layered works. Bloch begins each chapter with a mathematical idea--combinatorics, topology, geometry, information theory--followed by examples and illustrations that put flesh on the theoretical bones. In this way, he provides many fascinating insights intoBorges' Library. He explains, for instance, a straightforward way to calculate how many books are in the Library--an easily notated but literally unimaginable number--and also shows that, if each book were the size of a grain of sand, the entire universe could only hold a fraction of the books in the Library. Indeed, if each book were the size of a proton, our universe would still not be big enough to hold anywhere near all the books.
Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature but also exposes the reader--including those more inclined to the literary world--to many intriguing and entrancing mathematical ideas.
Written in the vein of Douglas R. Hofstadter's Pulitzer Prize-winning Gödel, Escher, Bach, this original and imaginative book sheds light on one of Borges' most complex, richly layered works. Bloch begins each chapter with a mathematical idea--combinatorics, topology, geometry, information theory--followed by examples and illustrations that put flesh on the theoretical bones. In this way, he provides many fascinating insights intoBorges' Library. He explains, for instance, a straightforward way to calculate how many books are in the Library--an easily notated but literally unimaginable number--and also shows that, if each book were the size of a grain of sand, the entire universe could only hold a fraction of the books in the Library. Indeed, if each book were the size of a proton, our universe would still not be big enough to hold anywhere near all the books.
Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature but also exposes the reader--including those more inclined to the literary world--to many intriguing and entrancing mathematical ideas.
Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature but also exposes the reader--including those more inclined to the literary world--to many intriguing and entrancing mathematical ideas.
"The Library of Babel" is arguably Jorge Luis Borges' best known story--memorialized along with Borges on an Argentine postage stamp. Now, inThe Unimaginable Mathematics of Borges' Library of Babel, William Goldbloom Bloch takes readers on a fascinating tour of the mathematical ideas hidden within one of the classic works of modern literature.

Contents
Acknowledgments vii
Preface xi
Introduction xvii
The Library of Babel 3
Chapter 1 Combinatorics: Contemplating Variations of the 23 Letters 11
Chapter 2 Information Theory: Cataloging the Collection 30
Chapter 3 Real Analysis: The Book of Sand 45
Chapter 4 Topology and Cosmology: The Universe (Which Others Call the Library) 57
Chapter 5 Geometry and Graph Theory: Ambiguity and Access 93
Chapter 6 More Combinatorics: Disorderings into Order 107
Chapter 7 A Homomorphism: Structure into Meaning 120
Chapter 8 Critical Points 126
Chapter 9 Openings 141
Appendix—Dissecting the 3-Sphere 148
Notations 157
Notes 159
Glossary 165
Annotated Suggested Readings 175
Bibliography 181
Index 187

Nature and Numbers a mathematical photo shooting

Georg Glaeser

Ambra Verlag | 2014 | 377 páginas | rar - pdf | 137 Mb

link (password : matav)

Mathematicians with special interest in biology, physics, geography, astronomy, architecture, design, etc., and being prepared to take pictures at any time, might try to answer unusual questions like the followings: What do a zebra, a tiger shark, and a hard coral have in common? How is this with drying mud, wings of dragon flies, and the structures of leaves? What is the "snail king" and is there also a "worm king"? Which curves stay of the same type after being photographed? Do fishes see like we do if we look through a fisheye lens? Which geometric properties of an object have physical consequences? Which kinds of geometric patterns appear when waves are interfering?
In Nature and Numbers you can find 180 double pages with at least as many questions of this kind. The principle to attack a problem is often similar: It starts with a photo that is for some reasons remarkable. In a short description an explanation is offered, including relevant Internet links. Additionally one can frequently find computer simulations in order to illustrate and confirm.

Strategies to Integrate the Arts in Mathematics

Linda Dacey e Lisa Donovan 

Shell Education Pub | 2013 | 280 páginas | rar - pdf | 20 Mb

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password: matav

This teacher-friendly resource provides practical arts-based strategies for classroom teachers to use in teaching mathematics content. Overview information and model lessons are provided for each strategy and ideas are provided for grades K-2, 3-5, 6-8, and 9-12. The strategies addressed within the book allow teachers to make mathematics instruction come alive and best meet students' needs.

Table of Contents 5 
Correlation to the Standards 21 
Creative Movement 23 
Drama 67 
Music 105 
Poetry 143 
Storytelling 183 
Visual Arts 225 
Appendix A: References Cited 268 
Appendix B: Assessment Forms 273 
Appendix C: Recommended Resources 277 
Appendix D: Contents of the Digital Resource CD 279 

Mathematics and Modern Art: Proceedings of the First ESMA Conference, held in Paris, July 19-22, 2010

(Springer Proceedings in Mathematics)

Claude Bruter

Springer | 2012 | 222 páginas | PDF | 9,3 Mb

link

The link between mathematics and art remains as strong today as it was in the earliest instances of decorative and ritual art. Arts, architecture, music and painting have for a long time been sources of new developments in mathematics, and vice versa. Many great painters have seen no contradiction between artistic and mathematical endeavors, contributing to the progress of both, using mathematical principles to guide their visual creativity, enriching their visual environment with the new objects created by the mathematical science.

Owing to the recent development of the so nice techniques for visualization, while mathematicians can better explore these new mathematical objects, artists can use them to emphasize their intrinsic beauty, and create quite new sceneries. This volume, the content of the first conference of the European Society for Mathematics and the Arts (ESMA), held in Paris in 2010, gives an overview on some significant and beautiful recent works where maths and art, including architecture and music, are interwoven. 

The book includes a wealth of mathematical illustrations from several basic mathematical fields including classical geometry, topology, differential geometry, dynamical systems.  Here, artists and mathematicians alike elucidate the thought processes and the tools used to create their work

Contents

A Mathematician and an Artist. The Story of a Collaboration . . 1

Richard S. Palais

Dimensions, a Math Movie  . . 11

Aurelien Alvarez and Jos Leys

Old and New Mathematical Models: Saving the Heritage of the Institut Henri Poincare . . 17

Francois Apery

An Introduction to the Construction of Some Mathematical Objects. . 29

Claude Paul Bruter

Computer, Mathematics and Art . . . 47

Jean-Franc¸ois Colonna

Structure of Visualization and Symmetry in Iterated Function Systems . . . 53

Jean Constant

M.C. Escher’s Use of the Poincare Models of Hyperbolic Geometry. . 69

Douglas Dunham

Mathematics and Music Boxes  . . 79

Vi Hart

My Mathematical Engravings. . 85

Patrice Jeener

Knots and Links As Form-Generating Structures. . 105

Dmitri Kozlov

Geometry and Art from the Cordovan Proportion. . . 117

Antonia Redondo Buitrago and Encarnacion Reyes Iglesias

Dynamic Surfaces . . 131

Simon Salamon

Pleasing Shapes for Topological Objects . . 153

John M. Sullivan

Rhombopolyclonic Polygonal Rosettes Theory . . 167

Francois Tard