cover

Bridges 2012

Towson, Maryland, USA
25–29 July 2012
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Front Matter
The Editors
Science, Art, Beauty, the Meaning of Life, and the James Webb Telescope
John Mather
Pages 1–8
Developing Mathematical Tools to Investigate Art
Ingrid Daubechies
Pages 9–16
Celebrating Mathematics in Stone and Bronze: Umbilic Torus NC vs SC
Helaman Ferguson and Claire Ferguson
Pages 17–24
Mitered Fractal Trees: Constructions and Properties
Tom Verhoeff and Koos Verhoeff
Pages 25–32
The Mathematical Art of Juggling: Using Mathematics to Predict, Describe and Create
Mike Naylor
Pages 33–40
My Parade of Algorithmic Mathematical Art
Greg N. Frederickson
Pages 41–48
An Algorithm for Creating Geometric Dissection Puzzles
Yahan Zhou and Rui Wang
Pages 49–56
Bringing M. C. Escher's Planaria to Life
George Hart
Pages 57–64
Mathematical Pattern Poetry
Sarah Glaz
Pages 65–72
Math in Poetry: Half of a Course
Marion Deutsche Cohen
Pages 73–78
Art of π: Mathematical History and Literary Inspiration
Tatiana Bonch-Osmolovskaya
Pages 79–84
Never-ending Storytelling with Discrete-Time Markov Processes
Yutu Liu, Ergun Akleman, Jianer Chen
Pages 85–92
From Möbius Bands to Klein-Knottles
Carlo H. Séquin
Pages 93–102
Sculptures in S3
Saul Schleimer and Henry Segerman
Pages 103–110
Splitting Tilings
Rinus Roelofs
Pages 111–118
Playing with the Platonics: A New Class of Polyhedra
Walt van Ballegooijen
Pages 119–124
Sculpture Inspired by Connectivity in Nature
William F. Duffy
Pages 125–132
Circle patterns in Gothic Architecture
Tiffany C. Inglis and Craig S. Kaplan
Pages 133–140
A 7-Fold System for Creating Islamic Geometric Patterns Part 1: Historical Antecedents
Jay Bonner and Marc Pelletier
Pages 141–148
A 7-Fold System for Creating Islamic Geometric Patterns Part 2: Contemporary Expression
Marc Pelletier and Jay Bonner
Pages 149–156
The Topkapı Scroll's Thirteen-Pointed Star Polygon Design
B. Lynn Bodner
Pages 157–164
Polyhedral Modularity in a Special Class of Decagram Based Interlocking Star Polygons
Reza Sarhangi
Pages 165–174
Tiles and Patterns of a Field: From Byzantine Churches to User Interface Design
Asaf Degani, Ron Asherov, Peter J. Lu
Pages 175–182
Sinuous Meander Patterns in Natural Coordinates
David Chappell
Pages 183–190
Broadening the Palette for Bobbin Lace: A Combinatorial Approach
Veronika Irvine
Pages 191–198
Two-color Fractal Tilings
Robert W. Fathauer
Pages 199–206
Mohr or Mascheroni?
Elaine Krajenke Ellison
Pages 207–214
Guernica
Javier Barrallo and Santiago Sánchez-Beitia
Pages 215–222
Moorish Fretwork Revisited
Paul Tucker
Pages 223–230
Polyhedra on an Equilateral Hyperboloid
Dirk Huylebrouck
Pages 231–238
The Experience Workshop MathArt Movement: Experience-centered Education of Mathematics through Arts, Sciences, and Playful Activities
Kristóf Fenyvesi
Pages 239–246
The Color Symmetries of the Solstices: Ritual Sandals from the Prehistoric American Southwest
Dorothy K. Washburn and Donald W. Crowe
Pages 247–250
Sacred Numbers and Tessellations in Aquileia's XI Century Mosaics
Marcella Giulia Lorenzi and Mauro Francaviglia
Pages 251–258
Simple Rules for Incorporating Design Art into Penrose and Fractal Tiles
San Le
Pages 259–266
Weaving Symmetry of the Philippine Northern Kankana-ey
Nathaniel A. Baylas IV, Teofina A. Rapanut, Ma. Louise Antonette N. De las Peñas
Pages 267–274
Patterned Triply Periodic Polyhedra
Douglas Dunham
Pages 275–282
Juan Gris' Compositional Symmetry Transformations
James Mai
Pages 283–290
Stigmmetry Prints from Patterns of Circles
Gary Greenfield
Pages 291–298
Geometry and Computation of Houndstooth (Pied-de-poule)
Loe M. G. Feijs
Pages 299–306
Art of the Quantum Moment
Robert P. Crease and Alfred S. Goldhaber
Pages 307–314
The Old Art of Rope Work and Fourier Decomposition
Nils Kr. Rossing
Pages 315–322
Twisted D-Forms: Design and Construction of D-Forms with Twisted Prismatic Handles with Developable Sides
Qing Xing, Gabriel Esquivel, Ergun Akleman
Pages 323–328
Balanço: The Contour of Relative Offbeatness
Mehmet Vurkaç
Pages 329–336
Introducing the Use of the Primary Isosceles Triangles of Regular Polygons to Produce Self Similar Patterns
Stanley Spencer
Pages 337–344
Commissioning a Bridge
Brent Collins
Pages 345–348
Architecture, Form, Expression: The Helicoidal Skyscraper's Geometry
Alessandra Capanna, Mauro Francaviglia, Marcella G. Lorenzi
Pages 349–356
Mathematical Sequential Art
Susan Happersett
Pages 357–358
Models of Stellations of the Icosahedron
Eve Torrence
Pages 359–360
Fisheye View of Tessellations
Radmila Sazdanovic
Pages 361–364
Point Symmetry Patterns on a Regular Hexagonal Tessellation
David A. Reimann
Pages 365–368
Knots as Processes in Art and Mathematics
Bojana Ginn
Pages 369–372
Building the Schwarz D-Surface from Paper Tiles
Stephen Luecking
Pages 373–376
Generating Chinese Knots from Arbitrary Shapes
Andrew Lee and Brandon M. Wang
Pages 377–380
Intersecting Helices
Paul Gailiunas
Pages 381–384
Rotate, Reflect, Recycle
Karl Kattchee
Pages 385–388
Fun with Chaotic Orbits in the Mandelbrot Set
Kerry Mitchell
Pages 389–392
Exploring the Visualization of Music
Robert J. Krawczyk
Pages 393–396
A Mathematica GUI for Generating Conway Tiles
Bruce Torrence
Pages 397–398
The Evolution of An Idea Inspired by 70
Charlene Morrow
Pages 399–402
The MathStudio Pendulum Project
Pau Atela
Pages 403–404
Optical Minimal Art
Hans Kuiper
Pages 405–408
From Two Dimensions to Four---and Back Again
Susan McBurney
Pages 409–412
Portraits of Groups in Three Dimensions
Jay Zimmerman and Kevin Zimmerman
Pages 413–414
Hierarchical Organization in Writing, Poetry, and Mathematics
Russell Jay Hendel
Pages 415–416
The ``Golden Canon'' of Book-Page Design: A Visual Presentation Using Geometer's Sketchpad
Stanley M. Max
Pages 417–420
Symmetry and Bivariate Splines
Tatyana Sorokina
Pages 421–424
Geometry and Art with a Circle Cutter
Roberta La Haye
Pages 425–428
Significance of Pointed Domes: Morphology, Typologies, and Geometrical Design
Maryam Ashkan
Pages 429–432
The Mazzocchio in Perspective
Kenneth Brecher
Pages 433–436
On the Geometry of Metafiction
Manil Suri
Pages 437–438
Dune Surfaces: A Spatial Visualization Technique for Medial Axes in the Plane or on the Sphere
Peter Calvache
Pages 439–442
To Trace a Creative Thought
Brian Evans
Pages 443–446
Images and Illusions from Orthogonal Pairs of Ellipses
Hartmut F. W. Höft
Pages 447–448
Crystallizing Topology in Molecular Visualizations
T. Hunter, K. Marinelli, D. Marsh, T. J. Peters
Pages 449–452
Mathematics in the World of Dance
Katarzyna Wasilewska
Pages 453–456
Fractal Geometry and Persian Carpet
Seyed Mahmood Moeini and Mehrdad Garousi
Pages 457–460
Escher Unraveled: Using Artwork to Investigate Transformations
Ming Tomayko, Sandy Spitzer, Linda Cooper
Pages 461–462
Structural Qualities and Serial Construction of Tournament Braids
D. Jacob Wildstrom
Pages 463–466
Music Synthesis Based on Nonlinear Dynamics
Maximos A. Kaliakatsos-Papakostas, Andreas Floros, Michael N. Vrahatis
Pages 467–470
Brand Values and the Perception of Symmetry
J. L. Marsden and B. G. Thomas
Pages 471–474
Diptych View on The Spiral
Françoise Beck-Pieterhons and Jacques Beck
Pages 475–478
Using Star Polygons to Understand Cyclic Group Structure
Sandy Spitzer
Pages 479–480
Harmonic Perspective
C. J. Fearnley and Jeannie Moberly
Pages 481–484
Extension of Neo-Riemannian PLR-group to Seventh Chords
Boris Kerkez
Pages 485–488
Tune and Rhyme: Translation Symmetry at Work
Alice Major
Pages 489–492
The Immersive Bridge Between Math and Art
John Miller
Pages 493–494
Steps Towards the Analysis of Geometric Decorative Motifs Using Shape-matching Techniques
Alice Humphrey and Michael Hann
Pages 495–498
Meta-Vermeer: A Topological Reinterpretation of a Masterpiece
Silvia De Toffoli and Yasuhiro Sakamoto
Pages 499–502
Beaded Realization of Canonical P, D, and G Triply Periodic Minimal Surfaces
Chern Chuang, Bih-Yaw Jin, Wei-Chi Wei, Chia-Chin Tsoo
Pages 503–506
Exploring the Projective Plane via Variations on the Faceted Octahedron
Frank Gould and S. Louise Gould
Pages 507–508
Analytical Calculation of Geodesic Lengths and Angle Measures on Sphere Tiling of Platonic and Archimedean Solids
Kyongil Yoon
Pages 509–512
The Mathematics behind Anamorphic Art
Kimberly Rausch
Pages 513–514
The Creative Process: Risk-taking in an Interdisciplinary Honors Course
Heather Pinson and Monica VanDieren
Pages 515–518
Training Teachers after Bridges
M. G. Marques and M. Pires
Pages 519–522
A Topology-Preserving Voxelization Shrinking Algorithm
Daniel Whalen
Pages 523–524
Spelunking Adventure III: Close-Pack and Space-Fill Octahedral Domains
Curtis Palmer
Pages 525–526
Tiling and Weaving with Permutation Functions
Robert Hanson
Pages 527–528
Mathematics and the Ballet Barre
Karl Schaffer
Pages 529–532
Amazing Labyrinths, Further Developments III
Samuel Verbiese
Pages 533–534
The Seven Principles of Angle Stitching---A Geometrically Based Beading Technique
Laura M. Shea
Pages 535–538
Depression Glass and Nested Symmetry Groups
Darrah Chavey
Pages 539–542
A Novel Geometric Pattern Extraction by Means of a Level-Set Method
Maryam Rahnemoonfar and Afshin Asefpour Vakilian
Pages 543–544
Domes, Zomes, and Drop City
Paul Hildebrandt and Clark Richert
Pages 545–548
A Non-Pythagorean Musical Scale Based on Logarithms
Robert P. Schneider
Pages 549–552
The Art and Mathematics of Tangrams
Xiaoxi Tian
Pages 553–556
Projecting Mathematical Curves with Laser Light
Merrill Lessley and Paul Beale
Pages 557–560
Digital Sangaku
Jean Constant
Pages 561–562
Teaching Temari: Geometrically Embroidered Spheres in the Classroom
Carolyn Yackel
Pages 563–566
Bead Crochet Bracelets: What Would Escher Do?
Ellie Baker and Susan Goldstine
Pages 567–572
Mathematical Synthesis and Making of Rope Mats and Rosettes
Nils Kr. Rossing
Pages 573–574
Evolve Your Own Basket
James Mallos
Pages 575–580
Using Technology to Explore the Geometry of Navajo Weavings
Mary Kay Kirchner and Reza Sarhangi
Pages 581–588
Space-filling Curves as Design Elements
Ellen Gergely, Kerry Mitchell, Martin Wesolowski
Pages 589–592
Creating Non-Systematic Islamic Geometric Patterns with Complex Combinations of Star Forms
Jay Bonner
Pages 593–598
Let's Make a (36)D (36)L Chiral Tessellation Dance
Joseph D. Clinton
Pages 599–606
Combinatorial Choreography
Tom Verhoeff
Pages 607–612
Exploring Braids through Dance: The ``Waves of Tory'' Problem
Andrea Hawksley
Pages 613–618
Math and Dance---Windmills and Tilings and Things
Karl Schaffer
Pages 619–622
Mathematical Eyes on Figure Skating
Diana Cheng, Tanya Berezovski, Cherie Farrington
Pages 623–626
Poetry-with-Mathematics Workshop
JoAnne Growney
Pages 627–628
Musical Composition Without Standard Musical Knowledge
Ana Pereira do Vale
Pages 629–636
Imagining Negative-Dimensional Space
Luke Wolcott and Elizabeth McTernan
Pages 637–642
A Workshop on Making Modified Truncated Icosahedra Using 4D Frame
Ho-Gul Park and Taeyoung Choi
Pages 643–646