cover

Bridges 2006

London, UK
4–8 August 2006
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Front Matter
The Editors
Collaboration on the Integration of Sculpture and Architecture in The Eden Project
Peter Randall-Page
Pages 1–8
The Work of Foster and Partners Specialist Modelling Group
Brady Peters and Xavier DeKestellier
Pages 9–12
The Borromean Rings - A Tripartite Topological Relationship
Louis H. Kauffman
Pages 13–18
Cultural Insights from Symmetry Studies
Dorothy K. Washburn and Donald W. Crowe
Pages 19–24
Non-Euclidean Symmetry and Indra's Pearls
Caroline Series and David Wright
Pages 25–32
Love, Understanding, and Soap Bubbles
Simon Thomas
Pages 33–40
Creating Penrose-type Islamic Interlacing Patterns
John Rigby
Pages 41–48
Steve Reich's Clapping Music and the Yoruba Bell Timeline
Justin Collannino, Francisco Gómez and Godfried T. Toussaint
Pages 49–58
Illuminating Chaos - Art on Average
Mike Field
Pages 59–60
Bridging the gap - a Search for a Braid Language
Jacqui Carey
Pages 61–68
Magic Stars and Their Components
Sergei Zagny
Pages 69–72
Introducing the Precious Tangram Family
Stanley Spencer
Pages 73–78
Sand Drawings and Gaussian Graphs
Erik D. Demaine, Martin L. Demaine, Perouz Taslakian and Godfried T. Toussaint
Pages 79–88
Symmetric Characteristics of Traditional Hawaiian Patterns: a Computer Model
Tony Cao and Jin-Ho Park
Pages 89–96
Circle Folded helices
Bradford Hansen-Smith
Pages 97–104
The Taming of Roelofs Polyhedra
Frits Göbel
Pages 105–108
A Program to Interpolate (and Extrapolate) between Turtle Programs
Ken Kahn
Pages 109–114
The Programmer as Poet
Russell Jay Hendel
Pages 115–116
Minkowski Sums and Spherical Duals
John M. Sullivan
Pages 117–122
Polygon Foldups in 3D
Kate Mackrell
Pages 123–130
Portraits of Groups
Jay Zimmerman
Pages 131–134
A New Use of the Basic Mathematical Idea of Twelve-Tone Music
Ward Douglas Maurer
Pages 135–136
A Braided Effort: A Mathematical Analysis of Compositional Options
James Mai and Daylene Zielinski
Pages 137–144
On a Family of Symmetric, Connected and High Genus Sculptures
Ergun Akleman and Cem Yuksel
Pages 145–150
Affine Regular Pentagon Sculptures
Douglas G. Burkholder
Pages 151–152
The Effect of Music-Enriched Instruction on the Mathematics Scores of Pre-School Children
Maureen Harris
Pages 153–156
Teaching Arabesque
Jean-Marc Castera
Pages 157–160
Slide-Together Structures
Rinus Roelofs
Pages 161–170
Repeated Figures
Susan McBurney
Pages 171–174
Seville's Real Alcázar: Are All 17 Planar Crystallographic Groups Represented Here?
B. Lynn Bodner
Pages 175–180
Math must be Beautiful
Carla Farsi
Pages 181–182
The Integrated Scale Desirability Function: A Musical Scale Consonance Measure Based on Perception Data
Richard J. Krantz and Jack Douthett
Pages 183–190
Tiled Artworks Based on the Goldbach Conjecture
Sharol Nau
Pages 191–194
Sculpture Puzzles
George W. Hart
Pages 195–202
The Mechanical Drawing of Cycloids, The Geometric Chuck
Robert Craig
Pages 203–210
Sashiko: the Stitched Geometry of Rural Japan
Barbara Setsu Pickett
Pages 211–214
Literatronic: Use of Hamiltonian Cycles to Produce Adaptivity in Literary Hypertext
Juan B. Gutierrez
Pages 215–222
Responsive Visualization for Musical Performance
Robyn Taylor, Pierre Boulanger and Daniel Torres
Pages 223–230
The Necessity of Time in Perception of Three Dimensions: A Preliminary Inquiry
Michael Mahan
Pages 231–236
An Interactive/Collaborative Su Doku Quilt
Eva Knoll and Mary Crowley
Pages 237–244
Patterns on the Genus-3 Klein Quartic
Carlo H. Séquin
Pages 245–254
The Lorenz Manifold: Crochet and Curvature
Hinke M. Osinga and Bernd Krauskopf
Pages 255–260
Playing Musical Tiles
Rachel W. Hall
Pages 261–268
Mathematics and the Architecture: The Problem and Theory in Pre-Modern Cultures
Zafer Sagdic
Pages 269–276
Towards Pedagogability of Mathematical Music Theory: Algebraic Models and Tiling Problems in Computer-aided Composition
Moreno Andreatta, Carlos Agon Amado, Thomas Noll and Emmanuel Amiot
Pages 277–284
Streptohedrons (Twisted polygons)
David Springett
Pages 285–292
Fractal Tilings Based on Dissections of Polyominoes
Robert W. Fathauer
Pages 293–300
Vortex Maze Construction
Jie Xu and Craig S. Kaplan
Pages 301–308
Models of Cubic Surfaces in Polyester
Sergio Hernández, Carmen Perea, Irene Polo Blanco and Cayetano Ramírez "Tano"
Pages 309–314
"Geometry" in Early Geometrical Disciplines: Representations and Demonstrations
Elaheh Kheirandish
Pages 315–318
Ant Paintings using a Multiple Pheromone Model
Gary R. Greenfield
Pages 319–326
Verbogeometry: The Confluence Of Words And Analytic Geometry
Kaz Maslanka
Pages 327–334
Zome-inspired Sculpture
Paul Hildebrandt
Pages 335–342
Developable Sculptural Forms of Ilhan Koman
Tevfik Akgün, Ahmet Koman and Ergun Akleman
Pages 343–350
Constellations of Form: New Compositional Elements Related to Polyominoes
James Mai and Daylene Zielinski
Pages 351–358
Transformations of Vertices, Edges and Faces to Derive Polyhedra
Robert McDermott
Pages 359–364
Chromatic Fantasy: Music-inspired Weavings Lead to a Multitude of Mathematical Possibilities
Jennifer Moore
Pages 365–370
Asymmetry vs. Symmetry in a New Class of Space-Filling Curves
Douglas M. McKenna
Pages 371–378
Modular Perspective and Vermeer's Room
Tomás García-Salgado
Pages 379–386
On the Bridging Powers of Geometry in the Study of Ancient Theatre Architecture
Zeynep Aktüre
Pages 387–394
The Gemini Family of Triangles
Alvin Swimmer and Mary C. Williams
Pages 395–402
Taitographs: Drawings made by Machines
Jack Tait
Pages 403–410
Photography and the Understanding Mathematics
Richard Phillips
Pages 411–418
Inference and Design in Kuba and Zillij Art with Shape Grammars
Ramgopal Rajagopalan, Eric Hortop, Dania El-Khechen, Cheryl Kolak Dudek, Lydia Sharman, Fred Szabo, Thomas Fevens and Sudhir Mudhur
Pages 419–428
Green Quaternions, Tenacious Symmetry, and Octahedreal Zome
David A. Richter and Scott Vorthmann
Pages 429–436
Mathematics and Music - Models and Morals
Meurig Beynon
Pages 437–444
Teaching Design Science: An Exploration of Geometric Structures
Carl Fasano
Pages 445–450
More "Circle Limit III" Patterns
Douglas Dunham
Pages 451–458
J-F Niceron's La Perspective Curieuse Revisited
J.L. Hunt
Pages 459–464
A Meditation on Kepler's Aa
Craig S. Kaplan
Pages 465–472
Approximating Mathematical Surfaces with Spline Modelers
Stephen Luecking
Pages 473–480
The Lost Harmonic Law of the Bible
Jay Kappraff
Pages 481–490
New Ways in Symmetry
María Francisca Blanco Martín and Elena Elvira Nieto
Pages 491–496
Linkages to Op-Art
John Sharp
Pages 497–502
D-Forms: 3D Forms from Two 2D Sheets
Tony Wills
Pages 503–510
Visualizing Escape Paths in the Mandelbrot Set
Anne M. Burns
Pages 511–516
The Math of Art: Exploring Connections between Math and Color Theory
Amina Buhler-Allen
Pages 517–520
Celtic Knotwork and Knot Theory
Patricia Wackrill
Pages 521–524
Islamic Art: An Exploration of Patterns
Carol Bier
Pages 525–532
In Search of Demiregular Tilings
Helmer Aslaksen
Pages 533–536
Tribute to the Atomium
Samuel Verbiese
Pages 537–540
RHYTHMOS: An Interactive System for Exploring Rhythm from the Mathematical and Musical Points of View
Jakob Teitelbaum and Godfried Toussaint
Pages 541–548
Spidron Domain: The Expanding Spidron Universe
Dániel Erdély and Marc Pelletier
Pages 549–550
An Introduction to Medieval Spherical Geometry for Artists and Artisans
Reza Sarhangi
Pages 551–560
Fabric Sculpture - Jacob's Ladder
Louise Mabbs
Pages 561–568
Eva Hild: Topological Sculpture from Life Experience
Nat Friedman
Pages 569–572
Interdisciplinary Bridges: A Novel Approach for Teaching Mathematics
Gail Kaplan
Pages 573–578
Concerning the Geometrical in Art
Clifford Singer
Pages 579–580
Knot Designs from Snowflake Curves
Paul Gailiunas
Pages 581–584
Asymmetry in Persian Symmetrical Art and Architecture
Hourieh Mashayekh and Hayedeh Mashayekh
Pages 585–586
Cultural Statistics and Instructional Designs
Darius Zahedi
Pages 587–594
Musical Scales, Integer Partitions, Necklaces, and Polygons
David Rappaport
Pages 595–598
1927: Two Processes of Creating Form in Music
Veryan Weston
Pages 599–604
On Mathematics, Music and Autism
Ioan James
Pages 605–610
Mathematics Investigations in Art-Based Environments
Mara Alagic and Paul Gailiunas
Pages 611–616
Moving Beyond Geometric Shapes: Other connections between Mathematics and the Arts for Elementary-grade Teachers
Virginia Usnick and Marilyn Sue Ford
Pages 617–624
A Geometric Inspection of Pennsylvanian Dutch Hex Signs
Evan G. Evans and Reza Sarhangi
Pages 625–630
Creating Sliceforms with 3D Modelers
Stephen Luecking
Pages 631–638
Paper Sculptures with Vertex Deflection
Tevfik Akgün, Ahmet Koman and Ergun Akleman
Pages 639–640
Understanding the Mathematics Based Formulation on Dome Tessellation in Architect Skinan's Mosques Design
Zafer Sagdic, Mujdem Vural and Gokce Tuna Taygun
Pages 641–644
Mandala and 5,6 and 7-fold Division of the Circle
Paul F. Stang
Pages 645–646
Mathematical Book Forms for Teachers
Susan Happersett
Pages 647–648
The Aréte of Line Designs
Michael Round
Pages 649–650
The Plato Bead: A Bead Dodecahedron
Laura Shea
Pages 651–654
Building Simple and Not So Simple Stick Models
Robert McDermott
Pages 655–660
Topological Mesh Modeling
Ergun Akleman and Vinod Srinivasan
Pages 661–662
Vermeer's "The Music Lesson" in Modular Perspective
Tomás García-Salgado
Pages 663–664
Zellij Multipuzzle
Jean Marc Castera
Pages 665–666