cover

Bridges 2005

Banff, Alberta, Canada
31 July – 3 August 2005
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Front Matter
The Editors
The Manifold Beauty of Piano-hinged Dissections
Greg N. Frederickson
Pages 1–8
Recursion in Nature, Mathematics and Art
Anne M. Burns
Pages 9–16
Fairfield Porter's Secret Geometry
Chris Bartlett
Pages 17–24
Meanders
Paul Gailiunas
Pages 25–30
An Introduction to the Golden Tangram and its Tiling Properties
Stanley Spencer
Pages 31–36
Spiral Tilings with C-curves Using Combinatorics to Augment Tradition
Chris K. Palmer
Pages 37–46
The Euclidean Algorithm Generates Traditional Musical Rhythms
Godfried Toussaint
Pages 47–56
Malekula Sand Tracings: A Case in Ethnomathematics
Marcia Ascher
Pages 57–64
Generative Art and Aesthetics
Susan Happersett
Pages 65–66
Geometry and Harmony
David Rappaport
Pages 67–72
Mathematical Measures of Syncopation
F. Gómez, A. Melvin, D. Rappaport and G.T. Toussaint
Pages 73–84
Mathematical Analogy and Metaphorical Insight
Jan Zwicky
Pages 85–92
Beauty in Art and Mathematics: A Common Neural Substrate or the Limits of Language?
Daniel J. Goldstein
Pages 93–100
Alice Boner and the Geometry of Temple Cave Art of India
Robert V. Moody
Pages 101–108
A Ukrainian Easter Egg Monument Stands for Thirty Years
Robert McDermott
Pages 109–116
The Harmony of the World
Christopher Arthur
Pages 117–118
Pedagogical Principles for Teaching Art in Mathematics Courses
Russell Jay Hendel
Pages 119–120
D-forms and developable surfaces
John Sharp
Pages 121–128
(Vector) Fields of Mathematical Poetry
Carla Farsi
Pages 129–130
Aspects of Symmetry in Arpachiyah Pottery
Duncan J. Melville
Pages 131–136
Abstract Art from a Model for Cellular Morphogenesis
Gary R. Greenfield
Pages 137–142
The Complexity of the Musical Vocabulary of the Nzakara Harpists
Barbra Gregory
Pages 143–148
A Computerized Environment for Learning and Teaching 3-D Geometry
Irit Wertheim, Emzar Panikashvili, Gershon Elber and Nitsa Movshovitz-Hadar
Pages 149–154
Symmetry and the Sacred Date Palm in the Palace of Ashurnasirpal II, King of Assyria
Sarah C. Melville
Pages 155–160
Three-Dimensional and Dynamic Constructions Based on Leonardo Grids
Rinus Roelofs
Pages 161–168
The Droste-Effect and the Exponential Transform
Bart de Smit
Pages 169–178
Some Surprising New Properties of the Spidrons
Dániel Erdély
Pages 179–186
Video Screening
Jinnah Yu and Ergun Akleman
Pages 187–194
Detecting Meter in Recorded Music
Joseph E. Flannick, Rachel W. Hall and Robert Kelly
Pages 195–202
Solidifying Wireframes
Vinod Srinivasan, Esan Mandal and Ergun Akleman
Pages 203–210
Splitting Tori, Knots, and Moebius Bands
Carlo H. Séquin
Pages 211–218
Symmetry and Symmetry-Breaking - An Approach to Understanding Beauty
Carol Bier
Pages 219–226
An Interdisciplinary Course: "On Beauty: Perspective, Proportion, and Rationalism in Western Culture"
Alison Fleming, Sharon Frechette and Sarah Luria
Pages 227–230
Looking At Math: Using Art to Teach Mathematics
Pau Atela
Pages 231–236
Using 3-D Models as Image Generators For Digital Fiction
Michael Mahan
Pages 237–244
Fermat's Spiral Mandalas
Robert J. Krawczyk
Pages 245–250
Symmetry, Proportion and Scale: Tools for the Jacquard Designer and Weaver of Silk Velvet
Barbara Setsu Pickett
Pages 251–254
Circular Distributions and Spectra Variations in Music, How Even is Even?
Richard J. Krantz and Jack Douthett
Pages 255–262
Illustrating Number Sequences
L. Kerry Mitchell
Pages 263–268
Geometrical, Perceptual, and Cultural Perspectives on Figure/Ground Differences in Bakuba Pattern
Donald W. Crowe and Dorothy K. Washburn
Pages 269–276
A Perspective on Infinity: Anamorphism and Stereographic Projection
Michael Frantz
Pages 277–284
A Geometric Analysis of the Seven Heavens
B. Lynn Bodner
Pages 285–292
On Parsimonious Sequences as Scales in Western Music
Richard Hermann and Jack Douthett
Pages 293–300
TSP Art
Craig S. Kaplan and Robert Bosch
Pages 301–308
Digitally Spelunking the Spline Mine
Curtis Palmer
Pages 309–312
An Approach in Coloring Semi-Regular Tilings on the Hyperbolic Plane
Ma. Louise Antonette N. De Las Peñas, Glenn R. Laigo and René P. Felix
Pages 313–320
Two and Three-Dimensional Art Inspired by Polynomiography
Bahman Kalantari
Pages 321–328
Tessellations from Group Actions and the Mystery of Escher's Solid
Ioana Mihaila
Pages 329–330
Wisdom in Art: Mathematics in Islamic Architecture in Iran
Hourieh Mashayekh
Pages 331–336
NAMAN: Dream Altars, Vietnam: A Search for use of the Golden Mean and its Affect on Design and Content
Michael McConnell and Jim Rose
Pages 337–338
Aesthetic Aspects of Venn Diagrams
Barry Cipra, Peter Hamburger and Edit Hepp
Pages 339–342
Dynamics on Discrete Structures: A Dialog between Squares and Circles
Tiziana Giorgi and Robert Smits
Pages 343–344
Strange Physical Motion of Balls in a Cylinder
Akihiro Matsuura
Pages 345–346
z-Irrationality search: After a Golden Section Approach, Another Esthetic but Vain Attempt
Dirk Huylebrouck
Pages 347–348
Aliasing Artifacts and Accidental Algorithmic Art
Craig S. Kaplan
Pages 349–356
Symmetries and Design Science: Two Graduate Courses for a Mathematics Education Program
Reza Sarhangi and Jay Zimmerman
Pages 357–366
Making Mathematical Posters
Ulrich Hermisson and Robert V. Moody
Pages 367–368
Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices
Jay Kappraff, Slavik Jablan, Gary Adamson and Radmila Sazdanovich
Pages 369–378
Space from Nonspace: Emergent Spatiality in Dynamic Graphs
Tim Boykett
Pages 379–380
Satellite Ballet by Flower Constellations
Daniele Mortari
Pages 381–382
Anamorphosis.com: Computers, Mathematics and Art
Phillip Kent
Pages 383–384
Mathematical Models of Gothic Structures
Javier Barrallo and Santiago Sanchez-Beitia
Pages 385–392
Donald Coxeter: The Man who Saved Geometry
Siobhan Roberts
Pages 393–402
Symmetric Linear Constructions in Motion
Douglas G. Burkholder
Pages 403–410
Coxetering Crystals
Marjorie Senechal
Pages 411–418
Two Results Concerning the Zome Model of the 600-Cell
David A. Richter
Pages 419–426
Fractal Tilings Based on Dissections of Polyhexes
Robert W. Fathauer
Pages 427–434
Mosaic Art: from Pebbles to Pixels
Irene Rousseau
Pages 435–442
Serial Polar Transformation Motifs Revisited
Gary R. Greenfield
Pages 443–448
Orderly Tangles Revisited
George W. Hart
Pages 449–456
Factor Group Transformations on Escher Patterns
Joshua Jacobs
Pages 457–462
Symmetrical Hamiltonian Manifolds on Regular 3D and 4D Polytopes
Carlo H. Séquin
Pages 463–472
Coxeter and the Artists: Two-Way Inspiration, Part 2
Doris Schattschneider
Pages 473–480
Polyhedral Transformation: Explosion-Implosion
Robert McDermott
Pages 481–488
Some New Tilings of the Sphere with Congruent Triangles
Robert J. MacG. Dawson
Pages 489–496
H.S.M. Coxeter and Tony Bomford's Colored Hyperbolic Rugs
Douglas Dunham
Pages 497–504
Paper Polylinks
George W. Hart
Pages 505–508
A Thousand Cranes and Statistics
Cheryl Whitelaw
Pages 509–510
A Method for Illustrating Border and Wallpaper Patterns
Gwen L. Fisher
Pages 511–518
Tessellation Techniques
Stefanie Mandelbaum and Jacqueline S. Guttman
Pages 519–520
Connecting Gross-motor Movement, Dance, and Mathematics in the Elementary Curriculum
Virginia Usnick and Marilyn Sue Ford
Pages 521–522
A Physical Proof for Five and Only Five Regular Solids
Robert McDermott
Pages 523–528
Playing Mathematics and Doing Music
John Belcher
Pages 529–530
Dynamic Geometry/Art in Mathematics Classroom
Mara Alagic and Diana Palenz
Pages 531–535