Bridges 2005: Renaissance Banff
Banff, Alberta, Canada
31 July – 3 August 2005
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Front matter
The Manifold Beauty of Piano-hinged Dissections
Pages 1–8
Recursion in Nature, Mathematics and Art
Pages 9–16
Fairfield Porter's Secret Geometry
Pages 17–24
Meanders
Pages 25–30
An Introduction to the Golden Tangram and its Tiling Properties
Pages 31–36
Spiral Tilings with C-curves Using Combinatorics to Augment Tradition
Pages 37–46
The Euclidean Algorithm Generates Traditional Musical Rhythms
Pages 47–56
Malekula Sand Tracings: A Case in Ethnomathematics
Pages 57–64
Generative Art and Aesthetics
Pages 65–66
Geometry and Harmony
Pages 67–72
Mathematical Measures of Syncopation
Pages 73–84
Mathematical Analogy and Metaphorical Insight
Pages 85–92
Beauty in Art and Mathematics: A Common Neural Substrate or the Limits of Language?
Pages 93–100
Alice Boner and the Geometry of Temple Cave Art of India
Pages 101–108
A Ukrainian Easter Egg Monument Stands for Thirty Years
Pages 109–116
The Harmony of the World
Pages 117–118
Pedagogical Principles for Teaching Art in Mathematics Courses
Pages 119–120
D-forms and developable surfaces
Pages 121–128
(Vector) Fields of Mathematical Poetry
Pages 129–130
Aspects of Symmetry in Arpachiyah Pottery
Pages 131–136
Abstract Art from a Model for Cellular Morphogenesis
Pages 137–142
The Complexity of the Musical Vocabulary of the Nzakara Harpists
Pages 143–148
A Computerized Environment for Learning and Teaching 3-D Geometry
Pages 149–154
Symmetry and the Sacred Date Palm in the Palace of Ashurnasirpal II, King of Assyria
Pages 155–160
Three-Dimensional and Dynamic Constructions Based on Leonardo Grids
Pages 161–168
The Droste-Effect and the Exponential Transform
Pages 169–178
Some Surprising New Properties of the Spidrons
Pages 179–186
Video Screening
Pages 187–194
Detecting Meter in Recorded Music
Pages 195–202
Solidifying Wireframes
Pages 203–210
Splitting Tori, Knots, and Moebius Bands
Pages 211–218
Symmetry and Symmetry-Breaking - An Approach to Understanding Beauty
Pages 219–226
An Interdisciplinary Course: "On Beauty: Perspective, Proportion, and Rationalism in Western Culture"
Pages 227–230
Looking At Math: Using Art to Teach Mathematics
Pages 231–236
Using 3-D Models as Image Generators For Digital Fiction
Pages 237–244
Fermat's Spiral Mandalas
Pages 245–250
Symmetry, Proportion and Scale: Tools for the Jacquard Designer and Weaver of Silk Velvet
Pages 251–254
Circular Distributions and Spectra Variations in Music, How Even is Even?
Pages 255–262
Illustrating Number Sequences
Pages 263–268
Geometrical, Perceptual, and Cultural Perspectives on Figure/Ground Differences in Bakuba Pattern
Pages 269–276
A Perspective on Infinity: Anamorphism and Stereographic Projection
Pages 277–284
A Geometric Analysis of the Seven Heavens
Pages 285–292
On Parsimonious Sequences as Scales in Western Music
Pages 293–300
TSP Art
Pages 301–308
Digitally Spelunking the Spline Mine
Pages 309–312
An Approach in Coloring Semi-Regular Tilings on the Hyperbolic Plane
Pages 313–320
Two and Three-Dimensional Art Inspired by Polynomiography
Pages 321–328
Tessellations from Group Actions and the Mystery of Escher's Solid
Pages 329–330
Wisdom in Art: Mathematics in Islamic Architecture in Iran
Pages 331–336
NAMAN: Dream Altars, Vietnam: A Search for use of the Golden Mean and its Affect on Design and Content
Pages 337–338
Aesthetic Aspects of Venn Diagrams
Pages 339–342
Dynamics on Discrete Structures: A Dialog between Squares and Circles
Pages 343–344
Strange Physical Motion of Balls in a Cylinder
Pages 345–346
z-Irrationality search: After a Golden Section Approach, Another Esthetic but Vain Attempt
Pages 347–348
Aliasing Artifacts and Accidental Algorithmic Art
Pages 349–356
Symmetries and Design Science: Two Graduate Courses for a Mathematics Education Program
Pages 357–366
Making Mathematical Posters
Pages 367–368
Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices
Pages 369–378
Space from Nonspace: Emergent Spatiality in Dynamic Graphs
Pages 379–380
Satellite Ballet by Flower Constellations
Pages 381–382
Anamorphosis.com: Computers, Mathematics and Art
Pages 383–384
Mathematical Models of Gothic Structures
Pages 385–392
Donald Coxeter: The Man who Saved Geometry
Pages 393–402
Symmetric Linear Constructions in Motion
Pages 403–410
Coxetering Crystals
Pages 411–418
Two Results Concerning the Zome Model of the 600-Cell
Pages 419–426
Fractal Tilings Based on Dissections of Polyhexes
Pages 427–434
Mosaic Art: from Pebbles to Pixels
Pages 435–442
Serial Polar Transformation Motifs Revisited
Pages 443–448
Orderly Tangles Revisited
Pages 449–456
Factor Group Transformations on Escher Patterns
Pages 457–462
Symmetrical Hamiltonian Manifolds on Regular 3D and 4D Polytopes
Pages 463–472
Coxeter and the Artists: Two-Way Inspiration, Part 2
Pages 473–480
Polyhedral Transformation: Explosion-Implosion
Pages 481–488
Some New Tilings of the Sphere with Congruent Triangles
Pages 489–496
H.S.M. Coxeter and Tony Bomford's Colored Hyperbolic Rugs
Pages 497–504
Paper Polylinks
Pages 505–508
A Thousand Cranes and Statistics
Pages 509–510
A Method for Illustrating Border and Wallpaper Patterns
Pages 511–518
Tessellation Techniques
Pages 519–520
Connecting Gross-motor Movement, Dance, and Mathematics in the Elementary Curriculum
Pages 521–522
A Physical Proof for Five and Only Five Regular Solids
Pages 523–528
Playing Mathematics and Doing Music
Pages 529–530
Dynamic Geometry/Art in Mathematics Classroom
Pages 531–535