cover

Bridges 2016

Jyväskylä, Finland
9–13 August 2016
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Front Matter
The Editors
Crystal Flowers in Halls of Mirrors: Mathematics Meets Art and Architecture
Kirsi Peltonen
Pages 1–8
World as Numbers: Living in an Algorithmic Culture
Raine Koskimaa
Pages 9–14
Squares that Look Round: Transforming Spherical Images
Saul Schleimer and Henry Segerman
Pages 15–24
Immersion in Mathematics
Judy Holdener
Pages 25–32
The Elevation of Coxeter's Infinite Regular Polyhedron 444444
Rinus Roelofs
Pages 33–40
From Klein Bottles to Modular Super-Bottles
Carlo H. Séquin
Pages 41–48
Tuti Weaving
Abdalla G. M. Ahmed and Oliver Deussen
Pages 49–56
Fostering Creativity in the Teaching of Mathematics with Project Based Learning
Javier Barrallo Calonge and Luis Martín Yagüe
Pages 57–64
The Size and Shape of Utopia
Andrew Simoson
Pages 65–70
Hypocycloid Juggling Patterns
Craig S. Kaplan
Pages 71–78
Visual Arts and Mathematics Education: Looking for Integrative Phenomena
Mirka Havinga and Päivi Portaankorva-Koivisto
Pages 79–86
Interlinking Polyhedral Wire-Frames
Walt van Ballegooijen and Carlo H. Séquin
Pages 87–96
Mathematics Learning through Arts and Collaborative Problem-Solving: The Princess and the Diamond-Problem
Markus Hähkiöniemi, Kristóf Fenyvesi, Johanna Pöysä-Tarhonen, Mirja Tarnanen, Päivi Häkkinen, Merja Kauppinen, Anne Martin and Pasi Nieminen
Pages 97–104
Three Mathematical Sculptures for the Mathematikon
Tom Verhoeff and Koos Verhoeff
Pages 105–110
Combinatorial Poppies
Karl Kattchee and Craig S. Kaplan
Pages 111–118
Tendril Motifs for Space-Filling, Half-Domino Curves
Douglas M. McKenna
Pages 119–126
Modeling Braids, Cables, and Weaves with Stranded Cellular Automata
Joshua Holden and Lana Holden
Pages 127–134
Helical Petrie Polygons
Paul Gailiunas
Pages 135–140
Some Girihs and Puzzles from the Interlocks of Similar or Complementary Figures Treatise
Reza Sarhangi
Pages 141–150
Turing-like Patterns from Cellular Automata
Gary R. Greenfield
Pages 151–158
From Checkerboard to Cloverfield: Using Wang Tiles in Seamless Non-Periodic Patterns
Tuomas Nurmi
Pages 159–166
Underlying Tiles in a 15th Century Mamluk Pattern
Ron Asherov
Pages 167–172
Artefacts to Enhance Geometrical Thinking
Zekeriya Karadag
Pages 173–178
The Conformal Hyperbolic Square and Its Ilk
Chamberlain Fong
Pages 179–186
Geometry and Aesthetics of Pentagonal Structures in the Art of Gerard Caris
Cornelie Leopold
Pages 187–194
A Taxonomy of Generative Poetry Techniques
Carolyn Lamb, Dan G. Brown and Charlie L.A. Clarke
Pages 195–202
Not only Art but also Rocket Science
S.J. Spencer
Pages 203–208
Hex Rosa
Markus Rissanen
Pages 209–216
Fractal Gaskets: Reptiles, Hamiltonian Cycles, and Spatial Development
Robert W. Fathauer
Pages 217–224
Shape-Changing Polyhedra
Roger Burrows
Pages 225–232
Planes and Frames: Spatial Layering in Josef Albers' Homage to the Square Paintings
James Mai
Pages 233–240
Portraits of Groups on Bordered Surfaces
Jay Zimmerman
Pages 241–246
Genera Esfera: Interacting with a Trackball Mapped onto a Sphere to Explore Generative Visual Worlds
Lali Barrière and Anna Carreras
Pages 247–254
Circular Forms in Aleksis Kivi's Texts
Tiina Katriina Kukkonen
Pages 255–262
Euler-Cayley Formula for ‘Unusual’ Polyhedra
Dirk Huylebrouck
Pages 263–268
Dancing Math: Teaching and Learning in the Intersection of Aesthetic and Mathematical Literacy
Paul Moerman
Pages 269–276
A Mathematical Approach to Obtain Isoperimetric Shapes for D-Form Construction
Ramon Roel Orduño, Nicholas Winard, Steven Bierwagen, Dylan Shell, Negar Kalantar, Alireza Borhani and Ergun Akleman
Pages 277–284
A Graph-Theoretic Approach to the Analysis of Contra Dances
Matthew Thomas and Crystal Peebles
Pages 285–292
Koch-Like Fractal Images
Vincent J. Matsko
Pages 293–300
A Study on Geometric Constructions on Brickwork Decorations in Iranian Architecture
Mahsa Kharazmi
Pages 301–308
The Rhythm of a Pattern
Sama Mara
Pages 309–316
The Analysis of the Geometric Decorations of the Stone Half-Columns of Friday Mosque of Isfahan
Molude Noori and Qobad Kiyanmehr
Pages 317–324
Another look at Pentagonal Persian Patterns
Jean-Marc Castera
Pages 325–330
Geometric Patterns as Material Things: The Making of Seljuk Patterns on Curved Surfaces
Begüm Hamzaoğlu and Mine Özkar
Pages 331–336
Colors and Incomputability
Donald Spector
Pages 337–344
Strictly Coding: Connecting Mathematics and Music through Digital Making
Pam Burnard, Zsolt Lavicza and Carrie Anne Philbin
Pages 345–350
A Bridges Center for Mathematical Connections in Art and Science
Sujan Shrestha and Reza Sarhangi
Pages 351–354
Constructing Meaning Through Making and Creating
Gail Tang and Alan Tollefson
Pages 355–358
Prime Portraits
Zachary Abel
Pages 359–362
Phylogenetic Analysis of the Ancient Greek Paeonic Rhythms
Godfried T. Toussaint
Pages 363–366
A New Algorithm for Rendering Kissing Schottky Groups
Kento Nakamura and Kazushi Ahara
Pages 367–370
Beautification of Islamic Patterns via Constraint Satisfaction
Yongquan Lu and Erik D. Demaine
Pages 371–374
Molecular Modeling of Four-Connected Zeolite Frameworks with Mathematical Beading
Chia-Chin Tsoo and Bih-Yaw Jin
Pages 375–378
Generalized Brunes Stars and System of Pythagorean Triples
Dmitri Kozlov
Pages 379–382
Knight Mazes
Mike Naylor
Pages 383–386
Mathematikon: A Mathematical Shopping Center
Bianca Violet and Andreas Matt
Pages 387–390
Lights Out Animations
Robert Bosch
Pages 391–394
A Recursion in Knitting
Susan Goldstine
Pages 395–398
Polyhedral Tableaux
Kenneth Brecher
Pages 399–402
Gödel, Escher, Bach: Just Another Braid
Hans Kuiper and Walt van Ballegooijen
Pages 403–406
A Musical Polyhedron Updated for the 21st Century
Cathleen O'Neil
Pages 407–410
Organic 3D Mesh Creation Through Particle-Based Physics Simulation
Sage Jenson
Pages 411–414
Pied de Pulse: Packing Embroidered Circles and Coil Actuators in Pied de Poule (Houndstooth)
Loe Feijs and Marina Toeters
Pages 415–418
Digital Mechanics and The Rolling Coin Clock
Bjarne Jespersen
Pages 419–422
Bridges as an Incentive to Collaborative Works II
Anusch Bayens, Carlo De Pauw, Carmen Geens, Mark Pieters, André Thomas, Alex Van Bogaert, Samuel Verbiese and Nico Willemsens
Pages 423–426
Representational Random Walks
Max Grusky
Pages 427–430
A Fast Algorithm for Creating Turing-McCabe Patterns
Markus Schwehm
Pages 431–434
A Zometool Model of the B-DNA
László Vörös
Pages 435–438
Off the Wall: A Brief Report
Charlene Morrow
Pages 439–442
Snub Polyhedral Forms Constructed from Flexible 60-120 Degree Rhombic Tiles
David A. Reimann
Pages 443–444
A Rose By Any Other Name...
Gregg Helt
Pages 445–448
Thoughts on Generative Art
David Chappell
Pages 449–452
Extracting Unit Cells from Tilings with Color Symmetries: Case of Counterchange Patterns
Venera Adanova and Sibel Tari
Pages 453–456
Sculpturing Surfaces with Cartan Ribbons
Matteo Raffaelli, Jakob Bohr and Steen Markvorsen
Pages 457–460
Mathematics Meets Cinema: La Figure de la Terre
Osmo Pekonen and Axel Straschnoy
Pages 461–464
Prelude Op. 11, No. 1 by A. Scriabin: ICVSIM Relations
Nikita Mamedov and Robert Peck
Pages 465–468
Sections of Coxeter Orbihedra
Motiejus Valiunas, Emilio Zappa and Briony Thomas
Pages 469–472
A Successful Art&Math Exhibition with Workshops II
Gisèle De Meur and Samuel Verbiese
Pages 473–476
Novel Textile Knot Designs Through Mathematical Knot Diagrams
Nithikul Nimkulrat and Janette Matthews
Pages 477–480
Chladni Figures Revisited: A Peek Into The Third Dimension
Martin Skrodzki, Ulrich Reitebuch and Konrad Polthier
Pages 481–484
L-System Nomographs: Aesthetics to Calculation
Leif Roschier and Ron Doerfler
Pages 485–488
Baton Rolling on a Series of Curved Surfaces
Akihiro Matsuura and Yuki Yamada
Pages 489–492
Texturing Coloured Images in Black and White
Hank Guss
Pages 493–496
The Hendecagonal Stars in the Alhambra
Dirk Huylebrouck and Antonia Redondo
Pages 497–500
The Golden Ratio and the Diagonal of the Square
Gabriele Gelatti
Pages 501–502
The Pythagorean Theorem as a Rooted In-tree Dependency Graph
Jesse Atkinson
Pages 503–506
Polygon Spirals
Nick Mendler
Pages 507–510
Pattern Design Using Cellular Automata and Iterative Relocation System
Jae Kyun Shin and Seung Ryul Choi
Pages 511–514
The Math and Art of Folded Books
Sharol Nau and Richard Nau
Pages 515–518
Two Non-Octave Tunings by Heinz Bohlen: A Practical Proposal
Reilly Smethurst
Pages 519–522
Repeating Fractal Patterns with 4-Fold Symmetry
Douglas Dunham and John Shier
Pages 523–524
Three-Dimensional Score: Seeing Music, Hearing Sculpture
Miika Karttunen and Atte Tenkanen
Pages 525–528
The Pentagonal Numbers Meet the Choose-4 Numbers
James Morrow
Pages 529–532
Pointillist Graphing of Iterated Function Systems
Risto A. Paju
Pages 533–536
Plane-filling Curves on Transitive Grids
Jörg Arndt and Julia Handl
Pages 537–540
The Fourth Dimension in Mathematics and Art
Jean Constant
Pages 541–544
A Eulogy in Honour of Anders Johan Lexell, an 18th Century Finnish Mathematician
Joonas Ilmavirta and Johan C.-E. Stén
Pages 545–548
Flatscape of Measure Polytopes
Glenn C. Smith
Pages 549–552
Teaching Combinatorics with “Poly-Universe”
Eleonóra Stettner and György Emese
Pages 553–556
Spelunking Adventure VI: An Equal Tempered Icosahedral Scale
Curtis Palmer
Pages 557–560
Some Interactive Tools for Examining Renaissance Ciphers
Alexander Boxer
Pages 561–564
Mathematics on TV? Yes, We Can!
Rogério Martins
Pages 565–566
Teaching and Learning Basic Group Theory Through Building Models of Polyhedra
Sviatoslav Archava, Leela Goel and Erin Traister
Pages 567–570
Scales and Temperament from the Mathematical Viewpoint
Steven A. Bleiler and Ewan Kummel
Pages 571–574
Blogging Math Art
Susan Happersett
Pages 575–578
Possibilities of the Parabola
Robyn Gibson and Melissa Silk
Pages 579–582
Classifying Hexagonal Tilings in Islamic Architecture with a Single Numerical Parameter
Peter J. Lu and Eric Broug
Pages 583–586
Creating the “Discover the Art of Math” Exhibition
Kertu Saks and Aare Baumer
Pages 587–590
Why Do Mathematical Presentations Sometimes Sound Like Cookery Shows?
Katie McCallum
Pages 591–594
The “Dual Nature” of the Point
János Szász Saxon
Pages 595–596
Mathematics Through the Matrix of Poetry
Tom Petsinis
Pages 597–600
Modelling Environmental Problem-Solving Through STEAM Activities: 4Dframe's Warka Water Workshop
Kristóf Fenyvesi, Ho-Gul Park, Taeyoung Choi, Kwangcheol Song and Seungsuk Ahn
Pages 601–608
Rhombic Triacontahedron Puzzle
George Hart and Elisabeth Heathfield
Pages 609–614
Fractal Flipbooks
Andrea Hawksley and Scott Duke Kominers
Pages 615–620
Elliptic Paraboloids in Circumpolar Vernacular Architecture
Nancy Mackin
Pages 621–624
Spinning Arms in Motion: Exploring Mathematics within the Art of Figure Skating
Tetyana Berezovski, Diana Cheng and Rachel Damiano
Pages 625–628
Exploring the Arts Online with the Wolfram Language
Christopher Carlson
Pages 629–632
Lumifold: a STEAM Activity
Melissa Silk and Jane Martin
Pages 633–634
Dual Models: One Shape to Make Them All
Mircea Draghicescu
Pages 635–640
Putting Your Best Foot Forward: Movement and Mathematics in College
Erik Stern and Julian Chan
Pages 641–648
Origami as a Tool for Exploring Properties of Platonic Solids
Natalija Budinski
Pages 649–654
(Pattern)2
Liz Shreeve and Melissa Silk
Pages 655–658
Euclid's Digital Elements: Straightedge and Compass Softwares as Aid for Geometrical Design
Vladmir Sicca
Pages 659–662
Legerdemain: Exploring Tessellation with CatsEye
Douglas Easterly
Pages 663–666
Similarity Drawn Freehand
Teresa Downard
Pages 667–672
How to Draw Perspective Directly on a 3D Plane
Tomás García Salgado
Pages 673–680
Mathematical and Physical Properties of Rope Made for Decorative Purposes
Alexander Åström and Christoffer Åström
Pages 681–688