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Bridges Linz 2019 Mathematics | Art | Music | Architecture | Education | Culture 2019 Conference Proceedings

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Bridges Linz 2019 Mathematics | Art | Music | Architecture | Education | Culture 2019 Conference Proceedings Bridges Linz 2019 Mathematics | Art | Music | Architecture | Education | Culture 2019 Conference Proceedings BRIDGES LINZ 2019 Editors Program Chair Susan Goldstine Department of Mathematics and Computer Science St. Mary's College of Maryland St. Mary’s City, Maryland, USA Short Papers Chair Workshop Papers Chair Douglas McKenna Kristóf Fenyvesi Mathemæsthetics, Inc. Finnish Institute for Educational Research Boulder, Colorado, USA University of Jyväskylä Jyväskylä, Finland Production Chair Craig S. Kaplan Cheriton School of Computer Science University of Waterloo Waterloo, Ontario, Canada Bridges Linz 2019 Conference Proceedings (www.bridgesmathart.org). All rights reserved. General permission is granted to the public for non-commercial reproduction, in limited quantities, of individual articles, provided authorization is obtained from individual authors and a complete reference is given for the source. All copyrights and responsibilities for individual articles in the 2019 Conference Proceedings remain under the control of the original authors. ISBN: 978-1-938664-30-4 ISSN: 1099-6702 Published by Tessellations Publishing, Phoenix, Arizona, USA (© 2019 Tessellations) Distributed by MathArtFun.com (mathartfun.com). Cover design: David Chappell, University of La Verne, California, USA Bridges Board of Directors Kristóf Fenyvesi George Hart Finnish Institute for Educational Research Wiarton, Ontario, Canada University of Jyväskylä Jyväskylä, Finland Craig S. Kaplan Carlo H. Séquin Cheriton School of Computer Science Computer Science Division University of Waterloo University of California, Berkeley Waterloo, Ontario, Canada Berkeley, California, USA Sujan Shrestha Eve Torrence Science, Information Arts & Technologies Department of Mathematics University of Baltimore Randolph-Macon College Baltimore, Maryland, USA Ashland, Virginia, USA Conference Organization Zsolt Lavicza Barbara Lichtenegger Johannes Kepler University Private University of Education, Diocese of Linz, Austria Linz Linz, Austria Sandra Reichenberger Johannes Kepler University Linz, Austria Artistic and Scientific Committee Members and Coordinators Steve Abbott Robert Fathauer Department of Mathematics Tessellations Company Middlebury College Phoenix, Arizona, USA Vermont, USA Art Exhibition Theater Event Kristóf Fenyvesi Sarah Glaz Finnish Institute for Educational Research The University of Connecticut University of Jyväskylä Storrs, Connecticut, USA Jyväskylä, Finland Poetry Reading Family Day Emily Grosholz Tiffany Inglis Pennsylvania State University D2L University Park, Pennsylvania, USA Waterloo, Ontario, Canada Poetry Reading Technical Support Uyen Nguyen Nathan Selikoff New York City, New York, USA Digital Awakening Studios Art Exhibition Orlando, Florida, USA Technical Support Bianca Violet IMAGINARY Berlin, Germany Short Film Festival Proceedings Program Committee Steve Abbott Kazushi Ahara Abdalla G. M. Ahmed Middlebury College Meiji University Khartoum, Sudan Vermont, USA Tokyo, Japan Mara Alagic Roger Antonsen Ellie Baker Wichita State University University of Oslo Lexington, Massachusetts, USA Kansas, USA Oslo, Norway Javier Barallo Tom Bates Debra K. Borkovitz The University of the Basque Santa Barbara, California, USA Wheelock College Country UPV/EHU Boston, Massachusetts, USA Vizcaya, Spain Robert Bosch Christopher Brownell Doug Burkholder Oberlin College Fresno Pacific University Lenoir-Rhyne University Ohio, USA California, USA Hickory, North Carolina, USA Christopher Carlson David Chappell Andrew Cooper Wolfram Research University of La Verne North Carolina State University Champaign, Illinois, USA California, USA Raleigh, North Carolina, USA Kelly Delp Neil Dodgson Mircea Draghicescu Cornell University Victoria University of Wellington ITSPHUN LLC Ithaca, New York, USA New Zealand Portland, Oregon, USA Doug Dunham Frank Farris Robert Fathauer University of Minnesota Santa Clara University Tessellations Company Duluth, USA California, USA Phoenix, Arizona, USA Loe Feijs Kristóf Fenyvesi Paul Gailiunas Eindhoven University of University of Jyväskylä Newcastle, England Technology Finland The Netherlands Susan Gerofsky Sarah Glaz Susan Goldstine University of British Columbia The University of Connecticut St. Mary’s College of Maryland Vancouver, Canada Storrs, Connecticut, USA St. Mary’s City, Maryland, USA Gary Greenfield Emily Grosholz Richard Hammack University of Richmond Pennsylvania State University Virginia Commonwealth Virginia, USA University Park, Pennsylvania, University USA Richmond, Virginia, USA George Hart Edmund Harris Andrea Hawksley Wiarton, Ontario, Canada University of Arkansas eleVR, HARC, YCR Fayetteville, Arkansas, USA San Francisco, California, USA Sara Hershkovitz Judy Holdener Patrick Honner Center for Educational Technology Kenyon College Brooklyn Technical High School Tel Aviv, Israel Ohio, USA New York City, NY, USA Rachael Horsman Guy Inchbald Tiffany Inglis Cambridge Mathematics Worchestershire, England D2L England Waterloo, Ontario, Canada Veronika Irvine Craig S. Kaplan Karl Kattchee University of Waterloo University of Waterloo University of Wisconsin Ontario, Canada Ontario, Canada La Crosse, USA Margaret Kepner Eva Knoll Lisa Lajeunesse Washington DC, USA Mount Saint Vincent University Capilano University Halifax, Nova Scotia, Canada North Vancouver, British Columbia, Canada Zsolt Lavicza Penousal Machado Alice Major Johannes Kepler University University of Coimbra Edmonton, Alberta, Canada Linz, Austria Portugal Vincent J. Matsko Elisabetta Matsumoto Dan May Spring Hill, Florida, USA Georgia Institute of Technology Black Hills State University Atlanta, Georgia, USA Spearfish, South Dakota, USA Douglas McKenna Kerry Mitchell Mike Naylor Mathemæsthetics, Inc. Phoenix, Arizona, USA Matematikkbølgen Boulder, Colorado, USA Math Creativity and Competency Center Vanvikan, Norway Uyen Nguyen Doug Norton Werner Olivier New York City, NY, USA Villanova University Nelson Mandela University Pennsylvania, USA Port Elizabeth, South Africa Osmo Pekonen Kirsi Peltonen Ulrich Reitebuch University of Jyväskylä Aalto University Freie Universität Berlin Finland Helsinki, Finland Germany Rinus Roelofs Radmila Sazdanovic Karl Schaffer Hengelo, The Netherlands North Carolina State University De Anza College and Raleigh, North Carolina, USA MoveSpeakSpin Scotts Valley, California Henry Segerman Carlo H. Séquin Sujan Shrestha Oklahoma State University University of California, Berkeley University of Baltimore Stillwater, Oklahoma, USA USA Maryland, USA Donald Spector Catherina Steyn John Sullivan Hobart & William Smith Colleges Nelson Mandela University Technische Universität Berlin Geneva, New York, USA Port Elizabeth, South Africa Germany David Swart Felicia Tabing Tara Taylor Waterloo, Ontario, Canada University of Southern California St. Francis Xavier University Los Angeles, California, USA Antigonish, Nova Scotia, Canada Briony Thomas Bruce Torrence Eve Torrence University of Leeds Randolph-Macon College Randolph-Macon College England Ashland, Virginia, USA Ashland, Virginia, USA Walt van Ballegooijen Tom Verhoeff Charles Wampler Wijk en Aalburg, The Netherlands Eindhoven University of General Motors Research and Technology Development The Netherlands Warren, Michigan, USA Ryan Webb Phil Webster Jiangmei Wu Maggie L. Walker Governor’s Phil Webster Design Indiana University Bloomington School Scotts Valley, California, USA Indiana, USA Richmond, Virginia, USA Carolyn Yackel Mercer University Macon, Georgia, USA Art Exhibition and Catalog Program Committee Robert Fathauer Uyen Nguyen Tessellations Company New York City, New York, USA Phoenix, Arizona, USA Co-curator Co-curator Conan Chadbourne Nathan Selikoff San Antonio, Texas, USA Digital Awakening Studios Catalog Orlando, Florida, USA Technical Support Barbara Lichtenegger Private University of Education, Diocese Linz Linz, Austria Local coordinator Short Film Festival Program Committee Susan Gerofsky Elisabetta Matsumoto University of British Columbia Georgia Institute of Technology Vancouver, Canada Atlanta, Georgia, USA Henry Segerman Bianca Violet Oklahoma State University IMAGINARY Stillwater, Oklahoma, USA Berlin, Germany Chair Math + Fashion Show Committee and Jurors Susan Goldstine Elisabeth Heathfield St. Mary’s College of Maryland Wiarton, Ontario, Canada St. Mary’s City, Maryland, USA Uyen Nguyen Frank Farris New York City, New York, USA Santa Clara University California, USA Loe Feijs Eindhoven University of Technology The Netherlands Contents Preface ............................................................................... xix Invited Papers That Is Not Art, It Is a Puzzle! ............................................................1 Oskar van Deventer Discrete and Computational Differential Geometry for Functional Pattern Design .............9 Helmut Pottmann The Foundations of Mathematics and Art: Form, Logic, Intuition ............................11 Lynn Gamwell The Seduction of Curves ................................................................12 Allan McRobie Regular Papers Walkable Curves and Knots .............................................................13 Robert W. Fathauer Exploring Szpakowski’s Linear Ideas ....................................................21 Robert Bosch, Abagael Cheng, and Ari Smith Making A Mystic Dream of 4 ............................................................29 Iggy McGovern Graeco-Latin Square Poems .............................................................35 Lisa Lajeunesse Folding Functions: Origami
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