New book! Jay Kappraff: Geometric Foundations of Design

We are honored to announce that in Jay Kappraff‘s new book entitled Geometric Foundations of Design, the author devotes several parts of the book to Slavik Jablan and Ljiljana Radovic‘s work, which was done in close collaboration with Kristóf Fenyvesi. Pedagogical results of these collaborations were introduced to several hundreds of teachers and thousands of students at Experience Workshop’s events. Among many others, the book provides an in-depth analysis of the work of Haresh Lalvani and Lajos Szilassi as well, whose mathematical-artistic innovations have been integral part of several Experience Workshop events and publications.

From the Preface of Geometric Foundations of Design: Old and New

This fourth book continues to expand the frontiers of this new discipline by inviting the reader to participate in the creation of their own designs while gaining an appreciation of how mathematics and design are deeply intertwined. Accompanying this text is a website in which many of my students’ designs are shown in color along with miscellaneous information. The website is open source and free to download. There will also be an opportunity to expand the book beyond its present timeline.

Image: Polyuniversal Play at the Symmetry Festival in Vienna in 2016. The author, Jay Kappraff (right) and Haresh Lalvani (left), artist, designer and scholar who created the iconic visual symbol on the back cover and in the front of each chapter of the book. (Photo by György Darvas, founder of the Symmetry Festivals.)

I began to develop my ideas about the relationship of mathematics and design in 1970 through my friendship with Mary Blade who was teaching math and design to students from the School of Architecture at Cooper Union College for more than 25 years. Following her lead, I taught a course on the mathematics of design for many years at New Jersey Institute of Technology (NJIT) to students from the College of Architecture and Design. Through teaching this course, it became clear to me that large ideas from the realm of geometry come forth from humble beginnings. I have written this book to give voice to this insight. Many of the topics in the 26 chapters of this book were inspired by ancient mathematics and also the craft of artists and designers.

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In Chap. 9 the mathematics of meanders is studied using permutations of integers. It is interesting that Albert Einstein wrote a paper on meanders early in his career. These meanders have roots in the study of knots and links, labyrinths and mazes. My colleagues Slavik Jablan and Ljiljana Radovic applied their work to the study of a new class of meander knots and links. Kristof Fenyvesi, another colleague, wrote a short history of Labyrinths presented in Chap. 9. The Cretan Labyrinth of ancient Greek mythology is constructed along with a Labyrinth building workshop that took place at the Bridges conference, a conference on mathematics, architecture and design that has been held each year since 1998. These ideas also lead to the construction of mazes.

Jay Kappraff: Geometric Foundations of Design: Old and New. Series on Knots and Everything: Volume 70. World Scientific, 2021
Read the Preface and Chapter 1. here

 

Contents:

• Triangle-circle and Square-circle Grids
• Margit Echols’ Magic Squares
• The Pythagorean Theorem as a Theme in Islamic Art: An Algorithmic Approach
• Tiling a Rectangle by Congruent and Non-congruent Squares
• Simple Tilings with Lattice Symmetry
• The Brunes Star
• Do You Like Paleolithic Op-art? by Slavik Jablan
• Truchet, Versatiles, Op-art and Kufic Tiles by Slavik Jablan and Ljiljana Radovic
• Meanders, Knots, Labyrinths, and Mazes by Jay Kappraff, Slavik Jablan, Ljiljana Radovic, Kristof Fenyvesi
• Why is a Donut Like a Coffee Cup?: An Introduction to Topology
• The Szilassi and Csaszar Polyhedra
• Curves of Constant Width and a Three Dimensional Sculpture that Rolls
• An Introduction to Fractals
• Creating a Fractal Wallhanging
• The Logarithmic Spiral in Geometry, Nature, Architecture, Design, and Music
• The Golden Mean
• Wythoff’s Game
• The Modulor of Le Corbusier
• Non-periodic Tilings of the Plane
• The Silver Mean
• A Unified Theory of Proportions
• Zonogons
• Tangrams and Amish Quilts
• Mirror Curves by Slavik Jablan and Ljiljana Radovic
• Lunda Designs by Slavik Jablan and Ljiljana Radovic
• Visual Illusions by Slavik Jablan and Ljiljana Radovic