Mind Doodles

Mind Doodles are visual puzzles – the product of various types of logic developed by cultures past and present. Each design has been selected to stimulate your visual perception or to challenge your logic.

The book is sized like a journal but its objective is to stimulate ideas, to provide a platform for creativity, to provide space for idle thoughts and concepts; a book to personalize and to keep over the years. The book is for creative people and thoughtful people, for people who are interested in the visual ideas of the past and the present: for designers, artists, students, architects, mathematicians, historians, and for the idly curious.

Published by Park City Publishing and available at parkcitypublishing.com – go to the menu item BOOKSTORE.

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This is what Thames & Hudson are saying about 3D Thinking:

This is what Thames & Hudson Ltd (London), my publisher, are saying about my latest book, “3D Thinking” (to be published Spring 2018):

The foundations, forms and patterns in architecture, design and decorative arts throughout the world have been deeply influenced by the geometries of past cultures. From the first path-like doodles on cave walls through to the higher abstractions developed to make accurate measurements and predictions, the three-dimensional forms we design and build are dependent upon available materials, human needs and the limitations of our imaginations.

The product of decades of teaching and research, this unique and inspirational design resource presents a history of the intimate relationships between geometry, mathematics and design throughout human history, from the Neolithic period through the Indian, Egyptian, Babylonian, Chinese, Greek, Celtic, Islamic, pre-Columbian and Renaissance cultures, to the present and the possible future. Explaining key principles that can be applied across all design disciplines, Roger Burrows reveals fresh insights into how geometry as a visual language has evolved to meet our needs, initiated new technologies, solved problems and changed the way we think about the world around us.

  • An essential sourcebook for design and architecture students and professionals.
  • Covers humankind’s approaches to design and architecture across the entire range of human history and culture.
  • Stimulates new ways of thinking about the pressing design challenges of our present and future.
  • Illustrated with hundreds of specially created diagrams and artworks.
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3D Thinking Update

The math edit has been completed – and so has the index. The cover seems to be on the right track but am waiting for the next visual. I think there might be one last round to make sure that all the editorial and design changes have been made correctly. So fingers crossed that the book will be ready for the printer very soon. We’re still on track for the Spring 2018 launch.

Have been developing different types of workshop that might compliment the book – as well more in the lecture series.

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3D Thinking – Last stages of editorial

The deadline for the final edit is August 15th – this includes the math edit which is almost complete. The last remaining task is to complete the Index. I had no idea that the editorial phase would take up so much time. We were a little held up last year due to an earthquake in central Italy where one of the editors lives – Kirsty, a great editor by the way! Even so time passes – but now the end is in site and the book is now ship-shape, so to speak.

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Altair Design – Page Update

Have updated the Altair design page with a new animation that shows the logic of how the designs are generated plus how the designs themselves can be perceived – with imagination, with logic, with creativity.

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Shape Changing Polyhedra – Updated Page

Have updated the Shape Changing Polyhedra page with movie clips and animations that introduce this new family of design and architectural structures.

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Dynamic Sphere Geometry – Updated Page

Have updated the “Dynamic Sphere Geometry” page. Applications are architectural, design, new materials. Revised page has updated animations showing how close packing sphere arrangements (of different sized spheres) are generated, examples of sequences and an example of an architectural lattice generated by the geometry.

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Bridges Conference 2016 University of Jyvaskyla, Finland

Just returned from the Bridges Conference held this year at the University of Jyvaskyla, Finland. Met some great people, mathematicians, architects, designers…

Presented “Shape Changing Polyhedra,” from my latest book “3D Thinking” to be published by Thames and Hudson Ltd Spring 2017. My presentation included stop frame animations and movie clips of shape-changing polyhedra full-shell modules connected in all sorts of ways so that when one part of an overall structure changes so do all parts.

My paper can be found at http://archive.bridgesmathart.org/2016/bridges2016-225.pdf

The images below show the shape-changing polyhedra  “Shell #1 Module” and some combinations of the module. My bridges presentation featured seven different types of shell module.



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Radio Interview

Just appeared on KPCW; this morning in fact. Questions raised have made me think a bit more broadly about October’s, “Geomorph – Everything Changes When Mathematics Meets Art,” exhibition at the Leonardo in Salt Lake City.

I made a comment on-air that, when we teach mathematics and science, we should go back to the point of invention; to recapture the dynamics of an idea, and to give our students the opportunity to think about the mathematical, or scientific, concepts that we teach, as the inventions that they are. To think about whether the inventions are the best way of thinking, or whether there are better ways of thinking. Is the Earth flat, or is it more like a sphere, or maybe it’s like something else that is completely different? A lot depends upon what we’re trying to accomplish: to navigate across the ocean, or to try to figure out if there’s a gravitational benefit to launching a rocket from one part of the Earth rather than another. Re-captuturing the point of invention, of a mathematical, or scientific, idea, means taking a step back in time to the point of need, or to the point of discovery; to when, for example, we needed to find our way across the oceans, and the ideas explored to do it; and to look at the merits of one idea over another. If nothing else we might learn to appreciate the navigational mathematics that we have but, on the other hand, we might come up with something better, something more dynamic, something that better takes into account changing conditions, such as the wind, and the ocean currents. The Geomorph exhibition is all about approaching mathematics in a new way, and making it a medium of discovery.

I made another comment on KPCW that there are two types of mathematics, “Calculator Mathematics,” and “Discovery Mathematics.” Where schools mostly teach calculator mathematics. That we’re moving towards a time where computers can really take over the calculator side of things and that we, as humans, can get more involved in the creativeness of logical ideas – so that there is more of a partnership between us and the computers. Emphasis, then, in schools should, I think, be based more on logical problem solving and discovery. That’s not to say that we should forget calculator math but rather, re-position it. In fact, in my opinion, all students need to be familiar with calculator math, and we need some students who love calculator math, but also we need some students who question it; who question the underlying principles of computer programs; so that we never become over-reliant on mathematical models that might become obsolete, or limiting, or even destructive, as the the world evolves and new opportunities present themselves.

On the show I made another comment about how numbers don’t really exist but are just an abstract idea linking one lot of things with another; for example, matching a number of fingers on your hand with a number of sheep in your field. Mathematics is really all about abstracting ideas and making models of things. Once we ran out of fingers, to “count” things, we learnt to count in groups of ten. But that’s just the way our culture handled the problem of counting more than the number of fingers on our hands; some ancient Chinese counted in groups of two, Babylonians in groups of twelve, and Mayans in groups of five. There were many ancient cultures that never got beyond counting up to ten; they just reckoned they had, “lots.” There are so many abstract ideas floating around that, because we don’t question them, they take on a reality that they do not deserve. Money is a great example. Money is something we’re desperate to have;  that world commerce completely relies upon, but where the concept is really abstract; where the idea of “money” is, on the one hand, based on the real goods it can be traded for, such as food, water, and a roof over our heads; or on the virtual value based on what something might be valued at, if the equity worth was realized; such as the valuation of stocks, and currency. But where the value systems are highly variable and where one variable undervalues another, dependent upon the “credit” value or actual, “supply and demand.” Abstract ideas are very useful but also dangerous if we don’t evaluate and recognize them for what they are. Geomorph is all about the evolution of mathematical and geometrical ideas, but also about changing the rules and creating completely new things, new shape-changing structures and new geometries with applications in architecture, new materials, new structures, design, art, …

Hope to see you at the Geomorph exhibition!






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Have been working with four Park City, Utah, high school students on projects for Rockwell Collins and Overstock.com – as part of the PCCAPS program. The idea is to have students work on valid projects for corporations and to build experience with professional protocol, new types of software, problem solving, etc.

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