Spheres Steiner Chain

In geometry, a Steiner chain is a set of n circles, all of which are tangent to two given non-intersecting circles (blue and red) where n is finite and each circle in the chain is tangent to the previous and next circles in the chain.

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Lectures: Geometry to enhance the human experience

My latest book, “3D Thinking,” to be published by Thames and Hudson Spring 2017 forms the basis for a new exhibition and lecture series, see below. Lectures feature photos, illustrations, movie clips, animations.

Please see my page, “Lectures and Exhibitions,” for descriptions.

Lectures include:

 The Golden Ratio – A Divine Proportion? Presented at the Leonardo Science and Technology Museum, Salt Lake City, March 2016.

The Future of Architecture. Presented at the Leonardo Science and Technology Museum, Salt Lake City, April, 2016.

Shape Changing Polyhedra. Presented at the Bridges Conference, University of Jyvaskyla, Finland August 2016.

Arabian Geometries.

The Pythagoreans.

A Dynamic Close-Packing Sphere Geometry. A unique new lattice generating geometry for architecture, design, science.

Labyrinths – Mysteries and Methods.

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Altair Designs Complete A Circle

For many years I’ve wondered where the original structure was that inspired the development of Altair designs.

Daud Sutton, a specialist in Islamic Design, sent me an email from Cairo just a few days ago. He has found found the original structure – a  latticed window – that has inspired so many of us – all that have explored Altair Designs, see below.

We can now complete the story of Altair:

A window’s lattice was constructed in about 1356 CE in the Mosque- Madrasa of Amir Salf al-din, Sargatmish in what is now, ‘Old-Cairo.’

Jules Bourgoin, in the early 1870’s, made a sketch of the window, created a schematic of it, and printed the schematic in his, “Les Elements de l’Arabe,” published in 1879 and numbered 151-  but gave no indication of the window’s location.

The design was then copied by Albert Calvert, without any mention of Bourgoin, in his, “Moorish Remains in Spain,” published in 1906.

Calvert’s book and design 151 found  its way to Dr.
Ensor Holiday’s hospital room in about 1968.

Ensor recognized the unique geometry of the design and started to create design variations. Close-packing circles were integral to the design and dovetailed my interest with Ensor’s – so we started working together – the rest is the story of Altair Designs.

So without that day in the early 1870’s, when a French architect sat down to make a drawing of a latticed window, a design that has inspired so many may have remained unknown and forgotten in the backstreets of an ancient town.

I wish Ensor Holiday and Aubrey Wolton (who helped place the designs with our first publisher, Longmans in the UK) were with us today – they would both be delighted to hear of the discovery.

Altair Window

 

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Think 3D to be published Spring 2017

Thames and Hudson will be the publisher! They will reformat the book and add their design and editorial magic. I cannot think of a better publisher! See my earlier posts re “Think 3D” and parts of my website to get an idea of the content. Will post more at a later date.

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Rethinking Randomness by Jeff Buzen

RR1 RR2Rethinking Randomness by Jeff Buzen introduces an alternative characterization of randomness and a new modeling framework that together explain the improbable success of these probabilistic models. Jeff used one of my close packing circle arrangements with a corresponding line lattice (connecting circle contacting points) and then an apparently random image selection (cover design) conjured by the line lattice – as a sort of analogy of his concept. Jeff’s book is a good read for those working probabilistic models.

 

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Crystal Cave – A new book of geometric designs to color

This is a new book that has just gone to print for Wooden Books (UK) and Bloomsbury (USA, Australia, India). Title is the “Crystal Cave.” The book is full of geometric designs to color by Ensor Holiday, Roger Burrows (me), Roger Penrose, John Martineau, and Haifa Khawaja. Each author has applied different math systems to generate the designs – and all the designs have been selected to stimulate the mind and creativity. Ensor Holiday and I have created designs based on close-packing circles bound by squares and triangles; Roger Penrose designs are based on non-periodic tilings (tiles extracted from regular pentagons); John’s designs are circle based but where circles ‘grow,’ from close packing circle points; Haifa’s designs are classic Islamic designs mostly based on tessellations with some overlap onto systems based on the Islamic ‘Ray,’ method.

Altair Crystal Cave UK

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Think 3D completed

The book has now been completed and will be published by Thames and Hudson Ltd in June 2016 (now Spring 2017).  I’ve constantly updated the work awaiting publication and have included the latest technologies and future applications for the various types of geometry and visual logic featured in the book – particularly the shape changers and the dynamic sphere geometry. Advance proof-copies are available for review. To see why the shape-changer geometries included in Think 3D are so relevant see the following two examples of a whole new wave of applications that will impact almost everything from architecture to aircraft, packaging, and land/space vehicle design:

https://www.youtube.com/watch?v=CihMimZc3Ac

https://www.youtube.com/watch?v=6cdfWdHZRrE

Think 3D contents are:

Introduction

Visual Logic

Old Traditions and New Directions

Perception and Conceptual Models

Development Of Architectural Form

Geometry Through Time

Neolithic Geometries

The River Cultures

The Indus

The Nile

The Yellow and Yangste

The Tigris and Euphrates

The Pythagoreans

European Tribal Geometry

Geometries of Early Islam

The Renaissance

Out of the Past Into the Future

Cartesian Geometries

Fractals

Shape-Changers

Dynamic Circles & Spheres

The Future of 3D Geometry

Conclusion

Index & Credits

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Think 3D – Update

Have completed the new chapters – the Renaissance and the River Valleys (Euphrates, Tigris, Nile, Yellow, Indus). The new material took longer to create than I thought. Have been working through the illustrations and securing rights for photos when needed. After that the index will need to be completed…The final page count will be just about 360 + pages.

Some of the material that appears in the book will be exhibited in an upcoming exhibition at the Leonardo.

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PCCAPS

Have been working with three high school seniors, and one junior, on projects for Rockwell Collins and Overstock.Com – as part of the PCAPS program, Park City, Utah. The CAPS concept is to link students with corporations and have them work on real projects that will build their professional skills, broaden their experience with hardware and software platforms, and push them into situations that need innovation and sheer hard work. The learning curve for some of the software is pretty steep – but the students are doing well. Next semester I’ll have ten students and we have some interesting projects lined up including one for the USAF.

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THINK 3D

The publisher has asked for new chapters and I have been in the process of adding chapters that cover the geometries of the “river cultures,” – Indus Vally; The Nile; The Euphrates; The Yellow River. I have also broadened the Celtic chapter content to include a broader range of European tribal geometries – primitive as they often are. Also a new chapter on the European Renaissance geometries. To develop the new sections and chapters I have had to do lots of research but the new material really helps show how visual concepts have developed over time, how local cultures have impacted concepts, and also how unique many of the concepts were, and still are – and how these unique concepts of the past can be applied in the present and possible future.

The page count will probably end up around 350 bt could reach 400 – full of illustrations, diagrams, designs, and links to animations, and movie clips. Throughout the book I’ve worked hard to be original and within the pages you’ll find many new discoveries and insights. I have printed samples of the book, “working copies still in process,” for review.

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