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The Geometry of Natural Structure

The Geometry of Natural Structure
Author: Robert Williams
Publisher:
Total Pages: 263
Release: 2009-01-01
Genre: Design
ISBN: 9780982346518

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First published by the McDonnell-Douglas Advanced Research Laboratories in 1969 with the title, Handbook of Structure, Research Communication 75, it became the most requested publication in the history of DARL. A significantly expanded version was published by Eudaemon Press in 1972 with the title Natural Structure: Toward a Form Language. The third edition appeared as a Dover Science Book Publication, titled, The Geometrical Foundation of Natural Structure beginning in 1979. In the forty years that The Geometry of Natural Structure has been available to the public, the work has continued to be a valuable resource tool for scientists, architects, and artists. The Geometry of Natural Structure is a comprehensive work on geometric form in space. A convenient and stimulating handbook for scientists and designers, it covers the regular and semi-regular polyhedra, their various symmetries, how they fit together to fill space, and other structural considerations. Beginning with an introduction that places geometric structure in its proper mathematical context, the author then presents a detailed description of the core geometric forms of natural structure: polygons, polyhedra, aggregations of spheres, and packings of polyhedra. Topics considered include: the inter-relationships among geometrical/ topological forms, the unit cell concept, Golden Section, surface area and volume relationships of polyhedra, sphere coverings, Euler's law, and polyhedra distortions. Mr. Williams concludes with a rewarding discussion of the methodologies by which forms can be generated: truncation, rotation-translation, augmentation-deletion, fistulation, and others. The many tables located through¬out the text are extremely valuable for reference.


Geometrical Foundation of Natural Structure

Geometrical Foundation of Natural Structure
Author: Robert Williams
Publisher:
Total Pages: 524
Release: 2015-07-01
Genre:
ISBN: 9780982346549

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This Unabridged Three Volume Set contains the extensive geometry-cosmology explorations of Robert Williams. Each book is signed by the author.


Structure in Nature Is a Strategy for Design

Structure in Nature Is a Strategy for Design
Author: Peter Pearce
Publisher: MIT Press
Total Pages: 268
Release: 1990
Genre: Architecture
ISBN: 9780262660457

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"The structural designs that occur in nature - in molecules, in crystals, in living cells - appear in this fully illustrated book as a source of inspiration and study of design of man-made structures" -- BOOK JACKET.


Modern Geometric Structures and Fields

Modern Geometric Structures and Fields
Author: Сергей Петрович Новиков
Publisher: American Mathematical Soc.
Total Pages: 658
Release: 2006
Genre: Mathematics
ISBN: 0821839292

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Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.


The Fractal Geometry of Nature

The Fractal Geometry of Nature
Author: Benoit Mandelbrot
Publisher: Echo Point Books & Media, LLC
Total Pages: 0
Release: 2021-07-16
Genre:
ISBN: 9781648370410

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Written in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.


Curved Space Diamond Structure

Curved Space Diamond Structure
Author: Peter Pearce
Publisher: CreateSpace
Total Pages: 58
Release: 2015-09-30
Genre:
ISBN: 9781517405373

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The Curved Space Structure, designed by Peter Jon Pearce, is derived from a comprehensive study of structure in nature, with a special interest in the geometry of atomic assemblies in crystals and patterns found in biomorphic form. This study was pursued with the aim of understanding the unity of formative principles exhibited by natural structure through spatial geometry. Nature universally manifests a principle of least energy where form can be considered a diagram of forces. In a very special way, the Curved Space Structure represents a 16 billion times enlargement of the diamond crystal, enabling children, and adults, to have an immersive experience with its spatial geometry. Not only that, the details of the construction methods of this structural assembly reveal a panoply of natural patterns including curved and minimal surfaces, tessellations, polygonal geometries, and applications of material science and technology. The name Curved Space was adopted as way of characterizing the spatial experience of engaging with these remarkable structures. There is no specific reference to Einstein's use of this term, although it certainly is implied. In June 1975 a Curved Space Structure was exhibited as part of the International Design Conference at Aspen, Colorado. This was the first public display of the Curved Space and served as a test assembly prior to the first permanent installation at the Brooklyn Children's Museum. There were three distinct structures that were installed at that museum in Brooklyn, New York, in August 1975. Unfortunately about 10 years later the museum was redesigned and the Curved Space installation was removed. One of the most important venues where a Curved Space Structure can still be found is the Hakone Open Air Museum in Japan. This amazing outdoor sculpture museum has had a Curved Space in its collection since 1978, when it was first installed. This structure was replaced and revised first in 1994 and then again in 2011. The Hakone Museum installation is largest single Curved Space Structure ever built. Although considered a work of sculpture, known as Peter Pearce's Diamond Sculpture, it has always been the intention of the Museum that children be able to access the structure. This structure has been extremely popular with the visitors to the Museum. The origins of the Curved Space system originated with Peter Jon Pearce's morphological research in 1965-66. This research explored natural structures as a theoretical basis for building system design. The emphasis of the this work involved the study of repeating geometric structures of the type characterized by the internal structure of crystals, as well as patterns of least energy exhibited by biomorphic structures in nature. Combining the study of minimal surfaces and repeating three-dimensional structures led to the Curved Space Structures. This work is comprehensively described in Pearce's book, Structure in Nature is a Strategy for Design, The MIT Press, 1978, 1990. Although out of print, the book is still available from some sources.


Form Geometry Structure

Form Geometry Structure
Author: Daniela Bertol
Publisher:
Total Pages: 523
Release: 2011
Genre: Architectural design
ISBN: 9781934493113

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"Form Geometry Structure is an architecture and generative design guide that introduces a scientific framework in the exploration of forms in nature and design. From their geometric definition to their structural potential, forms are created and transformed by simple computing algorithms following growth patterns found in nature. In the natural world, these geometric forms can provide great inspiration in the design of the man-made world. Although software independent, this book presents several digital models of parametric forms built in Bentley's generative design software GenerativeComponents. While the relationship between geometry and forces in nature has been explored for millennia, contemporary computational tools bring new insights and methodologies. Form Geometry Structure is beautifully illustrated and rigorously researched and will bridge the gap between art and science, bringing to contemporary terms the tradition of the treatises on art and architecture." -- Publisher's site.


New Foundations for Physical Geometry

New Foundations for Physical Geometry
Author: Tim Maudlin
Publisher: Oxford University Press
Total Pages: 374
Release: 2014-02
Genre: Mathematics
ISBN: 0198701306

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Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.