Geometry in nature

Author: Vagn Lundsgaard Hansen

Publisher: A K Peters Ltd

ISBN: 9781568810058

Category: Mathematics

Page: 238

View: 8250

Posted in Mathematics

Geometry in Nature

Exploring the Morphology of the Natural World Through Projective Geometry

Author: John Blackwood

Publisher: N.A

ISBN: 9780863159213

Category: Mathematics

Page: 190

View: 3019

From the simplest observations in nature to detailed measuring of intricate forms, we find geometry everywhere in the world around us.In this magnificent book, John Blackwood explores different kinds of symmetry in the diverse realms of nature. He considers the fundamental forms of minerals, plants, animals and humans, before going on to look at spirals, vortices, buds and other complex shapes. Using projective geometry as a basis, he shows how many forms in nature are generated by the same basic geometrical process, but significant disparities lead to the wondrous variety found in our universe.Fully illustrated with over 500 photographs, drawings and diagrams, this is both a beautiful and inspirational book.
Posted in Mathematics

The Fractal Geometry of Nature

Author: Benoit B. Mandelbrot

Publisher: Macmillan

ISBN: 9780716711865

Category: Juvenile Nonfiction

Page: 468

View: 8455

Three classic fractals, tamed. Galaxies and eddies. Scaling fractals. Nonscaling fractals. Self-mapping fractals. Randomness. Stratified random fractals. Fractional brown fractals. A book-within-the-book, in color. Random tremas; texture. Miscellany. Of men and ideas.
Posted in Juvenile Nonfiction

Fractal Geometry in Architecture and Design

Author: Carl Bovill

Publisher: Springer Science & Business Media

ISBN: 9780817637958

Category: Mathematics

Page: 195

View: 1833

na broad sense Design Science is the grammar of a language of images Irather than of words. Modern communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multi dimensional. Architectural renderings commonly show projections onto three mutual ly perpendicular planes, or consist of cross sections at different altitudes capa ble of being stacked and representing different floor plans. Such renderings make it difficult to imagine buildings comprising ramps and other features which disguise the separation between floors, and consequently limit the cre ative process of the architect. Analogously, we tend to analyze natural struc tures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures. Perception is a complex process. Our senses record; they are analogous to audio or video devices. We cannot, however, claim that such devices perceive.
Posted in Mathematics

Geometry and Nature

In Memory of W.K. Clifford : a Conference on New Trends in Geometrical and Topological Methods in Memory of William Kingdon Clifford, July 30-August 5, 1995, Madeira, Portugal

Author: William Kingdon Clifford,Hanna Nencka,Jean-Pierre Bourguignon

Publisher: American Mathematical Soc.

ISBN: 0821806076

Category: Science

Page: 296

View: 7396

This volume is the outgrowth of a conference devoted to William K. Clifford entitled, 'New Trends in Geometrical and Topological Methods', which was held at the University of Madeira in July and August 1995. The aim of the conference was to bring together active workers in fields linked to Clifford's work and to foster the exchange of ideas between mathematicians and theoretical physicists. Divided into 6 one-day sessions, each session was devoted to a specific aspect of Clifford's work. This volume is an attempt to bring the Clifford legacy in a new perspective to a larger community of mathematicians and physicists. New concepts, ideas, and results stemming from Clifford's work are discussed. Each article in the book is a self-contained paper that was presented at or submitted to the conference.
Posted in Science

The Hidden Geometry of Life: The Science and Spirituality of Nature

Author: Karen L. French

Publisher: Duncan Baird Publishers

ISBN: 178028845X

Category: Body, Mind & Spirit

Page: 240

View: 7124

Encompassing nature, science, art, architecture, and spirituality, and illustrated with over 700 photographs and line drawings, The Hidden Geometry of Life illuminates the secret underpinnings of existence. In her trademark easy-to-understand style, mathematician Karen French shows how sacred geometry permeates every level of being, manifesting itself in simple shapes and numbers, music and sounds, light and color, even in the mysteries of creation itself. But these geometrical archetypes are more than the building blocks of reality: they are gateways to profound new levels of awareness.
Posted in Body, Mind & Spirit

Sacred Geometry

Deciphering the Code

Author: Stephen Skinner

Publisher: Sterling Publishing Company, Inc.

ISBN: 9781402765827

Category: Mathematics

Page: 160

View: 8128

A fascinating and inspirational look at the vital link between the hidden geometrical order of the universe, geometry in nature, and the geometry of the man-made world. The Da Vinci Code has awakened the public to the powerful and very ancient idea that religious truths and mathematical principles are intimately intertwined. Sacred Geometry offers an accessible way of understanding how that connection is revealed in nature and the arts. Over the centuries, temple builders have relied on magic numbers to shape sacred spaces, astronomers have used geometry to calculate holy seasons, and philosophers have observed the harmony of the universe in the numerical properties of music. By showing how the discoveries of mathematics are manifested over and over again in biology and physics, and how they have inspired the greatest works of art, this illuminating study reveals the universal principles that link us to the infinite.
Posted in Mathematics

Fractal Geometry in Biological Systems

An Analytical Approach

Author: Philip M. Iannaccone,Mustafa Khokha

Publisher: CRC Press

ISBN: 9780849376368

Category: Science

Page: 384

View: 4627

Fractal Geometry in Biological Systems was written by the leading experts in the field of mathematics and the biological sciences together. It is intended to inform researchers in the bringing about the fundamental nature of fractals and their widespread appearance in biological systems. The chapters explain how the presence of fractal geometry can be used in an analytical way to predict outcomes in systems, to generate hypotheses, and to help design experiments. The authors make the mathematics accessible to a wide audience and do not assume prior experience in this area.
Posted in Science

Introduction to Landscape Design

Author: John L. Motloch

Publisher: John Wiley & Sons

ISBN: 9780471352914

Category: Architecture

Page: 369

View: 4405

Outstanding explorations of design concepts, principles, and processes This Second Edition of Introduction to Landscape Design offers even broader coverage of the environmental, human, technological, and aesthetic issues associated with landscape design than the first edition. Beginning with the way we perceive, manage, and design the landscape, it moves on to explore the forces that influence land design. An overview of landscape management, planning, and design includes a discussion of the roles and integration of the professions involved, modes of professional practice, and site scale design processes. The book explores the ecology of design and the integration of land design decisions into dynamic systems. This fully updated new edition: * Presents landscape design as a synergism of art and science * Addresses the interplay between buildings and sites * Provides insights into the breadth of people-environment relationships * Places special emphasis on our growing understanding of interrelationships between the landscape and human decisions A superb introduction for students as well as a useful reference for practicing professionals, this book is an excellent guide for anyone who wants to develop a better understanding of landscape design.
Posted in Architecture

Sacred Geometry of Nature

Journey on the Path of the Divine

Author: Francene Hart

Publisher: Simon and Schuster

ISBN: 159143274X

Category: Body, Mind & Spirit

Page: 224

View: 3490

A fully illustrated inspirational art book from visionary painter Francene Hart • Includes more than 80 full-color reproductions of Hart’s intricate watercolor paintings and the stories behind them • Recounts the evolution of her art and her discovery of the hidden order of Nature that led to her masterful artistic integrations of Nature, Spirit, and Sacred Geometry • Explores how to tap into the energies provided by spirit guides and power animals, like Jaguar, Raven, Octopus, and Dolphin, and harness the intelligence of the heart for creative inspiration and vision Every one of us possesses the potential to receive visionary experiences and integrate them into our lives. Artists become visionaries by cultivating their instinctive creative spark and sharing their profound visions with the world. In this lavishly illustrated memoir, including more than 80 full-color reproductions of her intricate watercolor paintings and the stories behind them, Francene Hart recounts the evolution of her art from formative influences to her masterful integrations of Nature, Spirit, and Sacred Geometry. Opening with her early work on mandalas and her explorations of the work of Joseph Campbell and C. G. Jung, Hart explains how her first works of art were in response to the solitary life she led in the forest, where she discovered the hidden order of Nature. She reveals how she learned to center her artistic explorations on the intelligence of the heart rather than the intellect, utilizing the wisdom and imagery of Sacred Geometry, reverence for the natural environment, and the interconnectedness between all things as her inspirations. She describes the shamanic lessons that accompanied her discoveries and shaped her understanding of sacred relationships with the self, others, and Mother Earth. She explores how to tap into the energies provided by spirit guides and power animals, like Jaguar, Raven, Octopus, and Dolphin, and explains her profound affinity for the ocean, including her discovery of water consciousness in Hawaii. Offering chronicles of her inspiring travels and transformational encounters around the world, Hart shares her experiences at sacred sites in the Amazon, Central America, Egypt, England, Scotland, Paris, Cambodia, and the Himalayas and how these places influenced her art. Exploring what is revealed as inspiration arises, Spirit informs, and vision is transformed into art, Francene Hart’s journey offers a window into the secret order of Nature, the power of sacred symbols for evolving consciousness, and a visionary artistic path that perfectly blends the mathematical rigors of sacred geometry and the numinous.
Posted in Body, Mind & Spirit

Exploring the Geometry of Nature

Computer Modeling of Chaos, Fractals, Cellular Automata, and Neural Networks

Author: Ed Rietman

Publisher: N.A

ISBN: N.A

Category: Computers

Page: 197

View: 4103

The science of chaos attracts the attention of researchers in many disciplines. The idea: by following simple principles of randomness and disorder, patterns emerge. Here, users on their own PC's can construct mathematical models duplicating processes found in nature.
Posted in Computers

The Hidden Geometry of Life

The Science and Spirituality of Nature

Author: Karen L. French

Publisher: Watkins Pub Limited

ISBN: 9781780281087

Category: Mathematics

Page: 240

View: 7900

Encompassing nature, science, art, architecture, and spirituality, and illustrated with over 700 photographs and line drawings, The Hidden Geometry of Life illuminates the secret underpinnings of existence. In her trademark easy-to-understand style, mathematician Karen French shows how sacred geometry permeates every level of being, manifesting itself in simple shapes and numbers, music and sounds, light and color, even in the mysteries of creation itself. But these geometrical archetypes are more than the building blocks of reality: they are gateways to profound new levels of awareness.
Posted in Mathematics

Geometrie und ihre Anwendungen in Kunst, Natur und Technik

Author: Georg Glaeser

Publisher: Springer-Verlag

ISBN: 364241852X

Category: Mathematics

Page: 508

View: 6720

Die „Geometrie und ihre Anwendungen“ ist für Personen geschrieben, die von relativ einfachen Problemen der ebenen Geometrie bis hin zu schwierigeren Aufgaben der Raumgeometrie Interesse an geometrischen Zusammenhängen haben. Ähnlich wie beim „mathematischen Werkzeugkasten“ stehen Anwendungen aus verschiedenen Disziplinen wie dem Ingenieurwesen, der Biologie, Physik, Astronomie, Geografie, Fotografie, Kunstgeschichte, ja sogar der Musik im Vordergrund. Die Anwendungsbeispiele veranschaulichen wichtige Begriffe der Geometrie wie Normalprojektion und Zentralprojektion, Krümmung von Kurven und Flächen, der Geometrie der Bewegung und sogar der Geometrie nichteuklidischer Räume. Stets hat die Raumvorstellung Vorrang. Das Buch kann daher auch von Personen ohne spezielle mathematische Vorbildung gelesen werden. Die 3. Auflage ist um gut 60 Seiten erweitert und enthält zahlreiche neue Anwendungen mit hochwertigen Grafiken.
Posted in Mathematics

Differential Geometry and Its Applications

Author: John Oprea

Publisher: MAA

ISBN: 9780883857489

Category: Mathematics

Page: 469

View: 4524

Differential geometry has a long, wonderful history it has found relevance in areas ranging from machinery design of the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole, it mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors, it is also for students in engineering and the sciences. Into the mix of these ideas comes the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Students will not only “see” geodesics on surfaces, but they will also see the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. Students will also see how particles move under constraints. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.
Posted in Mathematics

Geometry and Nature

In Memory of W.K. Clifford : a Conference on New Trends in Geometrical and Topological Methods in Memory of William Kingdon Clifford, July 30-August 5, 1995, Madeira, Portugal

Author: William Kingdon Clifford,Hanna Nencka,Jean-Pierre Bourguignon

Publisher: American Mathematical Soc.

ISBN: 0821806076

Category: Science

Page: 296

View: 5648

This volume is the outgrowth of a conference devoted to William K. Clifford entitled, 'New Trends in Geometrical and Topological Methods', which was held at the University of Madeira in July and August 1995. The aim of the conference was to bring together active workers in fields linked to Clifford's work and to foster the exchange of ideas between mathematicians and theoretical physicists. Divided into 6 one-day sessions, each session was devoted to a specific aspect of Clifford's work. This volume is an attempt to bring the Clifford legacy in a new perspective to a larger community of mathematicians and physicists. New concepts, ideas, and results stemming from Clifford's work are discussed. Each article in the book is a self-contained paper that was presented at or submitted to the conference.
Posted in Science

American Dreamer

Bucky Fuller and the Sacred Geometry of Nature

Author: Scott Eastham

Publisher: The Lutterworth Press

ISBN: 0718844688

Category: Biography & Autobiography

Page: 200

View: 8399

Synergetics can be defined as the exploratory strategy of starting with the whole. It was in the 1940s that Buckminster Fuller developed a series of spherical models which embodied the synergetic theory within geometry. This study of Fuller's sacred geometry describes with vigour and in detail how his spherical figures relate both to Nature and to the tenets of synergetics. CRCR The author assesses the legacy of Fuller, a scientist-artist-engineer extraordinaire whose visions were inspired by the American Dream, and portrays with enthusiasm and sympathy the creative and individual science of a man whose character was as multifaceted as the domes he created. Discover the theory behind the idea that the straight lines and boxes of science and maths are inadequate for representing Nature's spherical and cyclical patterns of growth. The ways in which Fuller's synergetics can be seen in the ancient iconographies of the past are also revealed with fresh insight. In addition, Eastham looks to the future artistic applications of Fuller's 'wholes', with the aim of inspiring the reader to think outside of the box themselves. "We sought for years to bring out a brief alternative geometry textbook. [...] It's not easy to produce a round thing in a square world... " Extract from the Introduction
Posted in Biography & Autobiography

Design and nature II

comparing design in nature with science and engineering

Author: C. A. Brebbia,M. W. Collins

Publisher: Wit Pr/Computational Mechanics

ISBN: 9781853127212

Category: Nature

Page: 624

View: 9700

Containing the proceedings of the Second International Conference on Design and Nature, this book brings together contributions from researchers working around the world on a variety of studies involving nature and its significance for modern scientific thought and design. The papers featured span a broad range of topics including: Architectural Design and Structures: Acoustics; Biology; Biomimetics; Design Philosophy and Methods; Human Biology and Medicine; Materials; Nature and Architectural Design; Space.
Posted in Nature

Complexity Science, Living Systems, and Reflexing Interfaces: New Models and Perspectives

New Models and Perspectives

Author: Orsucci, Franco

Publisher: IGI Global

ISBN: 1466620781

Category: Computers

Page: 466

View: 4285

There are new and important advancements in today’s complexity theories in ICT and requires an extraordinary perspective on the interaction between living systems and information technologies. With human evolution and its continuous link with the development of new tools and environmental changes, technological advancements are paving the way for new evolutionary steps. Complexity Science, Living Systems, and Reflexing Interfaces: New Models and Perspectives is a collection of research provided by academics and scholars aiming to introduce important advancements in areas such as artificial intelligence, evolutionary computation, neural networks, and much more. This scholarly piece will provide contributions that will define the line of development in complexity science.
Posted in Computers