The Geometry of Art and Life

Author: Matila Costiescu Ghyka

Publisher: Courier Corporation

ISBN: 9780486235424

Category: Mathematics

Page: 174

View: 1001

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This classic study probes the geometric interrelationships between art and life in discussions ranging from dissertations by Plato, Pythagoras, and Archimedes to examples of modern architecture and art. Other topics include the Golden Section, geometrical shapes on the plane, geometrical shapes in space, crystal lattices, and other fascinating subjects. 80 plates and 64 figures.

The Geometry of Art and Life

Author: Matila Costiescu Ghyka

Publisher: Courier Corporation

ISBN: 9780486235424

Category: Art

Page: 174

View: 9630

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This classic study probes the geometric interrelationships between art and life in discussions ranging from dissertations by Plato, Pythagoras, and Archimedes to examples of modern architecture and art. Other topics include the Golden Section, geometrical shapes on the plane, geometrical shapes in space, crystal lattices, and other fascinating subjects. 80 plates and 64 figures.

Geometry and the Visual Arts

Author: Daniel Pedoe

Publisher: Courier Corporation

ISBN: 9780486244587

Category: Mathematics

Page: 296

View: 3280

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This survey traces the effects of geometry on artistic achievement and clearly discusses its importance to artists and scientists. It also surveys projective geometry, mathematical curves, theories of perspective, architectural form, and concepts of space.

Art and Geometry

A Study in Space Intuitions

Author: William M. Ivins

Publisher: Courier Corporation

ISBN: 0486143589

Category: Art

Page: 128

View: 748

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This highly stimulating study observes many historical interrelationships between art and mathematics. It explores ancient and Renaissance painting and sculpture, the development of perspective, and advances in projective geometry.

The Painter's Secret Geometry

A Study of Composition in Art

Author: Charles Bouleau

Publisher: Courier Corporation

ISBN: 0486795500

Category: Art

Page: 272

View: 4786

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Richly illustrated examination of Western visual arts shows how great masters and modern painters employed the "golden mean" and other geometrical patterns. Cult classic and essential guide for art history students.

Connections

The Geometric Bridge Between Art and Science

Author: Jay Kappraff

Publisher: World Scientific

ISBN: 9789812811394

Category: Science

Page: 486

View: 2550

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The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in OC Mathematics, Chemistry, and Astronomy OCo Professional and ReferenceOCO in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition. Contents: Proportion in Architecture; Similarity; The Golden Mean; Graphs; Tilings with Polygons; Two-Dimensional Networks and Lattices; Polyhedra: Platonic Solids; Transformation of the Platonic Solids I; Transformation of the Platonic Solids II; Polyhedra: Space Filling; Isometries and Mirrors; Symmetry of the Plane. Readership: Polytechnic students, architects, designers, mathematicians and general readers."

The Golden Number

Pythagorean Rites and Rhythms in the Development of Western Civilization

Author: Matila C. Ghyka

Publisher: Inner Traditions

ISBN: 9781594771002

Category: Body, Mind & Spirit

Page: 448

View: 8301

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The first English translation of Ghyka’s masterwork on sacred geometry • Reveals how the Golden Number Phi underlies the spiritual nature of beauty and the hidden harmonies that connect the whole of creation • Explains how the spiritual mysteries of the Golden Number were passed down in an unbroken line of transmission from the Pythagorean brotherhoods through the medieval builders’ guilds to the secret societies of 18th-century Europe The Golden Number, or Phi (Φ), is a geometric ratio found throughout nature, often underlying the dimensions of objects considered especially beautiful. Simplified as 1.618 and symbolized by the Fibonacci sequence, the Golden Number represents the unique relationship within an object where the ratio of a larger part to a smaller part is the same as the ratio of the whole to the larger part. It appears in the proportions of the human face and body as well as in the proportions of animals, plants, and celestial bodies. Called the divine proportion by the monk Fra Luca Pacioli, whose book on the subject was illustrated by Leonardo da Vinci, Phi’s use in art and architecture goes back at least to the mystical mathematics of Pythagoras and his followers in the sixth century BCE. The perfect synthesis of spiritual and material, it can be found in the measurements of the sacred temples of Egypt, Ancient Greece, and Medieval and Renaissance Europe. The asymptotic series of integers that define Phi represent the macrocosm and microcosm as portrayed in Plato’s concept of the world soul. Presenting Matila Ghyka’s classic treatise on the Golden Number for the first time in English, this book reveals the many ways this ratio can be found not only in the organic forms of nature--such as in the spirals of shells or the number of petals on a flower--but also in the most beautiful and highest creations of humanity. One of the most important concepts of sacred geometry, its mysteries were passed down in an unbroken line of transmission from the Pythagorean brotherhoods through the medieval builders’ guilds to the secret societies of 18th-century Europe. Ghyka shows how the secrets of this divine proportion were not sought merely for their value in architecture, painting, and music, but also as a portal to a deeper understanding of the spiritual nature of beauty and the hidden harmonies that connect the whole of creation.

The Hidden Geometry of Life

The Science and Spirituality of Nature

Author: Karen L. French

Publisher: Watkins Media Limited

ISBN: 178028845X

Category: Body, Mind & Spirit

Page: 240

View: 998

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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.

The Divine Proportion

Author: H. E. Huntley

Publisher: Courier Corporation

ISBN: 0486131874

Category: Mathematics

Page: 208

View: 8054

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Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much more. Excellent bridge between science and art. Features 58 figures.

The Curves of Life

Being an Account of Spiral Formations and Their Application to Growth in Nature, to Science, and to Art : with Special Reference to the Manuscripts of Leonardo Da Vinci

Author: Sir Theodore Andrea Cook,Theodore Andrea Cook

Publisher: Courier Corporation

ISBN: 9780486237015

Category: Mathematics

Page: 479

View: 6750

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The significance of the spiral in nature, art, science, and the phenomena of life and growth is probed

Beautiful Geometry

Author: Eli Maor,Eugen Jost

Publisher: Princeton University Press

ISBN: 1400848334

Category: Mathematics

Page: 208

View: 3018

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If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.

The Geometry of Wealth

How to shape a life of money and meaning

Author: Brian Portnoy

Publisher: Harriman House Limited

ISBN: 0857196723

Category: Business & Economics

Page: 232

View: 6460

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How does money figure into a happy life? In The Geometry of Wealth, behavioral finance expert Brian Portnoy delivers an inspired answer, building on the critical distinction between being rich and being wealthy. While one is an unsatisfying treadmill, the other is the ability to underwrite a meaningful life, however one chooses to define that. Truly viewed, wealth is funded contentment. At the heart of this groundbreaking perspective, Portnoy takes readers on a journey toward wealth, informed by disciplines ranging from ancient history to modern neuroscience. He contends that tackling the big questions about a joyful life and tending to financial decisions are complementary, not separate, tasks. These big questions include: • How is the human brain wired for two distinct experiences of happiness? And why can money “buy” one but not the other? • What are the touchstones of a meaningful life, and are they affordable? • Why is market savvy among the least important sources of wealth but self-awareness is among the most? • How does one strike a balance between striving for more while being content with enough? This journey memorably contours along three basic shapes: A circle, triangle and square help us to visualize how we adapt to evolving circumstances, set clear priorities, and find empowerment in simplicity. In this accessible and entertaining book, Portnoy reveals that true wealth is achievable for many - including those who despair it is out of reach - but only in the context of a life in which purpose and practice are thoughtfully calibrated.

Proportion

Science, Philosophy, Architecture

Author: Richard Padovan

Publisher: Taylor & Francis

ISBN: 1135811113

Category: Architecture

Page: 400

View: 1303

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This handbook provides readers with a well-illustrated and readable comparative guide to proportion systems in architecture, setting out the mathematical principles that underlie the main systems and illustrating these with examples of their use in historical and modern buildings. The main body of the text traces the interplay of abstraction and empathy through the history of science, philosophy and architecture from the early Greeks through to the two early twentieth-century architects who made proportion the focus of their work: Le Corbusier and Van der Laan. The book ends with a reflection on the present and future role of proportion in architecture.

Squaring the Circle

Geometry in Art and Architecture

Author: Paul Calter

Publisher: John Wiley & Sons

ISBN: N.A

Category: Mathematics

Page: 554

View: 7696

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Geometry is a dynamic branch of mathematics that also serves as a creative tool for engineers, artists, and architects. Squaring the Circle: Geometry in Art and Architecture includes all the topics necessary for a solid foundation in geometry and explores the timeless influence of geometry on art and architecture. The text offers wide-ranging exercise sets and related projects that allow students to practice and master the mathematics presented. Each chapter introduces mathematical concepts geometrically and illustrates their nontraditional applications in art and architecture throughout the centuries. Appropriate for both basic mathematics courses and cross-discipline courses in mathematics and art, Squaring the Circle requires no previous mathematics.

Mathematics and Art

A Cultural History

Author: Lynn Gamwell

Publisher: Princeton University Press

ISBN: 0691165289

Category: Art

Page: 576

View: 9095

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This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell’s comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians’ search for the foundations of their science, such as David Hilbert’s conception of mathematics as an arrangement of meaning-free signs, as well as artists’ search for the essence of their craft, such as Aleksandr Rodchenko’s monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt Gödel posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked “What is art?” in the vocabulary of art. Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Benoît Mandelbrot to Max Bill and Xu Bing. Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.

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: 8998

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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.

Geometry of Design

Studies in Proportion and Composition

Author: Kimberly Elam

Publisher: Princeton Architectural Press

ISBN: 9781568982496

Category: Design

Page: 107

View: 5726

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This work takes a close look at a broad range of 20th-century examples of design, architecture and illustration, revealing underlying geometric structures in their compositions.

The Geometry of Creation

Architectural Drawing and the Dynamics of Gothic Design

Author: Robert Bork

Publisher: Routledge

ISBN: 1351888978

Category: History

Page: 488

View: 9344

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The flowering of Gothic architecture depended to a striking extent on the use of drawing as a tool of design. By drawing precise "blueprints" with simple tools such as the compass and straightedge, Gothic draftsmen were able to develop a linearized architecture of unprecedented complexity and sophistication. Examination of their surviving drawings can provide valuable and remarkably intimate information about the Gothic design process. Gothic drawings include compass pricks, uninked construction lines, and other telltale traces of the draftsman's geometrically based working method. The proportions of the drawings, moreover, are those actually intended by the designer, uncompromised by errors introduced in the construction process. All of these features make these drawings ideal subjects for the study of Gothic design practice, but their geometry has to date received little systematic attention. This book offers a new perspective on Gothic architectural creativity. It shows, in a series of rigorous geometrical case studies, how Gothic design evolved over time, in two senses: in the hours of the draftsman's labor, and across the centuries of the late Middle Ages. In each case study, a series of computer graphics show in unprecedented detail how a medieval designer could have developed his architectural concept step by step, using only basic geometrical operations. Taken together, these analyses demonstrate both remarkable methodological continuity across the Gothic era, and the progressive development of new and sophisticated permutations on venerable design themes. This rich tradition ultimately gave way in the Renaissance not because of any inherent problem with Gothic architecture, but because the visual language of Classicism appealed more directly to the pretensions of Humanist princes than the more abstract geometrical order of Gothic design, as the book's final chapter demonstrates.

Geometry & Art

How Mathematics Transformed Art During the Renaissance

Author: David Wade

Publisher: N.A

ISBN: 9781627951050

Category: Art

Page: N.A

View: 6418

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A fascinating and authoritative look at how geometry changed the world of art forever. Geometry & Art follows the artists of the Renaissance, whose search for perspective and visual depth led them to the study of geometry. Influencing the work of artists such as Paolo Uccello, Piero della Francesco, and Leonardo da Vinci, this incredible artistic breakthrough quickly spread to Germany, where a passion for polyhedral based geometrical designs flourished as a district new art in the mid-16th century. A period of enormous political and cultural change, the Renaissance empowered artists to draw upon a blossoming revival of classical art, philosophy, and culture. At the same time, a wealth of new ideas and concepts were flowing into Europe from the Islamic Middle East. And it was this flood of revolutionary new thought that would lead to the syntheses of mathematics, geometry, and art that characterises the painting, sculpture, and visual language of the Renaissance. This compelling volume uses engaging text, compelling historical accounts, and 250 beautiful illustrations to immerse readers in the fundamental Renaissance forms which, although conceived over five hundred years ago, still have the capacity to inspire us with their beauty.

Sacred Geometry

Deciphering the Code

Author: Stephen Skinner

Publisher: Sterling Publishing Company, Inc.

ISBN: 9781402765827

Category: Mathematics

Page: 160

View: 9752

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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.