The Geometry of Art and Life

Author: Matila Costiescu Ghyka

Publisher: Courier Corporation

ISBN: 9780486235424

Category: Mathematics

Page: 174

View: 6380

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: 3525

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 Painter's Secret Geometry

A Study of Composition in Art

Author: Charles Bouleau

Publisher: Courier Corporation

ISBN: 0486795500

Category: Art

Page: 272

View: 6386

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.

Geometry and the Visual Arts

Author: Daniel Pedoe

Publisher: Courier Corporation

ISBN: 9780486244587

Category: Mathematics

Page: 296

View: 4525

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: 3748

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 Geometric Bridge Between Art and Science

Author: Jay Kappraff

Publisher: World Scientific

ISBN: 9789812811394

Category: Science

Page: 486

View: 2857

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: 2767

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.

Geometry of Design

Studies in Proportion and Composition

Author: Kimberly Elam

Publisher: Princeton Architectural Press

ISBN: 9781568982496

Category: Design

Page: 107

View: 4750

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 Divine Proportion

A Study in Mathematical Beauty

Author: H. E. Huntley

Publisher: Courier Corporation

ISBN: 0486222543

Category: Mathematics

Page: 186

View: 5020

Explores the aesthetic, emotional, artistic and philosophical significance of geometric figures, scientific patterns and mathematical formulas

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: 7183

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.


Mathematical Perspective and Fractal Geometry in Art

Author: Marc Frantz,Annalisa Crannell

Publisher: Princeton University Press

ISBN: 9781400839056

Category: Mathematics

Page: 248

View: 305

An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students. Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery. Classroom-tested activities and problem solving Accessible problems that move beyond regular art school curriculum Multiple solutions of varying difficulty and applicability Appropriate for students of all mathematics and art levels Original and exclusive essays by contemporary artists Forthcoming: Instructor's manual (available only to teachers)

Mathematics and Art

A Cultural History

Author: Lynn Gamwell

Publisher: Princeton University Press

ISBN: 0691165289

Category: Art

Page: 576

View: 6359

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.

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: 6530

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


Science, Philosophy, Architecture

Author: Richard Padovan

Publisher: Taylor & Francis

ISBN: 1135811113

Category: Architecture

Page: 400

View: 9998

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.

Patterns in Nature

Why the Natural World Looks the Way It Does

Author: Philip Ball

Publisher: University of Chicago Press

ISBN: 022633256X

Category: Nature

Page: 288

View: 3798

Though at first glance the natural world may appear overwhelming in its diversity and complexity, there are regularities running through it, from the hexagons of a honeycomb to the spirals of a seashell and the branching veins of a leaf. Revealing the order at the foundation of the seemingly chaotic natural world, Patterns in Nature explores not only the math and science but also the beauty and artistry behind nature’s awe-inspiring designs. Unlike the patterns we create in technology, architecture, and art, natural patterns are formed spontaneously from the forces that act in the physical world. Very often the same types of pattern and form – spirals, stripes, branches, and fractals, say—recur in places that seem to have nothing in common, as when the markings of a zebra mimic the ripples in windblown sand. That’s because, as Patterns in Nature shows, at the most basic level these patterns can often be described using the same mathematical and physical principles: there is a surprising underlying unity in the kaleidoscope of the natural world. Richly illustrated with 250 color photographs and anchored by accessible and insightful chapters by esteemed science writer Philip Ball, Patterns in Nature reveals the organization at work in vast and ancient forests, powerful rivers, massing clouds, and coastlines carved out by the sea. By exploring similarities such as those between a snail shell and the swirling stars of a galaxy, or the branches of a tree and those of a river network, this spectacular visual tour conveys the wonder, beauty, and richness of natural pattern formation.

Beautiful Geometry

Author: Eli Maor,Eugen Jost

Publisher: Princeton University Press

ISBN: 1400848334

Category: Mathematics

Page: 208

View: 3349

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.

Geometry & Art

How Mathematics Transformed Art During the Renaissance

Author: David Wade

Publisher: N.A

ISBN: 9781627951050

Category: Art

Page: N.A

View: 370

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 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: 9902

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.

The Geometry of Love

A Novel

Author: Jessica Levine

Publisher: She Writes Press

ISBN: 1938314638

Category: Fiction

Page: 292

View: 9490

Julia, an aspiring poet, is living with her British boyfriend, Ben, a restrained Princeton professor, when she runs into Michael, a long-lost friend. A complex and compelling composer, Michael was once a catalyzing muse for her—but his return to her life is a destabilizing influence. Julia is drawn to Michael, but feels enormous guilt at the thought of betraying Ben—not to mention fear at the idea of giving up the security of her relationship with him. So, when Michael signals that he’s too wounded to make a commitment, she turns her triangular situation into a square: she sets him up with her cousin. Why is it easier for a woman to be a muse than to have one? Are security and imagination mutually exclusive? Can one be fully creative—in art or life—without the inspiration of erotic love? These are the questions asked in The Geometry of Love, a provocative and deeply psychological tale that explores the surprising choices we make in our romantic lives.

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: 9064

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.