The Geometry of an Art

The Geometry of an Art
Author: Kirsti Andersen
Publisher: Springer Science & Business Media
Total Pages: 837
Release: 2008-11-23
Genre: Mathematics
ISBN: 0387489460

This review of literature on perspective constructions from the Renaissance through the 18th century covers 175 authors, emphasizing Peiro della Francesca, Guidobaldo del Monte, Simon Stevin, Brook Taylor, and Johann Heinrich. It treats such topics as the various methods of constructing perspective, the development of theories underlying the constructions, and the communication between mathematicians and artisans in these developments.

The Geometry of Art and Life

The Geometry of Art and Life
Author: Matila Costiescu Ghyka
Publisher: Courier Corporation
Total Pages: 212
Release: 1977-01-01
Genre: Mathematics
ISBN: 9780486235424

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.

Art and Geometry

Art and Geometry
Author: William M. Ivins
Publisher: Courier Corporation
Total Pages: 130
Release: 2012-10-16
Genre: Art
ISBN: 0486143589

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.

Viewpoints

Viewpoints
Author: Marc Frantz
Publisher: Princeton University Press
Total Pages: 259
Release: 2011-07-05
Genre: Mathematics
ISBN: 140083905X

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)

Geometry of Design

Geometry of Design
Author: Kimberly Elam
Publisher: Princeton Architectural Press
Total Pages: 130
Release: 2001
Genre: Architecture
ISBN: 9781568982496

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.

Sacred Geometry for Artists, Dreamers, and Philosophers

Sacred Geometry for Artists, Dreamers, and Philosophers
Author: John Oscar Lieben
Publisher: Simon and Schuster
Total Pages: 538
Release: 2018-08-28
Genre: Body, Mind & Spirit
ISBN: 1620557029

An illustrated guide to harmonics--the sacred geometry principles that underlie the natural world--and its practical applications • Demonstrates how the vesica piscis is a matrix from which ideas and forms emanate, connecting cosmic time cycles, measures of space, and musical tones • Provides harmonic analyses of ancient sculpture, architecture, the solar system, the Earth-Moon relationship, and the structure of water and waves • Explains how to apply sacred geometry to create building floor plans, pottery figures, gardens, and sacred ceremonial spaces We are in the midst of a revival of an ancient way of looking at the world--an approach that enabled great civilizations of the past to bring forth inventions of great beauty and power. This school of thought--harmonics--envisioned the natural world and the solar system as an interlocking matrix of harmonious numbers, perfectly woven into the creative fabric of life and the surrounding universe. Exploring the art and science of harmonics, John Oscar Lieben shows how to create harmonious forms using the ancient tools of number, geometry, and musical tone--an approach that resonates with nature’s own ways of creation. He demonstrates many practical applications that result from the study of harmonics, providing analyses of ancient sculpture and architecture, as well as original examples of building floor plans, pottery figures based on planetary proportions, gardens based on harmonic principles, and ceremonial spaces that honor cosmic harmonies and sacred geometric relationships. Showing how harmonics can also be applied to the mysteries of time and space, the author demonstrates how the vesica piscis and many other variations of the vesica shape reveal numerical synchronicities and correspondences that connect cosmic time cycles, measures of space, and musical tones. The author applies harmonics and the “vesica construction” matrix to illustrate many of nature’s wonders, including the Earth-Moon relationship, the interactions of the Golden Number and the musical scale, and how the Flower of Life symbol connects the universal field with the pattern of raindrops falling on a pond. Offering an approach to sacred geometry that pairs the mystical with the practical, the cosmic with the earthly, the author reveals how the art and science of harmonics should be required study for both the artist and the seeker of eternal truths as well as the scientist who seeks an entrance into the sacred foundations of nature.

Geometry and its Applications in Arts, Nature and Technology

Geometry and its Applications in Arts, Nature and Technology
Author: Georg Glaeser
Publisher: Springer Nature
Total Pages: 694
Release: 2020-12-18
Genre: Mathematics
ISBN: 3030613984

This book returns geometry to its natural habitats: the arts, nature and technology. Throughout the book, geometry comes alive as a tool to unlock the understanding of our world. Assuming only familiarity with high school mathematics, the book invites the reader to discover geometry through examples from biology, astronomy, architecture, design, photography, drawing, engineering and more. Lavishly illustrated with over 1200 figures, all of the geometric results are carefully derived from scratch, with topics from differential, projective and non-Euclidean geometry, as well as kinematics, introduced as the need arises. The mathematical results contained in the book range from very basic facts to recent results, and mathematical proofs are included although not necessary for comprehension. With its wide range of geometric applications, this self-contained volume demonstrates the ubiquity of geometry in our world, and may serve as a source of inspiration for architects, artists, designers, engineers, and natural scientists. This new edition has been completely revised and updated, with new topics and many new illustrations.

The Polyhedrists

The Polyhedrists
Author: Noam Andrews
Publisher: National Geographic Books
Total Pages: 0
Release: 2022-05-03
Genre: Art
ISBN: 0262046644

A history of the relationship between art and geometry in the early modern period. In The Polyhedrists, Noam Andrews unfolds a history of the relationship between art and geometry in early modern Europe, told largely through a collective of ground-breaking artisan-artists (among them, Luca Pacioli, Albrecht Dürer, Wenzel Jamnitzer, and Lorentz Stöer) and by detailed analysis of a rich visual panoply of their work, featuring paintings, prints, decorative arts, cabinetry, and lavishly illustrated treatises. But this is also an art history of the polyhedra themselves, emblems of an evolving artistic intelligence, which include a varied set of geometrical figures—both Platonic, or regular, like the simple tetrahedron, and Archimedean, or irregular, like the complex yet beguiling rhombicosidodecahedron. Moreover, The Polyhedrists argues that the geometrical depictions of Dürer, Jamnitzer et al. were far more than mere follies from the dawn of perspective, at odds with a contemporary view of the Renaissance, and destined to be superseded by later developments in higher level mathematics. In fact, the evolution of the solids into innumerable “irregular bodies” constituted a sustained moment in the formulation of Renaissance mathematical knowledge and its engagement with materiality. This intense field of experimentation would birth a new language of geometrical abstraction that would ignite a century of novel form-making strategies, ultimately paving the way for developments in geometry and topology in the nineteenth and early twentieth centuries, and even prefiguring the more recent digital turn. The book, in this sense, is not just an applied history of geometry, nor a particular geometric reading of early modern art through some of its more celebrated practitioners, but a manifesto of sorts into the hitherto unexplored wilds of art and science.