“Without mathematics there is no art,” said Luca Pacioli, a contemporary of Da Vinci.
Just as the Golden Section is found in the design and beauty of nature, it can also be used to achieve beauty and balance in the design of art. This is only a tool though, and not a rule, for composition, but still a good Art 101 lesson on laying out a painting on a canvas.
The Golden Section was used extensively by Leonardo Da Vinci. All the key dimensions of the room, the table and ornamental shields in Da Vinci’s The Last Supper were based on the Golden Ratio, which was known in the Renaissance period as The Divine Proportion. -from GoldenNumber.net
An iinteresting article on the Golden Ratio in art.
Geometry & Art
by David Wade – Hardcover: 224 pages; Shelter Harbor Press (Mar 7, 2018)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 Paulo Uccello, Piero della Francesco and Leonardo Da Vinci, this breakthrough quickly spread to Germany, where a passion for polyhedral-based geometrical designs flourished as a district new art in the mid-16th century.
The Golden Ratio: The Divine Beauty of Mathematics
by Gary B. Meisner, Rafael Araujo (Artist) – Hardcover: 224 pages; Race Point Publishing (Oct 23, 2018) Best SellerThe Golden Ratio
examines the presence of this divine number in art and architecture throughout history, as well as its ubiquity among plants, animals, and even the cosmos. This gorgeous book—with layflat dimensions that closely approximate the golden ratio—features clear, enlightening, and entertaining commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo.
Pulling Your Paintings Together
by Charles Reid – Paperback: 162 pages; Echo Point Books & Media; Reprint edition (Feb 19, 2016)Pulling Your Paintings Together
is a book about making connections: interweaving lines, shapes, and colors; moving backgrounds into foregrounds, positive shapes into negative ones, lost edges into found boundaries-all with the intention to create a painting or drawing that is a harmonious unit, with all elements subordinated to the effect of the whole.
The Painter's Secret Geometry: A Study of Composition in Art
by Charles Bouleau – Paperback: 272 pages; Dover Publications (Aug 20, 2014)
This richly illustrated examination of visual arts in the European tradition shows how the great masters employed the "golden mean" and other geometrical patterns to compose their paintings. Author Charles Bouleau explores a tremendous variety of ancient and modern works: the Parthenon friezes, Italian mosaics, the Bayeux Tapestry, and Gothic stonemasons' marks of France and Germany as well as paintings by Picasso, Kandinsky, Klee, and Pollock. His insightful expositions cast new light on such well-known works as Raphael's "The School of Athens," Botticelli's "Birth of Venus," Rubens' "Descent from the Cross," and Renoir's "Le Moulin de la Galette."
Art and Geometry: A Study in Space Intuitions
by William M. Ivins – Paperback: 128 pages; Dover Publications (Nov 2, 2011)
One of Western civilization's jealously guarded myths is that of Greek cultural supremacy. In this controversial study, William Ivins shows that the limitations of the Greek worldview actually hampered the development of the arts and sciences and gives a stimulating history of the new ideas of the Renaissance, especially in painting and geometry, that freed us from ancient misconceptions.
by Henry Rankin Poore – Paperback: 104 pages; Dover Publications; Reproduction of 1967 edition (Jun 1, 1976)
A painting's technique, color, and perspective may all be excellent, yet the painting will fail unless its composition succeeds. Composition is the harmonious arranging of the component parts of a work of art into a unified whole. Henry Poore examines the works of old masters and moderns in this book and uses these examples to explain the principles of compositions in art.
A Painter's Guide to Design and Composition
by Margot Schulzke – Hardcover: 144 pages; North Light Books; 1st edition (Feb 7, 2006)
Design makes the difference between a decent painting and an unforgettable work of art. Learn from 26 modern masters as they bare their souls and their secrets for crafting magnificent works that delight the eye at every viewing. Daniel Greene, Albert Handell, Jan Kunz, James Toogood and 22 other award-winning artists share notable insights and practical advice for making a painting succeed no matter what the subject.
Vermeer's Camera: Uncovering the Truth behind the Masterpieces
by Philip Steadman – Paperback: 224 pages; Oxford Paperbacks; 1st edition (Sep 19, 2002) Best Seller
Art historians have long speculated on how Vermeer achieved the uncanny mixture of detached precision, compositional repose, and perspective accuracy that have drawn many to describe his work as "photographic." Indeed, many wonder if Vermeer employed a camera obscura, a primitive form of camera, to enhance his realistic effects?
In Vermeer's Camera
, Philip Steadman traces the development of the camera obscura--first described by Leonaro da Vinci--weighs the arguments that scholars have made for and against Vermeer's use of the camera, and offers a fascinating examination of the paintings themselves and what they alone can tell us of Vermeer's technique.
Eye of the Beholder
by Laura J. Snyder – Paperback: 448 pages; W. W. Norton & Company; 1st edition (May 17, 2016) Best Seller
...the painter Johannes Vermeer was using another optical device, a camera obscura, to experiment with light and create the most luminous pictures ever beheld.
In Eye of the Beholder
, Laura J. Snyder transports us to the streets, inns, and guildhalls of seventeenth-century Holland, where artists and scientists gathered, and to their studios and laboratories, where they mixed paints and prepared canvases, ground and polished lenses, examined and dissected insects and other animals, and invented the modern notion of seeing. With charm and narrative flair Snyder brings Vermeer and Van Leeuwenhoek―and the men and women around them―vividly to life. The story of these two geniuses and the transformation they engendered shows us why we see the world―and our place within it―as we do today.
Eye of the Beholder
was named "A Best Art Book of the Year" by Christie's and "A Best Read of the Year" by New Scientist in 2015. 16 pages of color illustrations
Geometry and the Visual Arts
by Dan Pedoe – Paperback: 320 pages; Dover Publications (Mar 17, 2011)
This survey traces the effects of geometry on artistic achievement and clearly discusses its importance to artists, scientists, architects, philosophers, and others. In addition to profiles of Vitruvius, Albrecht Durer, and Leonardo da Vinci, it includes a survey of projective geometry, mathematical curves, theories of perspective, architectural form, and concepts of space.
The Geometry of Art and Life
by Matila Ghyka – Paperback: 174 pages; Dover Publications; 2nd edition (Jun 1, 1977)
Is everything chaos and chance, or is there order, harmony, and proportion in human life, nature, and the finest art? Can one find a natural aesthetic that corresponds to a universal order? If so, what importance can it have for the scientist, artist, or layman? What is the "true" significance of the triangle, rectangle, spiral, and other geometric shapes? These are but a few of the questions that Professor Matila Ghyka deals with in this fascinating book.
Composition: Understanding Line, Notan and Color
by Arthur Wesley Dow – Paperback: 144 pages; Dover Publications (Aug 31, 2007)
At the turn of the twentieth century, Arthur Wesley Dow literally "wrote the book" on composition—and this is it! Dow's Composition exercised an enormous influence on emerging modern artists of a century ago. A thought-provoking examination of the nature of visual representation, it remains ever-relevant to all the visual arts.
A well-known painter and printmaker, Dow taught for many years at Columbia University and acted as a mentor to countless young artists, including Georgia O'Keeffe. His text, presented in a workbook format, offers teachers and students a systematic approach to composition. It explores the creation of freely constructed images based on harmonic relations between lines, colors, and dark and light patterns.