Infinite Measure: Learning To Design In Geometric Harmony With Art, Architecture, And Nature
Infinite Measure is both a creative workbook and an authoritative reference guide for teachers, students, and practitioners of design, including architecture, interior design, landscape architecture, painting, sculpture, the graphic arts, theater and stage design, and even musical instruments and crafts. Taking pages from books of nature, art, and architecture, Fletcher provides visual designers of all art forms and disciplines with geometric methods for composing harmonious spaces and places.
Infinite Measure: Learning to Design in Geometric Harmony with Art, Architecture, and Nature
Fletcher shares her professional knowledge and experience by offering practical techniques for design applications, including step-by-step elementary and advanced drawings for producing proportional schemes with a compass and rule; commentaries on geometric symbols and useful theorems; definitions; and etymologies of essential mathematical terms. A highlight of the book are Fletcher's original studies that analyze harmonious proportions in world-famous art, architecture, landscape design, and other compositions. These include the South Rose Window at Cathédrale Notre Dame de Paris, Andrea Palladio's Villa Emo and Teatro Olimpico, a Stradivari violin, Thomas Jefferson's Poplar Forest, Beatrix Farrand's garden courtyard for the Oriental Institute at the University of Chicago, the illuminated Lindisfarne Gospels, a Louis Sullivan stencil for the Chicago Stock Exchange, and Eero Saarinen's North Christian Church.
Geometric patterns are fantastic to use in design because, by nature, the human eye is naturally drawn to them. By pairing geometric patterns with an exciting color scheme, we can create engaging visual content that makes use of shape psychology and artistry.
Mathematics can be discerned in many of the arts, such as music, dance, painting, architecture, and sculpture. Each of these is richly associated with mathematics. Among the connections to the visual arts, mathematics can provide tools for artists, such as the rules of linear perspective as described by Brook Taylor and Johann Lambert, or the methods of descriptive geometry, now applied in software modelling of solids, dating back to Albrecht Dürer and Gaspard Monge. Artists from Luca Pacioli in the Middle Ages and Leonardo da Vinci and Albrecht Dürer in the Renaissance have made use of and developed mathematical ideas in the pursuit of their artistic work. The use of perspective began, despite some embryonic usages in the architecture of Ancient Greece, with Italian painters such as Giotto in the 13th century; rules such as the vanishing point were first formulated by Brunelleschi in about 1413, his theory influencing Leonardo and Dürer. Isaac Newton's work on the optical spectrum influenced Goethe's Theory of Colours and in turn artists such as Philipp Otto Runge, J. M. W. Turner, the Pre-Raphaelites and Wassily Kandinsky. Artists may also choose to analyse the symmetry of a scene. Tools may be applied by mathematicians who are exploring art, or artists inspired by mathematics, such as M. C. Escher (inspired by H. S. M. Coxeter) and the architect Frank Gehry, who more tenuously argued that computer aided design enabled him to express himself in a wholly new way.
A strand of art from Ancient Greece onwards sees God as the geometer of the world, and the world's geometry therefore as sacred. The belief that God created the universe according to a geometric plan has ancient origins. Plutarch attributed the belief to Plato, writing that "Plato said God geometrizes continually" (Convivialium disputationum, liber 8,2). This image has influenced Western thought ever since. The Platonic concept derived in its turn from a Pythagorean notion of harmony in music, where the notes were spaced in perfect proportions, corresponding to the lengths of the lyre's strings; indeed, the Pythagoreans held that everything was arranged by Number. In the same way, in Platonic thought, the regular or Platonic solids dictate the proportions found in nature, and in art. An illumination in the 13th-century Codex Vindobonensis shows God drawing out the universe with a pair of compasses, which may refer to a verse in the Old Testament: "When he established the heavens I was there: when he set a compass upon the face of the deep" (Proverbs 8:27), . In 1596, the mathematical astronomer Johannes Kepler modelled the universe as a set of nested Platonic solids, determining the relative sizes of the orbits of the planets. William Blake's Ancient of Days (depicting Urizen, Blake's embodiment of reason and law) and his painting of the physicist Isaac Newton, naked, hunched and drawing with a compass, use the symbolism of compasses to critique conventional reason and materialism as narrow-minded.Salvador Dalí's 1954 Crucifixion (Corpus Hypercubus) depicts the cross as a hypercube, representing the divine perspective with four dimensions rather than the usual three. In Dalí's The Sacrament of the Last Supper (1955) Christ and his disciples are pictured inside a giant dodecahedron.