MA3032: GEOMETRY FOR ART AND ARCHITECTURE

Pre-requisite: Nil

L T P C 3 1 0 3 Total Hours: 56 Hrs

Module 1: Golden Ratio, polygons, tilings, the platonic solids and sacred geometry (14 hours)

Great pyramid of Cheops, golden ratio, secrets of the great pyramid, squaring the circle, the rhind mathematical papyrus,rope stretchers triangle, music of the spheres, number symbolism, the equilateral triangle, tilings, hexagon & hexagram, pentagram & pentagon, golden triangle, the Timaeus, Polyhedra, polyhedra in art & architecture, vitruvius, ad quadratum, the sacred cut, pompeii and herculaneum, roman rectangle.

Module 2: Number, Weight and Measure (14 hours)

Biblical, classical and Islamic influences, symbolism of numbers and geometric figures, four & the square: the cross, tree of life, herms, pillars, five & the pentagon, six & the hexagon, seven & the heptagon, eight & the octagon, symbolism of the circle, celestial, ring, wheel, rainbow, crescent, calendar circles, stonehenge, the circle and gothic architecture. the gothic style, the masons, the gothic master plan, neolithic stone circles, mandala, hindu temple layout, Yin yang symbol.

Module 3: Celestial themes in art and perspective (14 hours)

The ptloemaic universe, the Sphaera mundi, the structuring of celestial space, nine ranks of angels, Dante's nine circles of heaven, Cigoli's Immacolata, portrayals of astronomers and allegories to astronomy, models of the cosmos, maps, globes, armillary spheres, orreries, domes, astonomical instruments, sundials, sun calendars, stone circles, twentieth-century astronomical art, sun symbols, temple orientation, pyramid placement, zodiac, radian measure, arc length, rotation, latitude and longitude, the conic sections, elliptical orbits ,perspective, Brunelleschi, Donatello, Masaccio, Mantegna, Alberti, from Euclid to Desargues, significance of perspective, later developments in perspective, perspective machines and cameras, The quadro or rectangular format,t he square format, the Tondo or round format, the roundel, Ovato Tondo and the elliptical format.

Module 4: Dynamic symmetry, Art and the Computer, Chaos and Fractals (14 hours)

Impact of the new geometries, the fourth dimension and physics on art, Lobachevski, Bolyai, Reimann, Einstein, Picasso, Braque, Mondrian, Malevich, abstraction, post-impressionism, cubism, constructivism , suprematism, De Stijl, Jay Hambidge, Irma Richter, the golden numberists, irrational numbers, logarithmic spiral, ratio and proportion, geometric art of M.C. Escher, Buckminster Fuller, Le Corbusier, geodesic domes, ratio and proportion, polyhedral, real landscapes, Mandelbrot, self-similarity, fractal art, randomness in art.

References: 1. Paul Calter, Squaring the circle: geometry in art and architecture, 4th edition, Wiley, 2008. 2. Brunes, Tons, The Secrets of Ancient Geometry - and its use. Copenhagen. Rhodos, 1967. 3. Janson, H. W. History of Art. 5th Edition. NY: Abrams, 1995. 4. Lawlor, Robert. Sacred Geometry. NY: Thames & Hudson, 1982.