Description & Requirements  Syllabus    Introduction    The Great Pyramid    Music of the Spheres    Number Symbolism    Polygons and Tilings    The Platonic Solids    Roman Architecture    Number Symbolism       in the Middle Ages    The Wheel of Fortune    Celestial Themes in Art    Origins of Perspective    What Shape Frame?    Piero della FrancescaArt    LeonardoArt    Façade measurement Art by Trigonometry    Early Twentieth Century Art    Dynamic symmetry &       The Spiral    The Geometric Art       of M.C. Escher    Later Twentieth Century       Geometry Art    Art and the Computer    Chaos & Fractals 1. Introduction   2. The Golden Ratio and Squaring the Circle in the Great Pyramid Great Pyramid of Cheops Introduction to the Triangle Pythagorean theorem Golden Ratio Secrets of the Great Pyramid Squaring the Circle Perimeters and areas of squares and circles The Rhind Mathematical Papyrus Rope stretchers Triangle Summary: The Importance of Egyptian Art   3. Music of the Spheres Pythagoras The Pythagoreans Music of the Spheres   4. Number Symbolism Elementary number symbolism Zodiac number symbolism Number symbolism in the Old Testament Pythagorean number symbolism Modern number terminology   5. Polygons and Tilings, and Sacred Geometry The Regular Polygons The Equilateral Triangle Tilings Hexagon & Hexagram Pentagram & Pentagon Golden triangle   6. The Platonic Solids Plato (427-347 B.C.) The Timaeus Polyhedra Polyhedra in Art & Architecture   7. Ad Quadratum, The Sacred Cut, and Roman Architecture Vitruvius The Square Ad quadratum The Sacred Cut Pompeii and Herculaneum Garden Houses of Ostia Roman Rectangle   8. Number, Weight, and Measure: the Medieval Cathedral Biblical, classical, & Islamic influences: Augustine, Hildegard von Bingen , Aquinas, Cabala, Gematria 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: The sacred, S. Giovanni Castel Del Monte   9. The Wheel of Fortune and the Rose Window Symbolism of the circle: Celestial, Ring, Wheel, Rainbow, Crescent, Calendar circles, Stonehenge Dante's circles of Heaven and Hell Geometry of the circle The circle and Gothic architecture: The Gothic style, The Masons, The Gothic Master Plan, Catherine Window, Wheel Window, Rose window, Rosettes, pavements, intarsia designs, Gothic arch, Gothic tracery Mandorla, Symbolism of the fish, Squaring the Circle: Neolithic Stone Circles, Mandala, Sacred cut, Hindu temple layout, Yin yang symbol   10. Celestial Themes in Art The Creation, God the Geometer 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   11. Brunelleschi's Peepshow and the Origins of Perspective What is perspective? Brunelleschi Donatello Masaccio Mantegna Alberti From Euclid to Desargues Significance of perspective Later developments in perspective: Perspective Machines and Cameras   12. What Shape Frame? Why Frame a Picture? What Shape Frame? The Quadro or Rectangular Format The Square Format The Tondo or Round Format The Roundel Ovato Tondo and the Elliptical Format Frequency Distributions, Mean, Standard Deviation   13. Piero della Francesca (1416-1492) Mathematical education in the Renaissance: Proportion and the Rule of Three, Gauging of solids Piero's math books Piero's paintings and geometry   14. Leonardo (1452-1519) The Ultimate Renaissance Man Leonardo's mathematics Leonardo's Writings Perspective Chaos and Fractals   15. Façade measurement by Trigonometry Historical background The method Trial at VTC The Torre Bernarda Right triangle trigonometry, law of sines, probability   16. Relativity, the Fourth Dimension, and Early Twentieth Century Art Imact of the new geometries, the fourth dimension, and physics on art: Lobachevski (1793-1856), Bolyai (1802-1860), Reimann (1826-1866), Einstein (1879-1955) Picasso, Braque, Mondrian, Malevich Abstraction, Post-impressionism, Cubism, Constructivism , Suprematism, De Stijl   17. Dynamic symmetry Jay Hambidge, Irma Richter The Golden Numberists Irrational numbers, Logarithmic spiral, Ratio and proportion   18. The Geometric Art of M.C. Escher Portrayal of Infinity Recursion and feedback Tilings Reflective transformations Symmetry   19. Geometry & Architecture in our Century Buckminster Fuller, Le Corbusier, Geodesic domes ratio and proportion, polyhedra   20. Art and the Computer The Artist-mathematician The Artist-Mathematician-Hacker The Computer in Art   21. Chaos & Fractals Real landscapes Mandelbrot Self-similarity Fractal Art Randomness in Art