Description & Requirements



   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


   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


  The Book



  • 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


    Hexagon & Hexagram

    Pentagram & Pentagon

    Golden triangle


  • 6. The Platonic Solids
  • Plato (427-347 B.C.)

    The Timaeus


    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


    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?






    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


    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


    Reflective transformations



  • 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



    Fractal Art

    Randomness in Art