Description and Requirements

 The Book




   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 Francesca


   Façade measurement 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

Egyptian Rope Stretchers

Egyptian Rope Stretchers
Tompkins, Peter. Secrets of the Great Pyramid. NY: Harper, 1971. p. 22.

Welcome to Geometry in Art & Architecture. We'll be taking a long journey together, starting in Egypt, like the travellers in this picture. There, the story goes, geometry got its start when rope stretchers were sent out to put back the boundary markers washed away by the Nile.

In addition to looking at art and architecture, we'll cover any mathematics-related topics as we go along. The Math Topics for the first unit will be an introduction to the triangle in general, and the so-called Egyptian triangle, contained in the great pyramid. Since the Egyptian triangle contains the golden ratio, we'll introduce the ideas of ratio and proportion here, and for squaring of the circle, we must be able to find perimeters and areas of the square and the circle.

The plan is to go more or less chronologically, following threads of Art, Mathematics, and Architecture, from Egypt to the present.

Fractal Tetrahedron Fractal Tetrahedron

We'll start our journey with a pyramid, and we'll also end with a very different pyramid, a Sierpinski tetrahedron, in our final unit on Chaos and Fractals.

We'll limit ourselves to Western art only, but even with that restriction the coverage is very wide. That means, of course, that we can't go too deeply into any one topic.

Things We'll Look For
Brune's Cover Brunes, Tons, The Secrets of Ancient Geometry - and its use. Copenhagen. Rhodos, 1967.

Brune's Cover

As we go through the material we'll be looking for:

  1. Proportions between the parts of a building, a painting, or a sculpture. In particular, we'll look for the golden ratio and the musical ratios.

  2. Use of geometric symbols, such as the circle, mandala, triangle, square, pentagram, hexagon, or octagon, and their use in so-called Sacred Geometry.

  3. Geometric Constructions, like squaring the circle, the Gothic Master Diagram, the sacred cut, and constructions of the pentagon.

  4. Shapes of Frames; how they are chosen and how they affect the contents of a painting.

  5. Art Motifs, especially recurring themes that we see over and over in art.

  6. Math content; any geometry or other math that is closely related to the art or architecture we're studying.

  7. People, ones that played a key role in developing the ideas related to this course, and especially those that were both mathematicians and artists or architects.

Skeptical Attitude

We'll see that writers in this field sometimes make unsupported claims. Rudolf Wittkower, in his Architecture in the Age of Humanism says

". . . in trying to prove that a system of proportions has been deliberately applied . . . one is easily misled into finding . . . those ratios which one sets out to find. Compasses in the scholar's hand do not revolt."

In other words, we tend to find what we're looking for, whether its there or not. We will hope to avoid that pitfall by questioning everything.

Mathematics Across the Curriculum



This course is one of several developed under a grant from the National Science Foundation to Dartmouth, called Mathematics Across the Curriculum. Some courses being developed at Dartmouth are ones that try to integrate math with:

physics and chemistry
textile design
psychology and medicine
earth sciences
Renaissance thought

and this one, combining math with art and architecture.

The Eternal Golden Braid
Hofstadter Cover Hofstadter, Douglas. Gödel, Escher, Bach: an Eternal Golden Braid. NY: Vintage, 1979.
Hofstadter Cover

In "Gödel, Escher, Bach:", Douglas Hostadter says

"I have sought to weave an eternal golden braid out of these three strands, Gödel, Escher, Bach, a mathematician, an artist, and a composer."

In other words, math, art, and music. In this course we hope to trace just two strands of his eternal golden braid, art (and architecture) and math, and sometimes connect them with strands from literature, mythology, and religion .

We've planned an exciting journey, to follow these strands over 5000 years and several continents, and we really hope that you'll join us for the trip!

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©Paul Calter, 1998. All Rights Reserved. Dartmouth College.