Description and Requirements
The Great Pyramid
Music of the Spheres
Polygons and Tilings
The Platonic Solids
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
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.
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
As we go through the material we'll be looking for:
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:
and this one, combining math with art and architecture.
The Eternal Golden Braid
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!
©Paul Calter, 1998. All Rights Reserved. Dartmouth College.