9780470412121

Geometry is a dynamic branch of mathematics that also serves as a creative tool for engineers, artists, and architects. Squaring the Circle: Geometry in Art and Architecture includes all the topics necessary for a solid foundation in geometry and explores the timeless influence of geometry on art and architecture. The text offers wide-ranging exercise sets and related projects that allow students to practice and master the mathematics presented. Each chapter introduces mathematical concepts geometrically and illustrates their nontraditional applications in art and architecture throughout the centuries. Appropriate for both basic mathematics courses and cross-discipline courses in mathematics and art, Squaring the Circle requires no previous mathematics.

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Paul A. Calter is a Visiting Scholar at Dartmouth College and Professor Emeritus of Mathematics at Vermont Technical College. He is a book review editor of the Nexus Network Journal and has interests in both the fields of mathematics and art. He received his B.S. from Cooper Union and his M.S. from Columbia University, both in engineering, and his Masters of Fine Arts Degree from Norwich University. Calter has taught mathematics for over twenty-five years and is the author of ten mathematics textbooks and a mystery novel. He has been an active painter and sculptor since 1968, has had many solo shows and participated in dozens of group art shows, and has permanent outdoor sculptures at a number of locations. Calter developed a course called “Geometry in Art & Architecture,” which he has taught at Dartmouth College and Vermont Technical College, and he has taught at Dartmouth College and Vermont Technical College, and he has given workshops and lectures on the subject. Calter's own art is concerned with astronomical and geometric themes; he searches for a link between the organic and geometric basis of beauty, what has been called the philosopher's stone of aesthetics.

Preface
To the Student
To the Instructor
Acknowledgments
About The Author
Music of the Spheres
Pythagoras and the Pythagoreans
Profile: Pythagoras
Ratio and Proportion
Pythagoras and the Musical Ratios
Sequences, Series, and Means
Plato and the Musical Ratios
Profile: Plato
The Musical Ratios in Architecture
Profile: Vitruvius
Profile
Profile
Summary
The Golden Ratio
The Golden Ratio
Profile: Euclid
The Fibonacci Numbers and the Golden Ratio
Profile
The Golden Ratio in Architecture
Profile
Summary
The Triangle
Angles Between Lines
Triangles
Right Triangles
Congruence, Symmetry, Isometry, and Similarity
Summary
Ad Quadratum and the Sacred Cut
The Square
The Rectangle
Other Quadrilaterals
The Rectangular Format in Painting
Profile
Profile
Architectural Proportions Based on the Square and the Rectangle
The Earthly and the Mundane
Summary
Polygons, Tilings, and Sacred Geometry
Polygons
Pentagons and Pentagrams
Profile
Other Polygons
Tilings with Polygons
Summary
The Circle
Geometry of the Circle
Radians
Lines Intersecting a Circle
The Round Format in Art
Profile: The Della Robbia Family
The Circle as a Symbol in Art
Summary
Circular Designs in Architecture
More Circle Geometry
The Circle in Gothic Architecture
Round Windows
Circular Ornamentation in Walls and Pavements
Arches and Vaults
The Vesica
Summary
Squaring the Circle
The Geometry of Squaring the Circle
Squaring the Circle in the Great Pyramid
Other Examples from Art and Architecture
Summary
The Ellipse and the Spiral
The Ellipse
Profile: Apollonius Of Perga
Graphing the Ellipse
Profile: Ren+ Descartes
The Spiral
The Spiral in Art and Architecture
Summary
The Solids
Surfaces and Solids
The Polyhedra
Cylinders and Cones
Similar Solids
The Platonic Solids
Profile: Archimedes
The Creation-by Geometry?
Polyhedra in the Renaissance
Profile: Piero Della Francesca
Profile: Luca Pacioli
Polyhedra as Art Motifs
Summary
The Sphere and Celestial Themes in Art and Architecture
The Sphere
The Dome
The Terrestrial Sphere
The Celestial Sphere
Profile: Johannes Kepler
Time
The Sphere and the Heavens as Art Motifs
Profile: Maurits Cornelius Escher
Profile: Dante Alighieri
Profile: Galileo Galilei
Summary
Brunelleschi's Peepshow and the Origins of Perspective
What Is Perspective?
A Perspective Primer
Paintings Before Perspective
Setting the Stage
Brunelleschi and Alberti
Profile
Three Renaissance Artists
Profile
Profile
Profile
Later Developments
Profile
Summary
Fractals
Dimension
Profile
Self-Similarity
How to Create a Fractal
Fractal-Related Art
Summary
Appendices
The Art-Math Tourist
Biographical Profiles
Listin
Table of Contents provided by Publisher. All Rights Reserved.

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Squaring the Circle Geometry in Art and Architecture

Squaring the Circle Geometry in Art and Architecture

0470412127

Summary

Author Biography

Table of Contents

Supplemental Materials