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Squaring the Circle: Geometry in Art and Architecture

Paul A. Calter
Key College Publishing
Publication Date: 
Number of Pages: 
Paperback with CDROM
[Reviewed by
Sarah Boslaugh
, on

Mathematics Across the Curriculum was a project at Dartmouth and other colleges whose aim was to introduce students to how mathematical ideas applied to other fields of study. A major goal of the program, funded by the National Science Foundation, was to encourage students to think mathematically about other fields of study, in part by encouraging them to use the mathematics they already knew, and in part by encouraging them to enroll in more math courses.

Squaring the Circle was written as part of this effort: it integrates the study of geometry with the study of art and architecture. The end result is an attractive volume which looks more like a coffee-table book than a traditional geometry text: it includes many color illustrations, discussions of historical and philosophical topics, and biographical sidebars on everyone from Euclid to Le Corbusier. People interested in the mathematical foundations of art and architecture, whether they are college students or not, will enjoy reading this volume, while it may also attract the more mathematically-minded to take a closer look at art.

The geometry content is cleverly tucked into chapters where most of the content concerns art and architecture, and the technical material is accompanied by admirably clear illustrations. Squaring the Circle also includes the type of exercises and solved problems you would expect to find in a college math book, plus some more creative exercises based on the art and architecture content. For instance, the chapter on circular designs includes analysis of mason’s marks and church windows and then directs the student to reconstruct the patterns and create their own variations.

Notes and a bibliography are provided for each chapter and several appendices provide useful references, including an index of the building and sites included in the illustrations, historical figures referenced in the text, constructions (e.g., golden ratio, angle bisection) referenced in the text, geometric signs and symbols, number symbolism and famous groupings in art, and a summary of geometric facts and formulas.

Each copy of Squaring the Circle comes with a code which allows students and instructors to access additional resources available from the publisher’s web site . Materials available for this text include a collection of downloadable images from the text, interactive files for some of the constructions in the text, links to appropriate journals and organizations, and (for instructors only) complete solutions to exercises from the text.

Paul A. Calter earned his MFA in sculpture from Norwich University and his M.S. in Mechanical Engineering from Columbia University . He is Professor of Mathematics Emeritus at Vermont Technical College and Visiting Professor at Dartmouth College , where he developed the course “Geometry in Art & Architecture” with funding from an NSF Grant for Mathematics Across the Curriculum. Among his previous books are Technical Mathematics with Calculus (5th ed., 2006) and Introductory Algebra and Geometry with Applications (1997).

Sarah Boslaugh ( is a Performance Review Analyst for BJC HealthCare and an Adjunct Instructor in the Washington University School of Medicine, both in St. Louis, MO. Her books include An Intermediate Guide to SPSS Programming: Using Syntax for Data Management (Sage, 2004), Secondary Data Sources for Public Health: A Practical Guide (Cambridge, 2007), and Statistics in a Nutshell (O'Reilly, forthcoming), and she is Editor-in-Chief of The Encyclopedia of Epidemiology (Sage, 2008).

  1. Music of the Spheres
  2. The Golden Ratio
  3. The Triangle
  4. Ad Quadratum and the Sacred Cut
  5. Polygons, Tilings, and Sacred Geometry
  6. The Circle
  7. Circular Designs in Architecture
  8. Squaring the Circle
  9. The Ellipse and the Spiral
  10. The Solids
  11. The Sphere and Celestial Themes in Art and Architecture
  12. Brunelleschi’s Peepshow and the Origins of Perspective
  13. Fractals