Paul Calter Says:
Math Can Be
Beautiful!
By M. D. Drysdale

Paul Calter of Randolph, a sculptor and painter who is retired as a professor of mathematics at VTC, in his studio with some of his geometric creations. (Herald / Bob Eddy)

Paul Calter of Randolph has just published the most beautiful mathematics book that you will ever see.

Beautiful? A mathematics book?

Yup. And that’s the whole point.

The book, "Squaring the Circle: Geometry in Art and Architecture," describes in hundreds of intriguing ways how mathematics and beauty are related. Its premise is that mathematics can be beautiful and that much beauty is mathematical.

Or, to quote Aristotle: "The mathematical sciences in particular exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful."

Examples abound through history, from the Pyramids of Egypt to the prehistoric stone circles in England, whose sides have been flattened so as to make the circumference an even multiple of the diameter.

In the Middle Ages, numbers and geometry "were built into every facet of the great cathedrals," Calter says. The same mathematical ratios that create music are built into architecture as well.

During the Renaissance, strict geometric figures were used in construction even though they were not evident to the viewer. The architects felt that geometric figures were depictions of perfection, and that building them into a cathedral was a way of bringing godly perfection to God’s house on earth.

Not only geometric figures but even individual numbers acquired their own mythology that was reflected in art—and Calter includes a particularly fascinating 30-page appendix about these numbers. Did you know, for instance, that "2" is considered the first female number and "3" the first male number?

This is the 10^th book for Calter, who is retired after teaching math at Vermont Technical College and is a sculptor and artist as well. It grew out of his studies for a later-in-life Masters degree in fine arts at Norwich, and then a course that he taught in 1997 on mathematics and art as a visiting scholar at Dartmouth College, and at VTC.

He’s been writing it since 2001, and in recent years has received valuable proofreading help, including assistance with checking all the mathematical proofs, from Susan Porter of Randolph. His publisher, Key College Publishing, has already been contacted by representatives of four colleges that might use the book in class.

The title, "Squaring the Circle," refers to one of the great insoluable problems in mathematics—how to construct a square whose perimeter is exactly the same as the circumference of a given circle.

In myth and philosophy, "squaring the circle" means something more profound. The square has long represented the earth, he noted, while the circle represents the boundless dome of heaven. To square the circle, then, is a way of reconciling the earthly with the divine.

To Calter, the book was also a way of reconciling two parts of himself. Trained as an engineer, his life has reflected his love of both numbers and art. Both, in fact, are on display at VTC, whose campus is marked by several of his geometrical sculptures.

(His favorite, he says, is the sundisk/moondisk between the library and Morey Hall, which is a sun calendar, telling the month of the year by the shadow of the sun at noon.)

The book also draws on Calter’s knowledge of Italian art, stemming from a time he spent there helping restoration authorities.

"Squaring the Circle" is chock-full of insights and inspired connections drawn from wide historical and artistic knowledge, as suggested by mathematics, especially geometry. A short section on "The Circle as a Symbol in Art," for instance, contains photographs of art from Tibet, the Scrovegni Chapel, an Aztec Sunstone, the Winchester Bible, the Carmina Burana manuscript, a Goya painting, and the Lord of the Rings movie.

The book contains more than 300 full-color photographs and fine art images and 800 illustrations. It’s a serious math book, too, with 160 constructions and fully-worked examples and a variety of suggested exercises. But for the generalist it’s also a romp through history and geography, a beautifully-illustrated tour with Paul Calter as a most interesting and provocative guide.

"Squaring the Circle" is in stock at Cover-to-Cover Books in Randolph.