Infinite Measure: Learning to Design in Geometric Harmony with Art, Architecture, and Nature

About

About the Author
Rachel Fletcher was born in Baltimore, Maryland, in 1947 and was raised there. She began her career in lighting and stage design for the theater with degrees from Hofstra University (B.A. in theater arts), SUNY Albany (M.A. in dramatic literature), and Humboldt State University (M.F.A. in lighting/stage design). She has been a faculty member of the New York School of Interior Design since 1996 and a contributing editor to the Nexus Network Journal since 2005. Her professional work designing theatrical spaces led to an interest in the principles of geometric proportion and harmony as a design system, including time as a geometer and teacher of geometry and proportion for school-age children and adult professionals and at dozens of universities, museums, and institutions in the United States and Europe. In this capacity, she received an International Center for Jefferson Studies Fellowship Award from the Thomas Jefferson Foundation to study geometric proportions in Jefferson’s architectural works. Fletcher was the creator/curator of the museum exhibits “Infinite Measure,” “Design by Nature,” and “Harmony by Design: The Golden Mean” and the author of the latter’s exhibit catalog. As a community activist, she is the founding director of the Housatonic River Walk in her home town of Great Barrington, Massachusetts, which was designated a National Recreation Trail by the National Park Service in 2009, and the co-director of the Upper Housatonic Valley African-American Heritage Trail. For her significant contributions to conservation and civic improvements, she has received an Environmental Merit Award from the U.S. Environmental Protection Agency, citations from the Garden Club of America, and the National Urban Hometown River Award in Grassroots Activism from American Rivers, among other honors.

About the Essayist
Kim Williams is a writer and editor living and working in Italy. She received her degree in architectural studies from the University of Texas in Austin, and is licensed as an architect in New York State. Her apprenticeship was done in the offices of Philip Johnson in New York City. She became interested in mathematics and architecture while writing Italian Pavements: Patterns in Space (Houston: Anchorage Press, 1997) about the role of decorated pavements in the history of Italian architecture. In 1996, she began the international conference series “Nexus: Architecture and Mathematics” and, in 1999, founded the Nexus Network Journal to provide a dedicated venue for scholarly research in architecture and mathematics. In 2000, Williams founded Kim Williams Books, an independent, peer-reviewed press for books about architecture and mathematics. Williams has published many articles in scholarly journals on the use of mathematical principles in architecture, including Mathematical Intelligencer and Leonardo, and her drawings have been displayed in both group and solo exhibits. Her latest book, with Lionel March and Stephen Wassell, is The Mathematical Works of Leon Battista Alberti (Basel: Birkhäuser, 2010).

Praise

The book will surely be appreciated by those architects and architecture historians interested in the relationship between architecture and mathematics, whose research is devoted to the study of geometrical diagrams and patterns of architecture of the past. We know from the historical literature that architects relied on chosen numbers, proportional ratios and chosen shapes to impart beauty and harmony to their projects, because the mathematicians themselves considered these numbers, ratios and shapes to be beautiful, meaningful and symbolic. Nevertheless architectural treatises hardly give any practical indications on how to manipulate these mathematical objects in order to achieve the fixed goals. The book Infinite Measure unveils many clues to the process of creating a geometrical pattern. The multiple constructions, the number of variations, the creativity, the infinite possibilities, will inspire researchers and, hopefully, designers.
— Nexus Network Journal, March 2015 (click to read a pdf of the full review)

“Rachel Fletcher’s new publication, Infinite Measure, is a wide-ranging book that defines geometry’s presence in the natural world, tracks the history and evolution of geometry from before the classical period through to the present day and presents a comprehensive and impressive body of knowledge simultaneously philosophical and practical. It explains the grammar of geometrical construction, from the initial simplicity and unity of the circle, through gradually more complex constructions that lead ultimately to sophisticated geometrical overlays defining proportional relationships in the natural and built environments. The emphasis throughout is on proportion and how the individual elements of a design should relate to one other, and to the whole, in a proportionate and visually harmonious way.” “…a comprehensive geometrical journey under enlightened guidance. This is an impressive book that presents extensive scholarship in a completely reader-friendly way.”
—Laurie Smith, Timber Framing (click to read a pdf of the full review)

“Infinite Measure by Rachel Fletcher is a fascinating book teaching artists how to design in geometric harmony with art, architecture, and nature. The discussion is based on the ancient knowledge that symmetry and proportion are evident in every form of nature and these are relational. The same geometric figures can be found (and are often quite obvious) throughout the history of all art objects, including architecture, pottery, design, paintings, etc. The ratios of dynamic symmetry, which are mathematically expressed, are the basis of the drawing exercises in this book and red bullets indicate each step. The book sound complicated because it dissects and explains almost everything you can think of, but the excellent teaching walks the student through each step until a thorough understanding enables intelligent design in any medium. This book should be a MUST for any art student, and you will feel satisfied when you gain this valuable, timeless understanding, which opens your eyes and mind to all you see everywhere. EXCELLENT!!!”
—Bonnie Neely, from her five-star book review for Amazon

“Geometry has always been the basis for creating beautiful art and architecture, but the methods used by the ancients have been a bit difficult to grasp. Rachel Fletcher sweeps away that problem with easy-to-understand explanations and examples in her new book. I had nearly reached the point of exasperation, struggling to understand Dynamic Symmetry and the use of compass and ruler to divide an area, when along came this book and made it all much easier to comprehend and use. For photographers and graphic artists, this book is particularly helpful, as it provides methods to organize the ‘canvas’ and align objects in an appealing manner. The methods explained by Fletcher will become part of your standard workflow. Highly recommended!”
—Michael G. Smith, Photographer, Detroit, from his five-star book review for Amazon

“Infinite Measure: Learning to Design in Geometric Harmony with Art, Architecture, and Nature is a 400-page compendium in which geometer and theater designer Rachel Fletcher (New York School of interior Design) provides visual designers of all disciplines and art forms with geometric methods and techniques for composing spaces and places harmoniously. Organized into two major sections (‘Geometry’s Shapes’ and ‘Symbols & Composing Space Plans’), readers are presented with a wealth of diagrams illustrating geometric design concepts of balance and proportion. A unique work of impressive scholarship, Infinite Measure: Learning to Design in Geometric Harmony with Art, Architecture, and Nature is an important and strongly recommended addition to professional and academic library collections as well as the supplemental reading lists for art and architecture students.”
—James A. Cox, Editor-in-Chief, Midwest Book Review

“Rachel Fletcher has written the definitive book on proportion as the design principle upon which most design principles and elements rest. When students and practitioners can master and absorb the import of this root principle through study, exploration, and experience, they are able to express themselves with a sense of assurance and command as rising designers, artists, and critics. I am an admirer of Rachel Fletcher and believe that this elegant, useful, and authoritative text should become intregral to every design curriculum.”
―Dr. Ellen S. Fisher, ASID, IPEC, NYS-CID, Vice President for Academic Affairs and Dean, New York School of Interior Design

“It may seem anachronistic to introduce a new book about the ancient science of geometry for design at a time when so many computer applications apply geometry automatically without the designer having to think about it, but it is precisely one of the contradictory characteristics of our world today that makes Rachel Fletcher’s book so relevant and necessary. What Fletcher does in this elegant, thoughtful, and practical book is to guide the reader to a knowledge and understanding of how geometry works for the designer. Specifically, she reveals design truths that are inherent in the use and movements of the compass and straight-edge rule in order to open all possible doors for the designer’s creativity. What she knows is not old or arcane knowledge but timeless geometrical facts that are as fresh today as they were when scratched in sand or on parchment hundreds, if not thousands, of years ago. The author’s unique capacity to explain the necessary geometric principles of proportion and harmony in a clear, step-by-step way is accompanied by her gentle manner of staying ‘off the page’ so that the geometry, and not the geometer, becomes the leading character. Whether the reader’s aim is to understand the great works of art, architecture, landscape, and other designs of the past or to create new works that express contemporary aesthetics, this book provides a fundamental and inspirational starting point.”
―Kim Williams, Editor-in-Chief, Nexus Network Journal, Torino, Italy

My Place

Before moving to Great Barrington in western Massachusetts thirty-two years ago, I learned to tell the hour and the season by the turning of the stars. Scorpio hung low in the sky during summer, the first glimpse of the Pleiades meant autumn was on the way. Here in the Berkshires, I learned to tell the time by observing the Housatonic River, whose waters collect from the 3,488-foot peak of Mount Greylock―the highest in the state―and low Sheffield Flats.

I know the Housatonic by its native flowers, from the first blush of shadbush to the last purple asters that withstand the frosts of fall. I know spring by vernal pools and the unmistakable clamor of peepers, summer by the ferns that green the banks. In autumn, the river sparks metallic, reflecting golden sugar maples and the deep steel-blue of sky. In winter, the river’s dark, brooding power rolls below sheets of ice.

Long after the Mahican people settled here, the Housatonic became a “working” river. Early European settlements became attractive towns and tidy cities, as modest gristmills grew into substantial paper and textile mills and ultimately into modern industrial plants. It was a time of denial, for the Housatonic, however, as its towns were built with their backs to the river, and the river fell prey to abuse and discarded waste. Although nineteenth-century artists such as Thomas Cole (1801–1848) and Frederick Edwin Church (1826–1900) revealed the river’s essential beauty, others, including Unitarian minister John Coleman Adams (1735–1826), saw in the Housatonic “a noble example of how hard a river dies.”¹

Another early advocate for the Housatonic River was Great Barrington native William E. B. Du Bois (1868–1963), the father of Pan-Africanism and champion of American civil rights. “I was born by a golden river,” he wrote of the Housatonic, and campaigned for its recovery throughout his life:²

For this valley, the river must be the center. Certainly it is the physical center; perhaps, in a sense, the spiritual center. Perhaps from that very freeing of spirit will come other freedoms and inspirations and aspirations which may be steps toward the diffusion and diversification and enriching of culture throughout this land.³

Du Bois’s pioneering vision tied the fate of all rivers to environmental health, social justice, and human rights. He advocated for the care of river-landscapes around the world, imagining peoples of all races and vocations coming to their aid to shape the destiny of rivers and their own.

Today, the Housatonic is winding its way back into the hearts of its towns and cities, in an evolving story of stewardship and renewal. Twenty-five years ago, a contingent of twelve local residents undertook the daunting task of clearing remains of a burned-out building from the banks of the Housatonic in downtown Great Barrington. Since then, 2,400 volunteers have reclaimed and transformed the town’s once-ravished riverbank into River Walk, a half-mile of trail and wetland gardens that meander along the river’s edge.⁴ Like much of New England’s landscape, its beauty is more handcrafted than wild.

When towns and cities reclaim abandoned rivers, a rich historical and natural heritage is revealed underfoot. There is a new regard for wildlife habitat, native flora, vistas and views, avenues of transport, geological formations, wetland and floodplain ecology, historic and prehistoric patterns of human settlement, and local legend. Rivers are places of confluence where culture and nature intersect; they cannot be separated from the people who live by them.

1. Adams, John Coleman, Nature Studies in Berkshire (New York: G. P. Putnam’s Sons, 1901), 110.
2. Du Bois, W[illiam] E[dward] B[urghart], Darkwater: Voices from Within the Veil (Mineola, NY: Dover Publications, 1999), 3; originally published in a hardcover edition in 1920 by Harbourt, Brace & Co., of New York City.
3. Du Bois, W[illiam] E[dward] B[urghardt], “The Housatonic River: Speech of W. E. Du Bois, ’84, at the Annual Meeting of the Alumni of Searles High School, July 21, 1930,” Berkshire Courier (July 31, 1930): np.
4. The Housatonic River Walk was designated a National Recreation Trail in 2009.

Copyright © 2013 Rachel Fletcher. All rights reserved.