Ernest Irving Freese's Geometric Transformations:
the Man, the Manuscript, the Magnificent Dissections!

by Greg Frederickson, now published by World Scientific Publishing -- See the publisher's announcement.

With exuberance tempered by a hint of reality, Los Angeles architect Ernest Irving Freese announced the completion of his opus on geometric dissections in a letter to a friend in 1957:
For the past 4 months I've let everything go hang — work, friends, correspondence, or what have you — BUT, it's finished — the first book on Geometric Transformations (Dissective Geometry) ever produced. 200 plates comprising about 400 original examples. Cost $28.00 just to get a blueprint copy of the dwgs. Well, it's off my chest — but who will publish it? Probably nobody!
Three months to the day later, Freese died of coronary arteriosclerosis and was soon cremated. Aside from copies of a dozen plates sent to friends, his book vanished. It was entombed for the next forty-five years in the house that he had converted from a prohibition-era shack to a studio, then enlarged as his first family moved in during the depths of the Great Depression, and in which he lived out the remainder of his life with a second family. Those few who knew of the manuscript tried to contact the widow, to encourage her to release it for publication. She never responded, so that by 1965 people had given up trying. Thirty years later, when I obtained copies of correspondence that identified Freese's old address, I was able to pick up the search. Although Mrs. Freese had also passed away, her son still lived in that same house and answered my letter.

Unfortunately, the son did not know if any of his father's work on dissections had survived. When the son was hospitalized with cancer in 2002, his cousin and designated heir started to clean out the house. Finding an unopened letter from me to her cousin alerted her to the existence and importance of the manuscript, which she then located several months later. What a thrill, to bring this legendary manuscript back from the brink of oblivion!

And how fascinating to examine this time capsule from the 1950s! The inventiveness that Freese brought to his geometric explorations is impressive. There are some remarkable gems, such as the 6-piece dissection of a regular dodecagon to a regular hexagon, or the 9-piece dissection of an unusual cross to a square, which is a double application of the so-called completing-the-tessellation technique. The range of new dissection puzzles is breathtaking. The graphic beauty of the pages is stunning: elegantly laid out drawings, with meticulously dotted dimensions and selective thickening of well-chosen line segments and letters, and the lovely text, with stylized, slanted lettering and numbers. What a feast for the eyes! Freese laid out each plate in pencil on an 8 1/2-by-11-inch sheet of paper, often with narrow margins.

The manuscript does have its problems. First, there is a frustrating lack of citations. Freese was aware of at least some but probably not all of the dissection work that preceded his. For example, did he know about the techniques of Harry Hart (1877) for transforming two similar copies of one figure to another? Or did he discover anew his limited version of them? Second, there is no introduction to the manuscript. We can only infer how Freese hoped readers would receive his work and what he thought of it. Third, Freese named various techniques but neither defined nor explained them. Finally, he made claims that are either wrong or for which neither he nor anyone else before or since has provided any substantiation.

Who was Ernest Irving Freese, and how had he come to craft his mesmerizing manuscript? Born in 1886 in Minneapolis, Minnesota, Freese was the older of two children of a cooper who had migrated there from Maine. He quit school after the eighth grade and entered the employ of an architect, working as a draftsman and as a construction superintendent. From 1911 to 1923, Freese was associated with a Los Angeles firm and claimed to be in complete charge of all of its architectural and structural design. Subsequently, he practiced architecture independently, aside from being the key man on army and navy projects in the First and Second World Wars. In a 1948 response to a query from the A. N. Marquis Company, Freese volunteered the following self-characterization:
Belong to no society, association, club, church or political organization: in fact am hated most cordially by most of them! Strictly a "lone wolf" who never knows which side of the fence his bread is buttered on, nor cares.
After his formal schooling, Freese continued his education through self-study and writing. He studied geometry, trigonometry, and calculus, producing exquisitely drafted notebooks. Over three decades, starting in 1912, Freese published more than a hundred articles on topics such as architectural drafting, house design, structural design, Hawaiian culture, and motorcycling. Some of the articles formed series, including a five-part series on perspective projection which blossomed into an influential book, a 22-part series series on architectural drafting, and a 14-part series on structural design. Taken as a whole, his articles demonstrated singular initiative and talent in proceeding with writing projects. With this substantial record under his belt, it is not so surprising that he would create his remarkable manuscript late in his life.

More information:

Table of contents.

Index of Dissections. (Sorry that I didn't include this index in the book itself---but better late than never! And a big thank-you to Rick Mabry for encouraging me to produce this index!)

publisher's announcement.

Comments, reviews, and news.

announcement in Purdue Today 4/13/2018 (under "Notables").

Updates and corrections.

A photo gallery

Reflections on the length of the title

Past and future events.



Last updated December 5, 2018.