Mabel Sykes: A Life Untold and an Architectural Geometry Book Rediscovered – Textbooks

Maureen T. Carroll (University of Scranton) and Elyn Rykken (Muhlenberg College)

Sykes put the teaching principles espoused in her articles into practice in her books on geometry and algebra, which included A Source Book of Problems for Geometry Based upon Industrial Design and Architectural Ornament (1912), Plane Geometry (1918, 1922 and 1932), Solid Geometry (1922 and 1933), Beginner’s Algebra (1922), A Second Course in Algebra (1924), and Key to Plane Geometry (1926). All but the Source Book are textbooks co-authored with Clarence E. Comstock, a professor at Bradley Polytechnic Institute in Peoria, Illinois. Both Plane Geometry and Solid Geometry were revised in the 1930s with an added co-author, Charles M. Austin, a local high school teacher who was the first president of the NCTM. Regarding the distribution of work between Sykes and her major co-author Comstock, Sykes wrote, “I do the major work on the geometries and Mr. Comstock on the algebras. The geometries are really mine” [24].

While the co-authored books are traditional high-school textbooks, Sykes’ solo work stands apart as a singular scholarly achievement. In her 1912 Source Book of Problems for Geometry, Sykes used complex and beautiful architectural designs, in her own words in the preface, “the best in historic ornament,” as her inspiration for over 1800 exercises on proof, construction and computation techniques. To pique the reader’s interest, we highlight a few of these designs, accompanied by GeoGebra applets, in the Source Book section of this paper. Before presenting the book examples, we first review the standard Euclidean constructions and give Sykes’ 1906 construction of a Persian arch.