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

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

Mabel Sykes (1868–1938) was a high-school mathematics teacher in Chicago at the start of the twentieth century. She authored textbooks and journal articles and served the greater mathematical community while teaching for almost four decades in the public school system. We share her biography and highlight her incredible compendium of geometry problems based on architectural design. We also provide GeoGebra applets to illustrate several of these designs.

As a real-world source for problems in Euclidean geometry, iconic buildings with ornate design—such as the Alhambra in Spain, the Taj Mahal in India, the Library of Congress in Washington, DC, or Westminster Abbey in England—offer interesting examples of shape and symmetry. Imagine the effort required to compile nearly 2000 exercises and 500 illustrations based on over one hundred such structures around the globe. Now imagine the level of scholarship necessary to do this a century ago, without our ease of travel and communication, not to mention our embarrassment of online resources. Published in 1912, Mabel Sykes’ A Source Book of Problems for Geometry Based upon Industrial Design and Architectural Ornament is an amazing example of scholarship that accomplishes this feat. In her preface Sykes offered the understatement, “Hitherto much material from geometric designs or historic ornament suitable for class use could be obtained only by long and careful search through widely scattered sources.” The compilation she created went well beyond surmounting these obstacles. As a testament to its continued relevance, this book was reprinted in 1994. It was through this reprinting that we learned of and became intrigued with Mabel Sykes.

In the reprint's preface, publisher Dale Seymour challenged readers to investigate Mabel Sykes so that his press could share any uncovered information. His query reflected the reality that in the pre-internet era biographical information on minor figures in the history of mathematics, such as Sykes, was not easily found. Even now, she has not been profiled in any history of mathematics books or websites with a focus on women in mathematicians. Had she completed a Ph.D., she would have garnered some attention, at the very least as a statistic in Judy Green and Jeanne LaDuke's 2009 Pioneering Women in American Mathematics: The Pre-1940 PhD’s [8]. While this article is certainly in answer to Seymour’s challenge from 25 years ago, our fascination with Sykes and her story is due even more to our admiration and awe at the breadth and depth of the collection of problems she created for her Source Book. Here, we champion this little-known mathematics scholar with the help of a tremendous amount of internet sleuthing.

Mabel Sykes in 1923.

Maureen T. Carroll (University of Scranton) and Elyn Rykken (Muhlenberg College), "Mabel Sykes: A Life Untold and an Architectural Geometry Book Rediscovered," Convergence (February 2020), DOI:10.4169/convergence20200201