Aiding the Teaching of Geometry and Affording Mathematical Recreation: Paper Folding in the Spirit of Sundara Rao of Madras – Conclusion

A number of disparate trends in the history of mathematics education came together in the small book by Sundara Rao. Inspired by Froebel’s kindergarten occupations, he considered how paper folding might be used to teach geometry. Geometrical Exercises in Paper Folding, published by Addison & Company in Madras in 1893, was noted in the Mathematical Gazette in 1894 and commended in an 1894 letter to Nature by mathematics teacher and founding editor of the Gazette Edward M. Langley. Perhaps through these references, the work came to the attention of the distinguished German mathematician Felix Klein, who mentioned it in one of his works. This reference in turn inspired two American mathematicians, David Eugene Smith and Wooster Woodruff Beman, to publish an American edition of Rao’s book, enhancing the presentation by adding photographic illustrations. Thus, Rao himself responded to various components of 19th-century efforts to reform the teaching of geometry, and the reception of his book threaded through a number of the organizations, publications, and individuals associated with those reform efforts.

Furthermore, the apparent influences on Rao and the subsequent discussions of Geometrical Exercises all affirmed that paper folding was an appropriate mathematical activity for a broad age range of students. Recall that Rao wrote in his preface:

I have sought not only to aid the teaching of Geometry in schools and colleges, but also to afford mathematical recreation to young and old, in an attractive and cheap form [Row 1893, p. vi].

The story of recreational paper folding additionally involved an expansive geographical area— spanning Germany, Great Britain, India, and the United States—and was shaped by the shifting geopolitical relationships between these nations in the late 19th century, most notably the British colonial administration of India that employed Rao, exposed him to British approaches to geometry teaching, and opened up markets for his book . . . but presumably also constrained his career in ways that are impossible to measure more than a century later. Nonetheless, and even though its direct pedagogical impact was limited, Geometrical Exercises found an enthusiastic audience among those engaged in mathematical recreations. It remains in print to this day.