Cubes, Conic Sections, and Crockett Johnson - Conclusion and About the Authors

Conclusion

For thousands of years, construction problems have captivated the imaginations of both professional and amateur mathematicians and, because of this interest, significant contributions to mathematics have been made while attempting to solve these problems.  Many of the propositions in Euclid’s Elements are actually construction problems.  As we have seen, conic sections arise in attempts to solve the early Greek construction problem we know as duplication of a cube.  Continued fascination with constructions, and specifically with the duplication of a cube, gave amateur mathematician and professional children's author Crockett Johnson inspiration for many of his mathematical paintings.  Along the way, he framed the question “What do the straightedge lines and compass arcs do when two parabolas and a hyperbola double a cube, just stand watching?”

To see images of 80 mathematical paintings by Crockett Johnson, visit Mathematical Paintings of Crockett Johnson, an online exhibit by the Smithsonian Institution's National Museum of American History.

To learn more about Crockett Johnson visit the Crockett Johnson Homepage.

About the Authors

Stephanie Cawthorne received a 1992 B.S. from Eastern Nazarene College, and a 1998 Ph.D. from the University of Maryland under the direction of David Kueker.  After spending the first part of her career at Marymount University in Arlington, VA, she is now Professor of Mathematics at Trevecca Nazarene University.  Her initial research was in mathematical logic in the area of model theory and, through the influence of Judy Green, she has become interested in the history of mathematics and the works of Crockett Johnson. 

Judy Green received a 1964 B.A. from Cornell University, a 1966 M.A. from Yale University, and a 1972 Ph.D. from the University of Maryland under the direction of Carol R. Karp.  She is now Professor Emeritus of Mathematics having spent the first half of her career at Rutgers University in Camden, NJ, and the second half at Marymount University in Arlington, VA.  Her early papers are in mathematical logic, the field of her dissertation, but she soon switched her research interests to the history of women in mathematics.  She first learned of the mathematical paintings of Crockett Johnson during a 1980 sabbatical spent studying the historiography of mathematics with Uta C. Merzbach at the Smithsonian Institution.