Occidental College mathematics professor Ramin Naimi has received the George Pólya Award from the Mathematical Association of America for his article, co-authored with Curtis Feist, "Topology Explains Why Automobile Sunshades Fold Oddly." The paper appeared in the College Mathematics Journal last year.
In their article, Naimi and Feist examine "automatic folding" sunshades that coil up when not in use. From the authors' experience, it seems impossible simply to fold such a sunshade in half (i.e., coil it into exactly two loops). The object of their article was to figure out how many loops can appear in the coil and to understand why.
The result is an engaging expedition into braid theory, a branch of knot theory. Specifically, the paper uses the concepts of braid position and linking number to investigate which numbers can be, and which cannot be, the number of coils in a closed sunshade.
"Braid position and linking number give students a nice demonstration that ‘abstract' mathematics can actually be quite visual and intuitive," says Laura McHugh of the MMA. "This article is a clear and well-illustrated introduction to an interesting and accessible branch of topology, and it is also a reminder that we should be on the lookout for mathematics everywhere we go. Finally, to those of us who have wrestled with those sunshades in an innocent but futile attempt to fold them in half, the article provides reassurance. It's not you, Feist and Naimi tell us: it's the topology."
Naimi obtained his Ph.D. in topology from Caltech in 1992 and has taught at Occidental since 1998. He enjoys collaborating in research and is currently working on projects involving symmetry groups of graphs embedded in 3-D space, and knots and links in spatial graphs.
The George Pólya Awards, established in 1976, are presented to authors of expository articles published in the College Mathematics Journal. The awards are named for George Pólya, a distinguished mathematician, well-known author, and professor at Stanford University.
Curtis Feist received his B.S. and M.S. from Cal Poly San Luis Obispo, and his Ph.D in topology from UC Davis. He is an associate professor of mathematics at Southern Oregon University.