Article from: The UMAP Journal Fall 1995 pages 251-253

Judge's Commentary:
The Outstanding Single Helix Papers

Typical industrial tasks for applied mathematicians are varied and many require a computational approach to solve a relatively simple problem. The single helix problem of the MCM was representative: the problem statement, solution techniques to be used, interpretation of the result, and techniques for checking the answer were all straightforward. Most of the submissions did, in fact, perform nearly all of the above steps. The judging criteria focused on how well each step was carried out as well as the overall organization and clarity.

Of course, really outstanding papers not only solve the problem, but they also consider possible extensions and possible limitations. Do these make the problem easier or harder? Do they make the problem applicable to another field? Restricting the problem to a finite length helix (which is more physically reasonable) was considered by several teams, including the teams from Harvey Mudd College and Iowa State University. Using a finite area sweeping plane was consider by the team from Harvey Mudd College. Additionally, one team considered more general helices, such as a spiral drawn on a cone.

About the Author

Daniel Zwillinger received an undergraduate degree in mathematics from MIT and a PhD in applied mathematics from Caltech. His PhD research dealt with the focusing of waves as they traveled through random media. He taught at RPI for four years, worked in industry for several years, and has been managing a consulting group for the last few years. His work areas have included many industrial mathematics needs: radar, sonar, communications, visualization, statistics, and computer aided design. He is the author of several mathematical reference books.