数学建模竞赛1995 A C Author’s Commentary The Outstanding Helix Intersections Papers参考.pdfVIP

Author’s Commentary 257 Author’s Commentary: The Outstanding Helix Intersections Papers Yves Nievergelt Dept. of Mathematics Eastern Washington University Cheney, Washington 99004 ynievergelt@ewu.edu The problem of computing all the intersections of a plane and a helix in general positions in space arose at a small company in the western U.S. that designs medical technology. The problem came in the design of a helicoidal part of a device that doctors and technicians together will have to manufac- ture to fit the particular measurements of each patient. With x-ray data from the patient loaded in a computer with numerical and three-dimensional graphics capabilities, and with a program to compute the requested inter- sections, doctors and technicians can quickly vary the parameters of the helix, view the helicoidal part superimposed in space with a model of the patient, and examine critical locations by sweeping a plane section through them. The mathematically accurate yet medically vague description given in the problem statement typifies a common situation of real applications of mathematics: The small start-up company does not want anyone else to know the object of its current research and development. Even the com- pany’s name must remain secret, lest anyone else conduct a computed search of the publications of the company’s staff and thence piece together a good guess of the objective. Such a situation explains, in part, the dearth of real applications of mathematics in textbooks. Nevertheless, because the mathematical problem fits in most undergrad- uate curricula in the mathematical sciences, one solution is scheduled to appear in 1995 in SIAM Review, published by the Society for Industrial and Applied Mathematics. The solution was developed in part with support from the National Science Foundation’s grant DUE–9255539. Inst