An Image for Tom's 65^{th} Birthday
Images from Siegle's Web Page

Greg Siegle '91Under Tom's guidance, I inherited the Vector code from Rashid Ahmad in 1988 and used it in TA'ing (the first?) computer labs for Math 35, third semester calculus, which Tom taught. This software allowed students to visualize parameterized surfaces, and concepts relevant to Math 35, such as normals and gradients. The following year, Tom helped me organize a Group independent study in mathematical visualization, for which he served as Instructor/Coach. With Tom's guidance, Curtis Hendrickson, Matthew Stone, Cassidy Curtis, Jeff Achter, and I wrote the second itteration of Vector, which featured attractive color graphics, the ability to create animations, and a command language. Tom used these features to enhance his Math 35 and differential geometry labs, making them quite popular. Students could readily interact with the beauty in mathematics, a pursuit that often eludes people who do not devote their lives to the subject. It was wild to see students stay long after labs were nominally over just to get a function to spin around the way they were seeing it in their heads. The immediate benefits of working with Tom involved an appreciation for mathematical visualization, its history, and possibly most importantly, how it could be used to inspire others and explain difficult mathematical concepts. Since then I've constantly used threedimensional visualization in both my mathematics courses as well as courses I've taught in other disciplines. One of the most important uses of the interactive teaching style I learned from Tom came in 1993 when I gave a guest lecture in an experimental mathematics class at Norhtwestern University. The class dealt primarily with fractals and nonlinear dynamics, for which powerful graphics and handson experimentation were considered necessary to understand. My lecture was devoted to showing how understanding nonchaotic functions, specifically variants of lissajous figures, could also benefit from visualization and experimental manipulation. We'd installed Vector on a Sun in the classroom and had used it to derive the formula for a Möbius strip with five twists, a function Tom had shown me. As the strip rotated horizontally, a woman I knew in the back of the class, who'd had some difficulty visualizing surfaces in the past, said that she believed this function might be interesting to look at from above. Fortunately Vector allowed us to see the surface from a birdseyeview. As the beautiful fivepointed star was revealed, the class gasped. The woman who asked the question and I became engaged a short time later and we're still married. The bond we continue to share involving visualization and discussion of mathematical functions, started that day. Another important benefit of working with Tom was his willingness to include students in his professional endeavors, which socialized us to academic life. Tom's having included me as an author on two papers about Vector was, I'm sure, important to my admission to graduate school. Today I'm an Assistant Professor in the department of Psychiatry at the University of Pittsburgh. My primarily research involves brain imaging, which necessitates regular visualization of at least fourdimensional data sets. Lessons learned from working with Tom are constantly employed in both my research and in lectures on statistical concepts. Visualization of parametrically defined mathematical functions is still a hobby. A recent picture of me is up at my web site, which also has a link to some functions I've more recently played with. Thanks Tom, for all your inspiration and education.


