Harry Lewis '68 flicked a switch in front of him. Orange lights began to flash, a blue cross flitted about the computer screen like Tinkerbell, and a circle on the screen was slowly--dot by dot--transformed into an airplane wing.
As Lewis gave instructions by running an electric "pen" across a network of pulsating wires, the machine first changed the circle into a flower, and then transformed the flower into a butterfly.
Lewis was lecturing via closed-circuit television in Applied Math 201, a graduate-level course which he took last year as a junior. He was demonstrating a technique he invented over the summer which makes it possible to visualize in a matter of minutes a complex mathematical transformation.
A television camera transmitted the pictures on the screen from the Cruft Hall computer room to the classroom in Pierce Hall and a loudspeaker hookup enabled students to hear Lewis' voice. After the lecture, students asked questions which Lewis could hear in Cruft, and he answered them.
Although closed circuit television has been used in applied math courses before, it has always been to demonstrate some aspect of how to program a computer, Anthony G. Oettinger, Gordon McKay Professor of Applied Mathematics, said yesterday. This was the first time it had been done actually to teach mathematics.
Lewis designed the program this summer, working on the staff of Technological Aids to Creative Thought (TACT). He can only map the circle a dozen different ways at present, but he said that within a few months he expects to be able to distort the circle to any algebraic map that a person could write out in his own handwriting on the computer tablet.
Conformal mappings, as these distortions are called, are important in the study of the effect of forces on bodies, such as the effect of wind currents on an airplane wing.