# Edward Scheinerman on Discrete Mathematics and Mechanical Engineering

In order for a robot to calculate its path across, say, a factory floor, it must first know where it is starting from. One expensive way to do this is to use lasers beams that shoot from the robot to the walls of the room; the beams measure the distance to the walls, and those distances can be used to calculate the robot's position. A clever new method was described in the lively lecture about applications of mathematics to mechanical engineering by Edward Scheinerman of Johns Hopkins University. In Scheinerman's method, inexpensive sensors are attached to the bottom of the robot, and a distinctive pattern of black and white squares is painted on the floor. As the robot moves across the floor, the sensors detect information about the floor pattern, and the robot uses that information to calculate its position. The mathematical concept of de Bruijn sequences is used to create the pattern for the floor. Scheinerman calculated that the sensing and computing costs of this method were very low; his engineering colleagues then joked that his method required a "million-dollar floor" because of the special pattern. In fact, it would be reasonable to invest in such a floor, which can be used over and over, rather than in the robots, which tend to break down. Scheinerman discussed a number of other problems in mechanical engineering for which mathematics can provide new insights and solutions.

--- Allyn Jackson, Deputy Editor, Notices of the AMS

[This AMS-MAA Invited Address was given January 15.]