Convex sets of constant widthЛекция
When does a steel pipe have an exactly circular cross section? When it features constant exterior width from every angle? That could easily be verified with a big caliper or slide gauge, and this procedure was used in the process of assembling booster rockets for the space shuttle. The authors of the corresponding manuals had overlooked that there are geometric shapes, so-called sets of constant width, that are not circles. This was a contributing factor to the Challenger disaster in 1986. In my talk I will point out that these odd sets show up in our daily life, how their knowledge can be used to drill square holes, and that there are interesting mathematical questions connected with them. The talk is directed at a general mathematical audience.