On a formula for sets of constant width in 2d
Analysis and Geometry Seminar
2nd October 2018, 3:00 pm – 4:00 pm
Howard House, 2nd Floor Seminar Room
Leonhard Euler considered around 1774 curves in 2d with he called 'curva orbiformis' and he gave an analytic formula that describes such curves. Although Meissner around 1910 considered Fourier series, he used geometrical arguments in his approximations. Hammer and Sobczyk in the 1950's called these curves 'curves of constant breadth', meaning of constant directional width, and gave an elaborate construction in a series of three papers. Through the centuries many other mathematicians were intrigued by these figures both in 2 and 3 dimensions and one expects that most is known, especially in the simpler 2d-case. Indeed no new result will be presented in the seminar except that in a joint work with Bernd Kawohl we exploited an alternative formula for the 2d-case, that allows us to give short proofs for several tedious approximation results by Meissner (±1910), Hammer-Sobczyk (±1953), Tanno (1976) and Wegner (1977).