Inserted: 19 jan 2010
Last Updated: 16 feb 2015
In 1938 Herman Auerbach published a paper where he showed a deep connection between the solutions of the Ulam problem of floating bodies and a class of sets studied by Zindler, that are the planar sets whose bisecting chords have all the same length. In the same paper he conjectured that among Zindler sets the one with minimal area, as well as with maximal perimeter, is given by the so-called ``Auerbach triangle''. We prove here that his conjecture was true.