On a conjecture by Auerbach
Summary: 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, which are the planar sets whose bisecting chords all have 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 the so-called ``Auerbach triangle''. We prove this conjecture.
scientific article; zbMATH DE number 5971511
scientific article