The four-vertex theorem of a plane curve and its generalizations (Q2760851)

The author discusses both the classical four-vertex theorem and its recently discovered space version which says that every smooth closed curve in the Euclidean 3-space which is weakly convex and has nonzero curvature has at least 4 flattening points. The latter theorem was first published in [\textit{V.~D.~Sedykh}, A theorem on four vertices of a convex space curve. Funct. Anal. Appl. 26, No. 1, 28-32 (1992; Zbl 0777.53004)]. NEWLINENEWLINENEWLINEThe article is based on a lecture given by the author for secondary school teachers in the framework of the ``International Soros Science Educational Program'' and is aimed at presenting contemporary developments in mathematics on an elementary level understandable for secondary school teachers and pupils.