Triangles inscribed in simple closed curves (Q1196144)

Papers by \textit{M. D. Meyerson} [Fundam. Math. 110, 1-9 (1980; Zbl 0372.57003)] and \textit{E. H. Kronheimer} and \textit{P. B. Kronheimer} [J. Lond. Math. Soc., II. Ser. 24, 182-192 (1981; Zbl 0423.52001)] contain proofs that given any triangle \(T\) and any simple closed curve \(J\) there is a triangle similar to \(T\) having its vertices on \(J\) (inscribed \(J\)). Here these considerations are generalized by showing the following theorem: Let \(J\) and \(T\) be as above. Then \(J\) admits infinitely many inscribed triangles similar to \(T\). More specifically, if \(v\) is a vertex of smallest angle in \(T\) then the set \(\{ p\in J | p\) is a vertex corresponding to \(v\) in a triangle similar to \(T\) and inscribed in \(J\}\) is dense in \(J\).