Remarks on the theorem of Napoleon (Q1312694)

Napoleon's theorem (``The circumcentres of the equilateral triangles constructed outward on the sides of a triangle \(ABC\) are the vertices of an equilateral triangle'') has been generalized by \textit{K. Schütte} [Math. Semesterber. 34, 256-268 (1987; Zbl 0698.51006) and Elem. Math. 44, No. 5, 133-138 (1989; Zbl 0698.51007)] by weakening the hypothesis to ``the sum of the angles \(\alpha,\beta,\gamma\) (of the constructed triangles) facing the sides \(BC\), \(CA\), \(AB\) is \(\pi\)'' and the conclusion to ``the vertices of the triangle formed by the circumcentres are \(\alpha, \beta, \gamma\)''. The author of this note states and proves this generalization by using the concept of oriented angle, which he developed in Geom. Dedicata 36, No. 2/3, 239-260 (1990; Zbl 0714.51005).