Grünbaum, BrankoKlamkin, Murray S.2005-11-302005-11-302005Mathematics Magazine vol. 79(2006), pages 122 – 130.0025-570Xhttp://hdl.handle.net/1773/2213A theorem of Euler concerns sums of ratios in which Cevians of a triangle are divided by a common point. Generalizations of this result in three directions are presented: polygons instead of triangles, higher-dimensional polytopes, and several kinds of ratios.159168 bytesapplication/pdfen-USpolygonpolytopeCevianSegment-ratiosArticle