The Harmonic Analysis of Skew Polygons as a Source of Outdoor Sculptures

The previous paper [4] on the subject of the finite Fourier series (f.F.s.) dealt with some known and some new applications to problems of elementary geometry. In the present second paper we apply it to a beautiful theorem of Jesse Douglas [3] on skew pentagons in space. It is shown here that Douglas’s theorem amounts to the graphical harmonic analysis of skew pentagons and that it is also the source of striking outdoor sculptures. This last opinion is shared by two great art experts, Allan and Marjorie McNab, whom I wish to thank for their encouragement.