Abstract
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.
Sponsored by U. S. Army Research Office, P. O. Box 12211, Research Triangle Park, North Carolina 27709, under Contract No. DAAG29-75-C-0024.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Douglas, Jesse, Geometry of polygons in the complex plane. J. of Math, and Phys. 19 (1940), 93–130.
Douglas, Jesse, On linear polygon transformations. Bull. Amer. Math. Soc. 46 (1940), 551–560.
Douglas, Jesse, A theorem on skew pentagons. Scripta Math. 25 (1960), 5–9.
Schoenberg, I. J., The finite Fourier series and elementary geometry, Amer. Math. Monthly 57 (1950), 390–404.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer-Verlag New York Inc.
About this paper
Cite this paper
Schoenberg, I.J. (1981). The Harmonic Analysis of Skew Polygons as a Source of Outdoor Sculptures. In: Davis, C., Grünbaum, B., Sherk, F.A. (eds) The Geometric Vein. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5648-9_10
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5648-9_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-5650-2
Online ISBN: 978-1-4612-5648-9
eBook Packages: Springer Book Archive