Abstract
If a point U i is chosen on each edge of a plane n -gon P , then the product of the n signed ratios in which the points U i divide the edges of P is called a cyclic product for P . The problem is to find geometric constructions for the U i such that, for every n -gon P , the cyclic product takes a fixed value. Many constructions are known which use lines or circles. Here we describe constructions that use conic sections.
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Received August 23, 2000, and in revised form November 27, 2000. Online publication May 4, 2001.
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Shephard, G. Cyclic Product Theorems for Polygons (II) Constructions using Conic Sections. Discrete Comput Geom 26, 513–526 (2001). https://doi.org/10.1007/s00454-001-0025-z
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DOI: https://doi.org/10.1007/s00454-001-0025-z