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Cyclic product theorems for polygons. II. Constructions using conic sections. (English summary) Discrete Comput. Geom. 26 (2001), no. 4, 513–526. If a point Ui is chosen on each edge of a plane n-gon P, then the product of the n signed ratios in which the points Ui divide the edges of P is called a cyclic product for P. The problem is to find geometric constructions for the Ui such that, for every n-gon P, the cycle product takes a fixed value. Classical examples are the theorems of Menelaus and Ceva. The author’s Part I: Constructions using circles [Discrete Comput. Geom. 24 (2000), no. 2-3, 551–571; MR1758071 (2001g:51014)] is here followed by Part II: Constructions using conic sections. Classical synthetic methods are used to prove complicated conjectures suggested by computer experiments

Year: 1769

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