Some New Transversality Properties |
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Authors: | Branko Grünbaum G C Shephard |
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Institution: | (1) Department of Mathematics, University of Washington, Seattle, WA, 98195, U.S.A; e-mail;(2) School of Mathematics, University of East Anglia, Norwich NR4, 7TJ, England. e-mail |
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Abstract: | The theorems of Ceva and Menelaus are concerned with cyclic products of ratios of lengths of collinear segments of triangles or more general polygons. These segments have one endpoint at a vertex of the polygon and one at the intersection point of a side with a suitable line. To these classical results we have recently added a selftransversality theorem in which the suitable line is determined by two other vertices. Here we present additional transversality properties in which the suitable line is determined either by a vertex and the intersection point of two diagonals, or by the intersection points of two pairs of such diagonals. Unexpectedly it turns out that besides several infinite families of systematic cases there are also a few sporadic cases. |
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Keywords: | Ceva Menelaus selftransversality transversal polygon cyclic product |
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