RecordNumber
122
Author
Branko Grünbaum and G. C. Shephard
Title of Article
Some New Transversality Properties
Title Of Journal
Geometriae Dedicata
PublishInfo
Springer
Publication Year
1998
Volum
71
Issue Number
2
Page
179-208
Keywords
Ceva . , Menelaus , selftransversality , transversal , polygon , cyclic product
Notes
براي دانلودو مشاهده مقاله به قسمت لينكهاي مرتبط مراجعه نماييد
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 lsquoselftransversality theoremrsquo in which the lsquosuitable linersquo is determined by two other vertices. Here we present additional lsquotransversalityrsquo properties in which the lsquosuitable linersquo 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 lsquosporadicrsquo cases.
URL
http://www.springerlink.com/content/q2hqk7816m8t3271/,/DL/Data Entry/DataEntryForm/EnterDocInfo.aspx,/DL/Data Entry/NewEdit/Documents/Math_English_Electronic_Articles_EditDoc_925.aspx