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A new Ceva-type theorem

Published online by Cambridge University Press:  01 August 2016

Branko Grünbaum  and
G. C. Shephard
Branko Grünbaum
Affiliation:
Department of Mathematics, University of Washington, Seattle, WA 98195 USA, B .Grunbaum@math.washington. edu
G. C. Shephard
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR14 7TJ, G.Shephard@uea.ac.uk
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Extract

The classical theorems of Ceva and Menelaus make assertions about the value of certain products of ratios of lengths in configurations in the affine plane. We shall use the term Ceva-type to describe any result of this general kind: one that specifies a configuration in affine space of n dimensions, defined only by incidences, about which one can make an assertion about a product of ratios of lengths, areas, etc. Several results of this kind are known. Apart from the classical results there are, for example, Ceva's and Menelaus' Theorems for n-gons, Hoehn's Theorem for pentagrams [1], and the Selftransitivity Theorem of [2].

Type
Articles
Information
The Mathematical Gazette , Volume 80 , Issue 489 , November 1996 , pp. 492 - 500
Copyright
Copyright © The Mathematical Association 1996

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References

1. Hoehn, L. A Menelaus-type theorem for the pentagram, Math. Mag. 66 (1993) pp. 121–123.CrossRefGoogle Scholar
2. Grünbaum, B. and Shephard, G. C. Ceva, Menelaus and the area principle, Math. Mag. 68 (1996) pp. 254–268.CrossRefGoogle Scholar
3. Grünbaum, B. and Shephard, G. C. Ceva, Menelaus and CMS-diagrams (to appear in Geometriae Dedicata).Google Scholar