منابع مشابه
Orthopoles and the Pappus Theorem
If the vertices of a triangle are projected onto a given line, the perpendiculars from the projections to the corresponding sidelines of the triangle intersect at one point, the orthopole of the line with respect to the triangle. We prove several theorems on orthopoles using the Pappus theorem, a fundamental result of projective geometry.
متن کاملA geometric identity for Pappus' theorem.
An expression in the exterior algebra of a Peano space yielding Pappus' theorem was originally given by Doubilet, Rota, and Stein [Doubilet, P., Rota, G.-C. & Stein, J. (1974) Stud. Appl. Math. 8, 185-216]. Motivated by an identity of Rota, I give an identity in a Grassmann-Cayley algebra of step 3, involving joins and meets alone, which expresses the theorem of Pappus.
متن کاملGENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES
The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.
متن کاملPappus-Desargues digraph confrontation
Like the Coxeter graph became reattached into the Klein graph in [3], the Levi graphs of the 93 and 103 self-dual configurations, known as the Pappus and Desargues (k-transitive) graphs P and D (where k = 3), also admit reattachments of the distance-(k − 1) graphs of half of their oriented shortest cycles via orientation assignments on their common (k−1)-arcs, concurrent for P and opposite for ...
متن کاملPappus in optical space.
Optical space differs from physical space. The structure of optical space has generally been assumed to be metrical. In contradistinction, we do not assume any metric, but only incidence relations (i.e., we assume that optical points and lines exist and that two points define a unique line, and two lines a unique point). (The incidence relations have generally been assumed implicitly by earlier...
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ژورنال
عنوان ژورنال: Demonstratio Mathematica
سال: 2009
ISSN: 2391-4661
DOI: 10.1515/dema-2013-0181