Generalizations of Pappus’ centroid theorem via Stokes’ theorem
نویسندگان
چکیده
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.
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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.
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2015
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2015.8.771