How to sum up triangles

2002/03/03 by F. Bakharev, Bakharev, F., K. Kokhas +3
Mathematics · #51A20 #51A30 #51E15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:51A20 #msc:51A30 #msc:51E15

paper · pdf · doi:10.48550/arxiv.math/0203022

12 pages (LaTeX), 7 figures (epsfig)

arxiv created 2002/03/03 · arxiv updated 2009/11/30

Abstract

We prove configuration theorems that generalize the Desargues, Pascal, and Pappus theorems. Our generalization of the Desargues theorem allows us to introduce the structure of an Abelian group on the (properly extended) set of triangles which are perspective from a point. In barycentric coordinates, the corresponding group operation becomes the addition in R³.

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