Geodesic
A Physical Archimedean Approach to Affine Geometry and the Remarkable 13 (Mixed) Configuration
Journal for geometry and graphics, Tome 26 (2022) no. 1, pp. 65-8 Cet article a éte moissonné depuis la source Heldermann Verlag

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We show how to introduce affine geometry via a calculus of balancing weights respecting Archimedes� law of the lever, relying on a fundamental associativity which is simply expressed with multiplicative algebra. Affine subspaces are represented by affine functionals, and vectors are interpreted as null weighted combinations of points. This is then applied to the mixed configuration of thirteen points and lines arising both from the duality between the Menelaus and Ceva theorems and the quadrangle / quadrilateral correspondence.
Classification : 51N10, 51N05
Mots-clés : Geometry, affine, Menelaus, Ceva, Archimedean, configuration 
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J. C. Ho; N. J. Wildberger . A Physical Archimedean Approach to Affine Geometry and the Remarkable 13 (Mixed) Configuration. Journal for geometry and graphics, Tome 26 (2022) no. 1, pp. 65-8. http://geodesic.mathdoc.fr/item/JGG_2022_26_1_JGG_2022_26_1_a9/