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Journal for Geometry and Graphics 26 (2022), No. 1, 065--080
Copyright Heldermann Verlag 2022

A Physical Archimedean Approach to Affine Geometry and the Remarkable 13 (Mixed) Configuration

Joshua C. Ho
University of New South Wales, Sydney, Australia

Norman J. Wildberger
University of New South Wales, Sydney, Australia

We show how to introduce affine geometry via a calculus of balancing weights respecting Archimedesí 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.

Keywords: Geometry, affine, Menelaus, Ceva, Archimedean, configuration.

MSC: 51N10; 51N05.

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