A simple proof for the theorems of Pascal and Pappus. (English) Zbl 0889.51025

Let \(\phi\) be a conic and \(1,2,\dots,6 \in \phi\) a hexagon. Consider \(\phi\) as intersection of a quadric \(\Phi\) with a plane \(\pi\) of symmetry. The author introduces cones \(\Gamma\) and \(\Delta\) symmetric to \(\pi\) such that the lines \(12\) and \(34\) are generators of \(\Gamma\) and the lines \(45\) and \(61\) are generators of \(\Delta\). He derives Pascal’s theorem by studying the intersections of \(\Phi\), \(\Gamma\), and \(\Delta\). A modification leads to the theorem of Pappus. Obviously, the author has only the real case in mind.


51M15 Geometric constructions in real or complex geometry
51M99 Real and complex geometry
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