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October 9[edit]

Pappus's hexagon theorem[edit]

I found a proof by analytic geometry for the Pappus's hexagon theorem here. Does anyone know if it could be described any simpler? יהודה שמחה ולדמן (talk) 22:46, 9 October 2017 (UTC)[reply]

It's basically a special/limiting case of Pascal's theorem, so you can adapt any of the proofs from that article; I'm especially fond of the proof using Bezout's theorem. This is a theorem on projective geometry, so things will go much more smoothly with projective coordinates rather than Cartesian coordinates. --RDBury (talk) 02:55, 10 October 2017 (UTC)[reply]

I understand "regular hexagon", I am happy with a non-regular hexagon. Can you really call six lines intersecting with each other a hexagon? Seems wrong somehow. So why is AbCaBc considered to be a hexagon? -- SGBailey (talk) 06:38, 10 October 2017 (UTC)[reply]

@SGBailey:, a polygon is defined as "a plane figure that is bounded by a finite chain of straight line segments closing in a loop". This includes self-intersecting polygons. Rojomoke (talk) 06:57, 10 October 2017 (UTC)[reply]

But I think the statement Regular specifically implies the concave version. Otherwise a regular pentagram would be considered one of two types of regular pentagon.Naraht (talk) 20:38, 10 October 2017 (UTC)[reply]