Mathematics desk
< October 8	<< Sep \| October \| Nov >>	October 10 >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

October 9

Pappus's hexagon theorem

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]