High Quality Content by WIKIPEDIA articles! In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points x, y, z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear. (Collinear means the points are incident on a line.) It holds in the projective plane over any field, but fails for the projective plane over any non-commutative division ringThe dual of this theorem states that given one set of concurrent lines A, B, C, and another set of concurrent lines a, b, c, then the lines x, y, z defined by pairs of points resulting from pairs of intersections A?b and a?B, A?c and a?C, B?c and b?C are concurrent. (Concurrent means that the lines pass through one point.)

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