Pappus's hexagon theorem

English

Etymology

Attributed to the Ancient Greek mathematician Pappus of Alexandria (c. 290–c. 350 AD).

Proper noun

Pappus's hexagon theorem

1. (geometry) A theorem valid for projective planes over any field, stating that, given one set of collinear points $A,B,C,$ and another set of collinear points $a,b,c,$, the intersection points $X,Y,Z$ of line pairs $Ab$ and $aB,Ac$ and $aC,Bc$ and $bC$ are collinear, lying on the "Pappus line". These three points are the points of intersection of the "opposite" sides of the hexagon $AbCaBc$.

Related terms

• Pappian
• Pappus line