Pappus's hexagon theorem

proper noun

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.

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Meanings

proper noun
  1. geometryA 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.

Origin

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

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Cite this entry
APA

Pappus's hexagon theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Pappus's%20hexagon%20theorem

MLA

“Pappus's hexagon theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Pappus's%20hexagon%20theorem. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Pappus's hexagon theorem,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Pappus's%20hexagon%20theorem.

Source: Pappus's hexagon theorem on Wiktionary, CC BY-SA 4.0.