<span class="mw-page-title-main">Pappus&#039;s hexagon theorem</span>

Pappus's hexagon theorem

In mathematics, Pappus's hexagon theorem states that  It holds in a projective plane over any field, but fails for projective planes over any noncommutative division ring. Projective planes in which the "theorem" is valid are called pappian planes. If one restricts the projective plane such that the Pappus line 
  
    
      
        u
      
    
    {\displaystyle u}
  
 is the line at infinity, one gets the affine version of Pappus's theorem shown in the second diagram. 