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 Oct 28 revised What is the point of having at least three points on every line of a projective plane? Updated the answer Oct 28 awarded Editor Oct 28 revised What is the point of having at least three points on every line of a projective plane? Updated the answer Oct 28 comment What is the point of having at least three points on every line of a projective plane? @StefanPerko For point b) Any structure satisfying axioms 1,2,4 and the "obvious" one: any line contains at least two points and there are at least two lines is either a "triangle" (3 points and 3 lines) a structure like in the picture or a "honest" projective plane. I'll edit the answer. Oct 28 comment What is the point of having at least three points on every line of a projective plane? @StefanPerko: For point a) see this. The lines are $12,13,14, 15$ and $12345$. Oct 26 answered What is the point of having at least three points on every line of a projective plane? Apr 17 awarded Student Apr 16 asked Dévissage for complex manifolds Dec 15 awarded Caucus Feb 3 answered Find a parametrization of the intersection curve between surfaces Aug 31 awarded Yearling Aug 26 answered Is Poincare-Hopf index theorem connected with Leftschetz fixed point theorem? Aug 6 answered Getting started with Lie Groups Aug 5 answered Rigorous Textbook for Introduction to Complex Numbers/Analysis? Aug 5 answered Why are topological spaces interesting to study? Dec 7 awarded Enthusiast Oct 22 awarded Supporter Sep 23 awarded Teacher Sep 23 answered Fluid mechanics resources for pure mathematicians?