Synthetic Proof of the Cevian Nest Theorem

Igor Minevich

March 28, 2009

Research in plane projective geometry was perhaps started by Pappus of Alexandria in the third century, and continues even today. It is essentially Euclidean geometry with the "line at infinity" added in. By considering projective geometry instead of Euclidean geometry, we can derive more general theorems and truly see the beauty of duality between points and lines in plane geometry. I will give a brief introduction to plane projective geometry and give a synthetic proof of the cevian nest theorem, a proof that has been missing for some time.