1 GENERALIZATION OF THE THEOREM OF MENELAUS USING A SELF-RECURRENT METHOD

This generalization of the Theorem of Menelaus from a triangle to a polygon with n sides is proven by a self-recurrent method which uses the induction procedure and the Theorem of Menelaus itself. The Theorem of Menelaus for a Triangle is the following: If a line (d) intersects the triangle Δ A1A2A3 sides A1A2, A2A3, and A3A1 respectively in the points M1, M2, M3, then we have the following equality: 1 1 2 2 3