Crosscut Convex Quadrilaterals

摘要

In all that follows, A is an arbitrary convex plane quadrilateral; let's call such a polygona quad. We let the vertices of A be given cyclically by the four-tuple (A_0, A_1,A_2, A_3)and name a midpoint M, on each segment (A_i, A_(i+1)), taking all subscripts modulo4, as in FIGURE 1. We then crosscut quad A by drawing medians (A_i,M_(i+2)).Thesemedians intersect one another at the vertices of a new "inner quad" B in the interior ofthe "outer quad" A.