> > But I at least offer these: > > 1. Which quadrilaterals tesselate the plane? > > 2. (i'm groping) Given a tesselation of the plane into congruent triangles, > which quadrilaterals can be formed from a finite union of these triangles? > > 3. (groping...groping...) Which quadrilaterally shaped billiard tables > allow for ball trajectories which touch fewer than four sides? (no friction... > no ball size...cross reference this weeks problem of the week!) > > (Note: the answers to these all include the trapezoids...but the answers > do not include generic quadrilaterals.) > > Ken
I haven't looked into the second and third, but it is not true that general quadrilaterals do not tile the plane. -To make that a positive statement- Any quadrilateral will tesselate the plane. There is no restriction on the quadrilateral (not even convexity).