Projective Generalization of Maxwell's Theorem
Michel Cabart has observed that Maxwell's theorem is of projective nature. The projective formulation goes like this:
Assume there are two triangles ABC and MNP and two triples of points on L such that A0, B0, C0 are intersections of L with sides of ΔABC and also with cevians of ΔMNP; A1, B1, C1 are intersections of L with sides of ΔMNP and also with cevians of ΔABC.
Choosing the infinite line as line L gives Maxwell's theorem as a particular case.
The applet below illustrates the projective generalization. You can drag the vertices of the two triangles as well as the triangles themselves, line L and the points on that line. I must admit that the original theorem is by far the easier to illustrate.
|What if applet does not run?|