## Self-Transversality Theorem

Let , , and be distinct Integers (mod ), and let be the point of intersection of the side or diagonal of the -gon with the transversal . Then a Necessary and Sufficient condition for

where and

is the ratio of the lengths and with a plus or minus sign depending on whether these segments have the same or opposite direction, is that

1. is Even with and ,

2. is arbitrary and either and , or

3. and .

References

Grünbaum, B. and Shepard, G. C. Ceva, Menelaus, and the Area Principle.'' Math. Mag. 68, 254-268, 1995.