Date of Award

August 2020

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

Jeb Willenbring

Committee Members

Allen Bell, Craig Guilbault, Kevin McLeod, Yi Ming Zou


Given four generic lines in FP3, we ask, "How many lines meet the four?" The answer depends on the field. When F = C, the answer is two. When F = R, the answer is either zero or two.

If we work over a finite field there are only finitely many projective lines. We compute the probability four lines are met by two. The main result is that as q approaches infinity, this probability approaches 1/2. Asymptotically, the other half of the time zero lines will meet the four.

Included in

Mathematics Commons