Mathematics Problem Of the Week

Spring 2006

POW #5

Plane Division

In the figure below, 4 lines are used to divide the plane into 11 different regions.

(a) Is it possible to get more than 11 regions with just 4 straight lines?

(b) In general, what is the greatest number of regions the plane can be divided into by n straight lines?

(c) What’s the greatest number of regions with finite area that can be created with n straight lines in the plane?

Be sure to justify your answers in each case.

Due Friday, March 3^rd Noon

Solutions should be submitted to Dr. R. Lock's mailbox in the Math office or sent via e-mail to rlock@stlawu.edu.