CONNECT-THE-DOTS, BUT DON'T CROSS YOUR LINES!
Daniel C. Slilaty
SUNY at Binghamton
Take a sheet of paper and place four dots on it anywhere you want. Try to connect each pair of dots with a line, but don't let the lines cross. You don't have to make the lines straight. Can you do it? You should be able to do this without too much trouble.
Okay! Take another sheet of paper and place five dots on it. Try connecting each pair of dots with a line, again not letting the lines cross. Could you do it? Actually, it's impossible! Why? What can be said about similar connect-the-dots type games?
This talk is accessible from the freshman level on.
Daniel received his BS in Mathematics from Binghamton University in 1993 and his MS in Mathematics from the University of Illinois at Urbana-Champaign in 1997. He is currently in the process of writing his dissertation in the area of graph theory and matroids and is teaching classes in calculus and differential equations. Daniel is planning on pursuing a career in mathematical teaching and research. He is a fellow in the "Preparing Future Faculty" Program in the Department of Mathematical Sciences.