In January 1999 at the Joint Mathematics Meetings in San Antonio, I attended a talk by Kathleen Shannon based on joint work with Michael Bardzell (both of Salisbury State University) involving coloring Pascal's Triangle by using modular arithmetic and other group operations. See http://www.pascgalois.org/ for more information on their work and some amazing pictures. I was so enthralled with the beautiful patterns in the samples that Professor Shannon showed during her talk that I wanted to come up with some on my own. I found a page on the web that had Maple code for doing a triangle mod 2 and then modified it to work for other moduli. (I wish I could cite the page, but I have lost the URL :*( ) Below are some pictures that I generated using Maple V, Release 5.

During the Fall 2000 semester, I had an undergraduate student Tim Pierce in my abstract algebra course, who chose to do his course project on Pascal Triangle Colorings. Tim wrote a program in Maple which calculated the group tables and then colored Pascal's triangle for groups with 2 generators. He presented his research at the Kansas Section of the MAA 2001 spring meeting (winning 2nd place) and at the KME Mathematics Honor Society National Convention. His paper appeared in the Fall 2001 of the KME journal "The Pentagon".

Pascal's Triangle mod 2 using the color assignment 0 = black and 1= yellow.

Pascal's Triangle mod 3 using the color assignment 0 = black, 1= blue and 2 = red.

Pascal's Triangle mod 4 using the color assignment 0 = black, 1= blue, 2 = red and 3 = turquoise.

Pascal's Triangle mod 5 using the color assignment 0 = black, 1= blue, 2 = red, 3 = turquoise and 4 = yellow.

Pascal's Triangle mod 6 using the color assignment 0 = black, 1= blue, 2 = red, 3 = turquoise, 4 = yellow and 5 = white.

Pascal's Triangle mod 7 using the color assignment 0 = black, 1= blue, 2 = red, 3 = turquoise, 4 = yellow, 5 = white and 6 = bright green.