The PascGalois Project: Visualizing Abstract Mathematics#
The PascGalois project has its origin in a simple exercise with Pascal’s triangle. Take each entry in the triangle and replace it with its congruent value mod n, where n is a positive integer larger than 1. By assigning each of the values \(0, 1, \ldots, n - 1\) a distinct color, patterns reminiscent of fractals appear. Our interest in this construction lies in the fact that addition mod n is the group operation of the cyclic group \(\mathbb{Z}_n\) and the patterns seen in the triangles are related to the structure of these groups. By replacing \(\mathbb{Z}_n\) with other finite groups one can use the same fractal-like patterns to visualize the structure of these non-cyclic groups.
The PascGalois Project was made possible through two grants from the National Science Foundation, DUE-0087644 and DUE-0339477.
For more information or questions about the project please contact us at,