Albion College
Mathematics and Computer Science
COLLOQUIUM
Visual Representations of Natural Numbers using Geometric Patterns
David A. Reimann

Professor

Mathematics and Computer Science

Albion College

Natural numbers can be visually represented by a geometric arrangement of simple visual motifs. This representation is not unique because any partition of an integer $n$ can generate at least one geometric pattern. Thus the number of partitions of $n$ is a lower bound on the number of geometric patterns. For example, there are 17977 partitions for the number 36; it is both a square number $(6^2)$ and a triangular number $(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8).$ Aesthetic considerations often favor patterns with some degree of symmetry, such as patterns that fix a single point or wallpaper patterns. A series of geometric designs for the numbers 1–100 were created to visually highlight some properties of each number. The designs use a variety of motifs and arrangements to provide a diverse yet cohesive collection. One application of these patterns is as a teaching tool for helping students recognize and generalize patterns and sequences.
3:30 PM
All are welcome!
Palenske 227
September 16, 2021