Mathematics (B.S.)

Document Type and Release Option

Thesis (open access)

Faculty Mentor

Hua Wang


The triangular numbers is a series of number that add the natural numbers. Parabolic shapes emerge when this series is placed on a lattice, or imposed with a limited number of columns that causes the sequence to continue on the next row when it has reached the kth column. We examine these patterns and construct proofs that explain their behavior. We build off of this to see what happens to the patterns when there is not a limited number of columns, and we formulate the graphs as musical patterns on a staff, using each column as a line or space on the treble staff. By listening to the pattern, we can pick up on elements of the pattern that are missed by simply glancing over the graphic or formulaic versions.

graph.pdf (1538 kB)
K=24 repeated graph

K=15.m4a (915 kB)
Music file K=15

K=16.m4a (977 kB)
Music file K=16 overlapping

K=15, 16, and 17.m4a (1024 kB)
Music file K=15, 16, 17

K=10, 15, and 20.m4a (1155 kB)
Music file K=multiples of 5