Representations of the Natural Numbers Using Box Arrangements

Mr. Joakim Jakovleski
PhD Student
University of Wisconsin – Milwaukee

Natural numbers can be presented as sums of numbers in boxes, where we are subject to certain rules about how we generate the boxes and the numbers in them. In this talk, we will explore this presentation and investigate the properties of boxes of different sizes. We will center on a simplified way to obtain all numbers in all boxes using a certain subset of them, and use it to ultimately produce a formula for these numbers. We then manage to provide some generalizations, and pave the field for potential future work.