#### Title

#### Document Type

Other

#### Publication Date

12-2014

#### Department

Mathematics

#### Abstract

Magic figures are discrete, two-dimensional (2-D) objects. We translated the definitions of magic squares and magic circles in an attempt to find three-dimensional (3-D) surfaces that adhere to the same definitions. This is what we defined as a magic surface.

First, we translated these definitions by thinking of the discrete integer entries in the magic squares and magic circles as volumes under the magic surfaces; these were evaluated by volume integrals. We then translated these definitions in a similar way to apply line integral constraints.

We found polynomial functions that satisfied thse re-definitions of conditions for a magic surface. In the case over magic squares using volume integrals, we were able to form conjectures about the polynomial solutions and the systems of equations that formed them.

#### Recommended Citation

Moore, Brandi Crystal, "Magic Surfaces" (2014). *Mathematics Undergraduate Theses*. 1.

https://aquila.usm.edu/math_undergraduate_theses/1