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