One of the first presentations I ever gave was in a "Foundations of Mathematics" class in college. I chose to do my presentation on Fractals. We are familiar with dimensions of every day objects. A line is one-dimensional, a piece of paper is two-dimensional, a football is three-dimensional. Fractals are objects that have fractional dimensions. In nature, scientists use fractals to model lungs, trees, and clouds among other things. Jackson Pollock paintings have also been analyzed from a fractal viewpoint.

• ::Intro to Fractals::

The number three is the thing that a set of three chairs or three pineapples or three kilograms have in common, an abstract three-ness. The same designation can be used to think about sizes of sets containing infinitely many objects. For instance, which is biggest, the set of counting numbers, the set of possible fractions, or the set of real numbers? Find out more in this article.

• ::Sizes of Infinity::

In grad school, my final project was to write a paper about a common fractal called the Cantor Set, shown to the left. The thrust of my paper was to address a "wild" Cantor Set formed from doughnuts instead of line segments. Below, you'll find the link to my paper, as well as a summary.

::On Cantor Sets (Full Paper)::

::Summary of the paper::