Faculty interested in undergraduate research
Contact information: [email protected]
Office: MAK A-2-108
Research areas: Discrete Geometry, Spherical and Hyperbolic Geometry
1) Circle and Sphere Packing: Suppose you have seven cans of soda pop, what is the smallest box with a square cross section that can hold them standing upright in a single layer? By examining the cross section of the box, you can see that this is equivalent to determining the smallest square that contains seven equal and non-overlapping circle. This is a problem in Discrete Geometry. The optimal densities and arrangements are known for packings of small numbers of equal circles into hard boundary containers, including squares, equilateral triangles and circles. This project centers on exploring packings of small numbers of equal circles onto boundaryless containers like flat Klein bottles and flat Tori. Don't know what a Klein bottle or flat torus is? Come and talk to me and I would love to explain.
2) Spherical and Hyperbolic Geometry: In my heart, I believe that every result in Euclidean geometry has a clean, beautiful and analogous result in spherical and hyperbolic geometry. I enjoy playing in the trigonometric briar patch that results when you attempt to move Euclidean results in to these other geometries. The Pythagorean Theorem has already been moved into these other geometries... or has it? That depends on your definition of right triangle and I think that is up for grabs! Come ask me about the possibilities.
Share this spotlight
Return to the listing of faculty interested in undergraduate research.