# Projects Directed by Dr. Ron Umble

## Published Papers Written by or Coauthored with Students

- Edge Tessellations and Stamp Folding Puzzles, preprint (with Matthew Kirby), Math. Magazine, in press
- Gereralizations of the Brachistochrone Problem (with J. Gemmer and M. Nolan), Pi Mu Epsilon J., 13(4) (2011), 207-218
- Periodic Orbits of Billiards on an Equilateral Triangle (with Andrew Baxter), Am. Math. Monthly, 115(6) (2008), 479-491
- Double Bubble Experiments in the Three-Torus (N. Brubaker, S. Carter, S. Evans, D. Kravatz, S. Linn, S. Peurifoy, and R. Walker), Math Horizons, April 2008, 18-21
- Minimal Paths on Some Simple Surfaces with Singularities (with Joel Mohler), Pi Mu Epsilon J., 12(8) (2008), 461-472, (galley proofs)
- Obstructions to Deformations of DG Modules (with Trina Armstrong), Proc. AMS, 129(12) (2001), 3447-3452

## Software Projects

- "Animated Cycloid" -- Software by Robert Painter
- "Geodesics on a Tin Can" -- Software by Robert Painter
- "Orbit Tracer 1" -- Software for Generating Orbits on a General Triangle by Stephen Weaver
- "Orbit Tracer 2" -- Software for Generating Orbits on an Equilateral Triangle via Tessellation by Stephen Weaver
- "Animated Osculating Circle" -- Mathematica Notebook by John Mease
- "Visualizing Normal Curvature" -- Mathematica Notebook by John Mease
- "Visualizing Geodesics" -- Mathematica Notebook by John Mease
- "Orbit Mapper" -- by Josh Pavoncello

## Poster Presentations

- Geodesics on a Conical Drinking Cup with Lid by Joel Mohler
- Periodic Orbits on a Triangular Air Hockey Table by Baxter, Gemmer, Laverty and Weaver
- The General Brachistochrone Problem by John Gemmer
- Double Bubble Experiments in the Three-Torus by N. Brubaker, S. Carter, S. Evans, D. Kravatz, S. Linn, S. Peurifoy, and R. Walker
- Periodic Orbits on a 120-Isosceles Iriangular Billiads Table by B. Baer, D. Brown, F. Gilani, and J. Pavoncello

## Theses

- Mohler, Joel. Distance Minimizing Paths on Certain Simple Flat Surfaces with Singularities, Dec. 2002
- Baxter, Andrew. Periodic Oribits on a Triangular Air Hockey Table, May 2005
- Weaver, Stephen. Computing the Saneblidze-Umble Diagonal on Permutahedra, May 2005
- Gemmer, John. Generalizations of the Brachistochrone Problem, May 2006
- Kravatz, Daniel. Diangonal Approximations on an n-gon and the Cohomology Ring of Closed Compact Orientable Surfaces, May 2008
- Evans, Sean. 2-In/3-Out A-infinity Bialgebras, May 2008
- Schreffler, Morgan. Fixed Point Theorems in Topology and Geometry, May 2011

## PowerPoint Presentations

- Periodic Orbits on a Triangular Air Hockey Table by Andrew Baxter
- Computing the S-U Diagonal on Permutahedra by Stephen Weaver
- Generalizations of the Brachistochrone Problem by John Gemmer
- Double Bubble Experiments in the Three-Torus by N. Brubaker, S. Carter, S. Evans, D. Kravatz, S. Linn, S. Peurifoy, and R. Walker
- Periodic Orbits on a 120-Isosceles Triangular Billiads Table by B. Baer, D. Brown, and F. Gilani assisted by J. Pavoncello

## Students noted in the press

## Project Proposals

- Periodic Orbits of Billiards on a Polygon whose reflections Tessellate the Plane
- Project Proposals by Prof. J. Robert Buchanan
- London Math Society Project Proposals
- Washington University Project Proposals