I created the above gif using Wolfram Research's program Mathematica, version 8. This powerful but difficult-to-use software has some interesting possiblities for image manipulation and creation, among its many other capabilities. By careful selection of parameters, one can produce intriguing effects. See my math-gifs page for a couple of examples inspired by Vaclav Havel's funeral and also for a year-of-the-dragon example.
See colorful outerplanar layouts for some circulant graphs for some fairly recent slides illustrating embeddings with low crossing numbers and book thickness. The drawings of graphs there are also done via Mathematica software which was developed here in the lab.
In Spring 2012, I'm teaching Applied Combinatorics . The original announcement for the course is here . Math 410 meets from 5:00 to 6:15 pm, on Tuesday in St. Mary's 326 and on Thursday in Reiss 283. We are using Bigg's Algebraic Graph Theory, 2nd Edition, as well as Spectral Graph Theory by Fan Chung. See the syllabus, which is available at my explore.georgetown page . Getting to the syllabus requires two log-ins and is only for georgetown students, so I've put a copy of this pdf file here .
I am also giving a Research Module in the Cognitive Science program; see 2012 modules. The module will be related to development of the Math User Interface designed to make Mathematica more accessible to math and computer science students.
I am Director of the Laboratory for Visual Mathematics (Lab4VM) . I've had two GUROP (Georgetown Undergraduate Research Opportunities Program) assistants, Adam Persing and Jun Oh Yoon, who assisted me in preparing the older pages which are accessible there. Adam and Jun Oh were also the founders of the Psychophysics Club. Currently, Adam has gone back to academia for his Ph.D. work in economics in London, while Jun Oh is a Financial Analyst in the Washington, DC area. I have benefited from advice from several senior members of the Georgetown faculty: Professors Karl Pribram, George Farre, and Patrick Healon, S.J.
My brother Dan is an artist and inventor. His website has a new 3-D display technique for printing, which will be available soon as a coffee-table book, called "Safari: A MotionPicture(TM) Book" - see the description for it .
My former index page contains links to other pages.
My ``homely page'' with information on my research and other interests is here .
Office: 315D St. Mary's, phone 202-687-2703
e-mail: Kainen at Georgetown dot edu
My office hours this semester are T/Th 6:30 to 8 pm and Wed. 2 to 4 pm.