A long-standing research interest of mine is the problem of dissecting a p:q rectangle into n smaller rectangles, no two of the same size. I have been able to find all such dissections for values of n through 13. The logo on the Web site of the Grinnell College Mathematics Department depicts one example: a 64 by 192 rectangle (ratio 1:3) dissected into eleven 1:3 rectangles
These dissections arise from deriving and solving a large number of systems of linear equations. The computation to find all dissections into 13 rectangles, the largest number we have attacked, is carried out by Maple-based computer programs. A description of the underlying mathematics can by found in the paper "Dissections of p:q rectangles in thirteen p:q rectangular elements." This Web site provides access to the Maple-based programs and to the paper.
The programming was done by former Grinnell College student Ming Gu as part of a summer research project. My colleague Eugene Herman created this Web site. The programs are free software and are licensed for redistribution under the General Public Licence, a copy of which is included with the programs.