Department of Mathematics and Statistics, Grinnell College

The logo for the Department's Web site shows a dissection of a rectangle with integer sides in the ratio of 1:3 into eleven distinct rectangles with integer sides that are also in the 1:3 ratio. This dissection was discovered in 1994 by Professor Charles H. Jepsen and first published in his article Dissections of p : q rectangles (Mathematics of computation 65 (1996), 771-778).

This dissection is simple, which is to say that it contains no proper subrectangles made up of two or more of the component regions, and perfect, which is to say that no two of the components are the same size. Professor Jepsen has proved that no simple, perfect dissection of a 1:3 rectangle into smaller integer-sided 1:3 rectangles has fewer than eleven components.

The dimensions of the entire rectangle are 64 by 192. The dimensions of the components, in descending order by area, are:

37 by 111 (white, top left)
27 by 81 (scarlet, bottom left)
24 by 72 (scarlet, middle right)
23 by 69 (gray, bottom right)
17 by 51 (black, top right)
14 by 42 (black, bottom middle)
13 by 39 (gray, just above the laurel-leaf logo)
10 by 30 (gray, top middle)
27 by 9 (black, just above center)
7 by 21 (white, above the large scarlet component)
9 by 3 (white, below and right of center)

The drawing is at a scale of three pixels per unit, with single-pixel boundaries demarcating the regions. The boundaries at the top and left of each rectangle are included in the height and width for that rectangle, and the graphic is actually 193 pixels high and 577 wide, so to accommodate the single-pixel boundaries at the bottom and right.

The drawing was executed by the Graphical Image Manipulation Package (GIMP), running this Script-Fu program, and then revised manually to reflect the separation of the Department of Computer Science and the Department of Mathematics and Statistics. The program does not internally generate the four-laurel-leaf graphic, but simply includes it from a file created for the College's Web site by Jim Powers of the Office of Communication and Events.