Perhaps the most interesting, and definitely the hardest and most pleasant to grade, homework assignment in MAT 103 is the one where the students have to produce their own wallpaper patterns, belonging to two of the 63 two-colored types of their choice. Several students simply imitate one or two of the many patterns they have seen so far, but some students would rather be creative, coming up with designs as unusual as those shown in the MAT 103 "gallery" .

Three or four weeks after I graded and returned the homework assignment in question, and on the last day of classes (5/4/00), just a couple of hours before taking off for Donald Crowe's retirement conference , something unusual happened: "back-row" student and music major Eric Zirbel, who had kept suggesting to take the isometry-illustrating soccer balls (and our class) out to the unusually warm sunshine, approached me at the end of the hour to ask me whether I would be willing to have a look at his homework assignment ... that he had forgotten in his car; normally I would have said that it simply was too late, but somehow I said "yes".

With very little time ahead of me, I realized at once that Eric's idea was precious and mathematical enough to merit serious attention: use two kinds of two-colored parallelograms to "eliminate" all isometries (save for the ever-present color-preserving translation) by way of "color inconsistency"!

Indeed the point here is that there is no half turn center -- notice that there exist four kinds of such centers -- that either sends all black triangles to black triangles and all white triangles to white triangles ("preserving colors") or sends all black triangles to white triangles and vice versa ("reversing colors"); moreover, all translations preserve colors, allowing therefore the "two-colored" design to be classified as one-colored (p1).

"Killing" all pre-existing half turns by way of coloring is not so easily done: there exist designs very similar to Eric's where some centers "work". So I decided that his idea was worthy of immortalization: I knew the way to Oswego Printing, and with some technical assistance from my SuperPaint tutor Michael Nichols (former MAT 103 student) and further advice by art professor Matthew Friday, the third MAT 103 postcard came to life! Notice that the three colors employed are Eric's favorite; as he puts it, "now the last thing left is for students to see this and realize that white is a color, not just a backround".

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