Faculty Notes Faculty Notes

Pascal's Triangle Mod n Faculty Notes

One exercise that students in any level class can do is to construct Pascal's triangle mod n for some number n; choose n colors to represent the n possible answers and color the triangle. If you do six of these and paste them together to make a hexagon, then sometimes, if you look at them just so, you can see a cube in perspective. It helps to have a template with open circles to work with:

One additional note: we added the second set of examples of Pascal's Triangle mod 3, 4, and 5 in different colors because, although red, green, blue, yellow and black are very distinguishable colors for most of us, they may be indistinguishable for those with the not uncommon condidtion of red/green color blindness. Neither of the authors suffers from red/green color blindness so it is difficult to choose colors that work well for the roughly five percent of the population who do. In fact, it is not clear that such a choice would be possible or that a choice that works for one color-blind reader would necessarily work for others. There are a number of open questions regarding the way that people perceive colors. Frequently color choices that work well for those with red/green color blindness do not work well for others. So that the largest possible number of people can understand the article, we have tried to vary our color choices somewhat throughout without losing coherence or making ourselves sea-sick. If you use visualization exercises in class, you might want to find out if any of your students are color blind and if so, ask for their help in choosing colors they can distinguish. Another interesting complication is that colors are generated significantly differently for the computer screen than for print. Even if you find colors that work well on the screen, they may not work at all in print.