The Roanoke College Robotics course (CPSC 310A) completed their final exam on Thursday morning. Their exam was a simplified version of the international RoboCup. Each student was tasked with designing, building, and programming a robot using Arduino microcontrollers (essentially a low power, simplistic computer), motors, various sensors, 3d printed components, and a lot of wires and hot glue. The goal of the game was to move as many cubes as possible to their respective goal locations. Congratulations to all of the competitors!
Rich Grant, Associate Dean
There are those who say that a faculty member who takes on administrative duties has turned to The Dark Side. I would never say such a thing. Rich Grant is trading in his Physics faculty duties for a term as Associate Dean for Academic Affairs and Student Engagement. Roanoke College will benefit immensely from his leadership in a variety of areas directly involved in student development, including Experiential Learning, Career Services, the Writing Center, and the Center for Learning and Teaching. MCSP, on the other hand, will miss his leadership as Physics Coordinator. Students will miss his excellence in the classroom. Rich is a winner of the Roanoke College Exemplary Teaching Award and the Exemplary Service Award, one of the few faculty members who have won two of the college’s top awards. This makes it especially hard to see Rich become a Sith Lord. However, we wish Rich well in his new duties, and thank him for his service to students and Roanoke College. May the Force be with you, Rich!
Those of us of a certain (large) age will remember the colorful mod art of the late 1960s; think Peter Max or the Beatles’ Yellow Submarine. Professor Jan Minton’s HNRS 301: Mathematics and Art class has decorated a Trexler stairwell with what is truly mod art. Modular arithmetic, that is. An example of modular arithmetic is (almost) clock arithmetic, where 11+4=3 because 4 hours after 11:00 is 3:00. The “almost” comes into play because mod 12 arithmetic uses the numbers 0, 1, 2, …, 11. It is still true that 11+4=3 mod 12, but we would say that 9+3=0 mod 12 instead of 9+3=12. One definition of the value of x mod y is the (positive) remainder when x is divided by y. 15 mod 12 = 3 because when you divide 15 by 12 you get 1 with a remainder of 3.
Modular arithmetic may seem a little weird, but it has numerous important applications beyond clock arithmetic. Its usefulness is tied to its ability to reveal important patterns. For example, if you square an odd number (3 squared is 9, 5 squared is 25, and so on) you will always get a number that equals 1 mod 4. So quickly answer the following: is 403 a perfect square? It can’t be, because when you divide 403 by 4 you get a remainder of 3, and all odd squares have remainders of 1.
So here (finally) is the art: the patterns revealed by modular arithmetic are often very pleasing to the eye. The stairwell is decorated with (x2 + y2) mod 9. Choose a value for x (say, x=4) and locate the vertical line of tiles between the x-value at the top and the x-value at the bottom. Choose a value for y (say y=3) and locate the horizontal line of tiles between the y-value on the left and the y-value on the right. The lines intersect in one place. The color pattern at that location is determined by x2 + y2 mod 9; in our example, 16+9=25 mod 9 = 7. The yellow square represents 7. Where else do you see yellow? See if you can explain the borders of yellow squares that form around the blocks of blue.
It is interesting to see what happens when you use the same function with a different modulus, like x2 + y2 mod 11 or x2 + y2 mod 12. Some of the results are intricate and beautiful, some are not. As with fractals, the fact that fairly simple mathematical formulas can create such detailed patterns is surprising and perhaps revealing about life in general.