Academic Distractions

The fields of mathematics and computer science are so large that no one can possibly know everything about them. That is why I enjoy books like "The Wonder of Numbers" by Clifford Pickover and "The New Turning Omnibus" by A.K. Dewdney. Through their short chapters on a diverse set of topics, I am reminded of the beauty that is waiting to be found. Computers and mathematics make the perfect pair for this exploration, and when a topic grabs my interest, it frequently pulls me away from the things I should be doing.

Trigometric Inequality Art

Inequalities are plotted using shaded regions, and when the expressions contain trigometic functions (sin, cos, tan, etc), the periodic nature of the these functions make spectacular patterns. If we also allow both Cartesian and Polar coordinates, then we can put together "interesting" inequalities such as cos(r) < sin(x) (shown in the image on the left).

I was originally exposed to these patterns when playing with the "graphing calculator" on Macintosh computers during college. The beauty of these images ultimately led me to write my own program to randomly generate inequalities and display the resulting image.

Flocking

In 1986, Craig Reynolds created the first sucessful animation of computer-controlled birds. He called the project Boids, and the technique has become the standard method of creating a group of autonomous agents.

The mathematics required to implement "flocking" is based on simple vector sums and scalar products, and the concepts can be explained using only high school mathematics. This made it the perfect topic for the college's annual "Math Matters at Moravian (M^3)" program, and in 2005, I gave a presentation on this topic. Since then, I have given this same presentation at a number of area high schools.

Asteroids

During the spring 2005 semester, I offered a course in game programming. The first major project for the course was to implement a version of asteroids. To ensure that the project was feasible, I had to implement my own version. The projet requires collision detection and accurate physics responses along with a significant amount of planning to keep things organized. For some reason, my students remained motivated, and a number of their versions were quite impressive.

The Look and Say Sequence

Can you determine the next number? The pattern is called the Look and Say Sequence, and it has some interesting properties. During the fall 2006 semester, I gave an "Epsilon Talk" for the Moravian College Math Society on this sequence, and I shared a handout discussing how quickly the sequence grows and the distribution of the numbers 1, 2, and 3.