Pride of the Mountains Marching Band Selfies -- By Axelle Faughn

Western Carolina University is famous for the quality of its band. The fact that a mathematically inclined mind is more often than not also musically inclined, means that several of our students in the mathematics department do play an instrument in band. With intensive band practice almost every day of the week, we were bound to see some creative submissions from this aspect of their lives.

Band Placement on a Grid

Imagine yourself as a freshman, first day on campus a week before regular students arrive; indeed, band practice requires you to get acquainted with campus life before classes start. Next thing you know the band director instructs you to get into formation and be ready to follow instruction: the photograph on the right is what you must picture in your head. Of course, the grid helps you position yourself, and the numbers help understand the symmetry of the band structure. Although not a traditional cartesian coordinate plane, this is not very different from the day Descartes was lying in bed and decided to add a grid to his ceiling where a fly had just landed, so he could describe its specific position.

Octagonal Percussion

Now that you know where to stand during band practice, it is time for you and your new friends to pull out your instruments. Once again you realize mathematics is omni-present. This photograph of a drum pad nicely illustrates the need for regularity and symmetry in many musical instruments. If you pay attention you will also find this regularity and symmetry in the rhythm of the music itself.

Symmetrical Band Formation

Game day is finally here! Practice pays off as the crowd cheers you on and you aptly perform the choreography long rehearsed through a series of rotations and translations, which allows band performers to keep various symmetrical arrangements while playing. Supporters await half-time with excitement and anticipation, but of course you are ready, and you don't let them down. Well done!

String Tangency

Game is over, back to the dorm. But let us not forget your other musical friends, those whose instrument is not so conducive to band practice, but still reveals plenty of mathematical connections. This photograph of a cello with the bow positioned tangential and perpendicular to the string helps us understand the proper position for a better sound on string instruments. As a cello player myself, I can assure you that for your ear's sake, you would not want the bow to be placed any other way. The student who submitted this also noted the relationship between pitch and string width, string length, and string density, which most musicians intuitively understand, and most mathematicians can explain using derivatives.


We hope you have a chance to see our Pride of the Mountains Marching Band someday. Their performance is really worth the side trip to our small mountain town, and their fame is the reason why many prospective students choose to join the student body at Western Carolina University.