The Fibonacci Sequence: Melody and Harmony
Department of Mathematics
Michigan State University
The Fibonacci numbers are famous for their intriguing appearances in art and nature, and their mathematical properties have been extensively studied. Remarkably, the Fibonacci sequence is periodic mod n, for any positive integer n. In fact, we can produce many such periodic sequences by simply changing our initial conditions. We interpret these sequences in terms of points on a torus, and then as a musical score.