Karl did research on a specific geometric series. This complicated series seems divergent at the first site, but he showed through Algebraic Manipulation using a version of Riemann's analytical continuation, that this series actually converges. Besides proving it algebraically, he also created a “real life” model to validate his assumption. He built a bounded harmonic system using a variable frequency saw and metal wiring. He was able to predict where node intervals would occur, and how many nodes there were in particular harmonic systems based on some of the characteristics that this particular geometric series converged to. He said, “using creativity and trial and error to modify and approach the problem from different angles, so that when I finally got my bounded harmonic system to work, it was indeed a "Eureka!" moment”
