Moser’s Circle Problem: False Induction and A Beautiful Solution.
<p>I recently came across a video by 3Blue1Brown on Moser’s Circle Problem, a math puzzle that has long fascinated me. This enigmatic puzzle first caught my attention in MATH 0235 at the University of Pittsburgh, when added as homework by my professor, Dr. Christopher Lennard. If you’re here after attending his lecture or a similar class, I implore you to attempt a solution on your own. I dedicated over 20 hours at Hillman Library unraveling its intricacies — I’d urge you to give it the time it warrants before seeking the solution.</p>
<p>3Blue1Brown’s exploration utilized planar graphs and Euler’s characteristic formula to derive a solution. Although the animations were visually stunning, the method seemed a tad esoteric, especially for those unfamiliar with such concepts. Thus, my aim in this post is to offer a fresh perspective on Moser’s Circle Problem. Rather than delving into graph theory, I show the problem through the lens of series and summation, and breaking the problem down by representing it recursively, to arrive at the answer.</p>
<p><a href="https://medium.com/@Quentinromero/mosers-circle-problem-false-induction-and-a-beautiful-solution-f26684c41e61"><strong>Website</strong></a></p>