Analytic, Geometric, and Numeric Analysis of the Shrinking Circle and Sphere Problems

The Shrinking Circle Problem is an example of a simple-to-state geometry problem that is visually appealing yet quite challenging to solve. A combination of geometry and analysis is used to completely solve the general problem in the plane, and its extension to three dimensions: the Shrinking Sphere Problem. We show why traditional numerical attempts to answer even the simplest problem is futile. The original problem was generalized based on visual evidence produced by dynamic geometry software. Only with this insight was it possible to utilize symbolic computation tools to put together the complete proofs. All supplemental materials that accompany this paper can be found online at either of the folowing URLs