Application of Renormalization Techniques to the Classical Arbelos Problem

Abstract

This application of renormalization techniques offers a modern take on the classical Arbelos geometry problem. Keeping within the context of the original problem, two semicircles, meeting at chord T, are together circumscribed by a third semicircle. Separate from the original Arbelos result, both circumscribed semicircle areas are found in terms of chord T and the third circumscribing semicircle radius R. This approach eliminates the additional variables of the circumscribed semicircle radii.