A novel approximate asymptotic method is presented to identify the optimum geometrical dimensions of fins. This technique is based on a similar approach that has been used to determine optimum fin spacing associated with both free and forced convection heat exchanger analysis. The technique, however, does not appear to have been applied to the important area of heat conduction related to fin performance and optimization. The utility of the method is that it yields an approximate algebraic relationship for the optimum fin dimensions, in terms of relevant fin parameters. Furthermore, this approximate procedure is shown to compare well with the results obtained from more complex general optimization procedures. In this paper, the application of the method is illustrated for the three basic 1D fin configurations: (1) Profile fins, (2) Pin fins, and (3) Annular fins. In each case, the selected optimization criteria was to maximize the heat transfer rate for a given fin volume (or profile area). The results clearly show that the approximate asymptotic method well-represents the "true" optimum fin parameters for the three common classes of 1D fins. Hence, it has the potential to also provide a basis for simplifying more complex (e.g., 2D, or multi-parameter) fin geometry optimization currently under investigation.