Appell F1 and Conformal Mapping

TL;DR

This paper introduces a new calculation of the conformal center of gravity for isosceles triangles, linking it to logarithmic capacity and extending the trilogy on triangle centers.

Contribution

It presents a novel computation of the conformal center of gravity for isosceles triangles, a previously obscure concept, and relates it to logarithmic capacity.

Findings

Calculation of the conformal center of gravity for isosceles triangles

Connection to logarithmic capacity and transfinite diameter

Results align with Haegi (1951)

Abstract

This is the last of a trilogy of papers on triangle centers. A fairly obscure "conformal center of gravity" is computed for the class of all isosceles triangles. This calculation appears to be new. A byproduct is the logarithmic capacity or transfinite diameter of such, yielding results consistent with Haegi (1951).