STABILITY OF BROCARD POINTS
OF POLYGONS

ADI BEN-ISRAEL AND STEPHAN FOLDES

Abstract:

A continuous nested sequence of similar triangles converging to the Brocard point of a given triangle is investigated. All these triangles have the same Brocard point. For polygons, the Brocard point need not exist, but there is always a limit object for an analogously defined nested sequence of inner polygons. This limit object is a Brocard point if and only if the inner polygons are all similar to the original polygon. The similarity of two distinct inner polygons already suffices. In that case, all the inner polygons have the same Brocard point.