Date: 16 Nov 2012

Functions of triples of positive real numbers and their use in study of bicentric polygons

Abstract

We consider some functions defined on the set of ordered triples \((R,r,d)\) , where \(R,r,d>0\) and \(R>r+d\) . The introduced properties of functions are used to study bicentric polygons where conics are circles. The article’s principal result is the so-called cyclical method for establishing Fuss’ relations for bicentric n-gons. The achieved method is a valuable contribution to the solution of the centuries-old Fuss’ relations problem.