Power of a point: from Jakob Steiner to modern applications

Abstract

"What should we use?" seems to be the question when one approaches a plane geometry problem. In many ways, Euclidean geometry is a laboratory in the realm of logic, an ideal place where one can see how alternative methods can be employed to solve problems. What detail might represent a hint? And from among many choices, what method could one consider? Does the geometric structure suggest a certain type of approach?