UCLA Olga Radko Endowed Math Circle

11/23/2008: Group A: Graphs (Prof. Bruce Rothschild);
Group B: Inversion with respect to a circle (Olga Radko)

Graphs: We will learn about simple properties of graphs through problem-solving.
Inversion: Inversion with respect to a circle is a spectacular geometric transformation of the plane that allows to solve some seemingly unapproachable problems. E.g., the following two problems posed by an ancient Greek mathematician Appolonius:
  • Using a compass and a ruler, construct a circle tangent to three given circles;
  • Given two fixed points on the plane, find the set of all points whose distance to the first fixed point is k times the distance to the other point.