Geometry of numbers and its applications

Abstract

Some geometrical results which are difficult to prove by purely Euclidean methods and approaches involving coordinate geometry or trigonometry are not always appropriate or may lead to messy algebraic manipulation. An alternative approach is to use complex numbers and for some results this may be the most convenient method of proof. Here we demonstrate the method by looking at a few results about polygons. That squares feature here is perhaps not surprising, since multiplication by i corresponds to a rotation through 900. Here we shall see, complex numbers may also help with results involving regular polygons.