At a very early age we are taught such theorems as “the angle on the circumference of a circle subtended by a diameter is a right angle”. This is part of our Euclidean heritage. But from Euclid's terse deductive style it is often difficult to draw links between the geometrical arguments which he presents and more modern mathematics. The purpose of this article is to step off the Euclidean path, dispense with the obligation to present formal deductive arguments and explore. The treatment is elementary and we make use of computer graphics. The graphs in this article were produced by the Picaso graph plotting package using the Calcomp 960 plotter on a Vax 11/785 computer.