Geometry plays a central role in game programming, underlying not only graphics, but also physics and spatial AI. A lot has happened since geometry was first formalised by the Greeks more than two thousand years ago, most notably the invention of coordinates and vectors. These inventions are indispensible for doing geometry on machines (at least, the kind of geometry that is useful for games).
This article introduces the basic concepts of vectors. In a following article, we will look at how vectors can be used to solve geometric problems that arise in computer graphics, physics and AI.