If you are given two line segments, it is easy to construct a line segment whose length is the sum of their lengths, purely geometrically: use the line segment obtained by placing the two line segments next to each other. Its length is the sum. Differences of lengths can be found purely geometrically too: place the line segments on top of each other and use the extra amount on the longer segment. But what about products? That is, if you have a line segment with length x and a line segment with length y, can you construct geometrically out of these a line segment with length xy? Or how about a line segment with length x/y?

We will see (and practice!) how to make constructions like these using the tools of classical Greek geometry: an unmarked straightedge and a compass. As an application we will meet a purely geometric construction of a regular pentagon.