In fact, constructions using other sets of tools have been examined, but we will not go into that here. For example, you might be interested in what can be constructed using only a straightedge, or just a compass, or perhaps a straightedge and a ``rusty compass''--a compass that is frozen into one particular setting, or even constructions using more interesting tools.
Or what if you are allowed to put marks on the straightedge, effectively turning it into a ruler? What if the straightedge is only a fixed finite length? What if one circle has already been drawn, but you no longer have a compass? There are any number of other possibilities.