  It is well known that several classical geometry problems (e.g., angle
trisection) are unsolvable by compass and straightedge constructions. But what
kind of object is proven to be non-existing by usual arguments? These arguments
refer to an intuitive idea of a geometric construction as a special kind of an
`algorithm' using restricted means (straightedge and/or compass). However, the
formalization is not obvious, and different descriptions existing in the
literature are far from being complete and clear. We discuss the history of
this notion and a possible definition in terms of a simple game
