2018/05/31 by Uspenskiy, Vladimir, Shen, Alexander
#51M15 #F.1 #FOS: Mathematics #History and Overview (math.HO)
paper · doi:10.48550/arxiv.1805.12579
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