Algorithms and Geometric Constructions

Por • 11 jun, 2018 • Sección: Opinion

Vladimir Uspenskiy, Alexander Shen

Abstract: 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

arXiv:1805.12579v1 [math.HO]

History and Overview (math.HO)

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