math.GT — Geometric Topology
Inscribed Square Problem and an Embedding of M¨obius Band in a Family of Solid Toruses
In this paper, we relate the space of line segments induced by a Jordan curve in the plane to the space of line segments induced by the plane by embedding the M¨obius band associated with the curve into the family of toruses associated with the plane; we further demonstrate how the geometric ”square condition” of the curve translates into a topological property through this embedding.
Primarily human-written textHuman understanding: all partsM¨obius bandRotationSquare.Torus