{"id":"hexagon/2610.00442","pdf":"https://hexagonmath.org/pdf/2610.00442v1","url":"https://hexagonmath.org/abs/2610.00442v1","tags":["math.AT","math.GN","math.GR","msc:30L05","M¨obius band","Rotation","Square.","Torus"],"score":0,"title":"Inscribed Square Problem and an Embedding of M¨obius Band in a Family of Solid Toruses","domain":"math.GT","source":"hexagon","authors":["Faris ELmikdad"],"reviews":0,"subject":"math.GT","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}