Inscribed Square Problem and an Embedding of M¨obius Band in a Family of Solid Toruses

Faris ELmikdad

Inscribed Square Problem and an Embedding of M¨obius Band in a Family of Solid Toruses

Primarily human-written textHuman understanding: all partsmath.GT — Geometric Topology math.AT — Algebraic Topology math.GN — General Topology math.GR — Group Theory

Contributed by Faris ELmikdad ↗

Version 1 / Oct 22, 2026 / CC BY 4.0

Abstract

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.

Provenance statement

I wanted to learn how to write beautiful math equations,i heard about latex then i learned it from youtube and maked an account in overleaf. I writed it in overleaf by latex.

References

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Version history

v1Submitted by Faris ELmikdadInitial depositCurrentOct 21, 2026