Exploring Orientability: An Investigation of the Möbius Strip Using Cut and Paste Technique

Akanksha Singh¹ , Garima Singh² , Anshu Singh³

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.3 , pp.38-42, Jun-2024

Online published on Jun 30, 2024

Copyright © Akanksha Singh, Garima Singh, Anshu Singh . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The Möbius strip carries the pure and essential example of non-orientable manifold, presents a challenge in understanding its inherent properties. This research investigates the orientability of the Möbius strip through a new approach. Our study aims to explore the possibility of altering the Möbius strip’s topology through cutting and pasting . We employ a combination of geometric visualization, topological manipulation, and mathematical analysis to systematically dissect Möbius strip and perform surgical modifications and reassemble the resulting structures. Through this process, we examine the consequences of each cutting and pasting operation on the orientability of the Möbius strip and explore how these actions affect its orientability. We will employ known results of topology and differential geometry methods to prove orientability of cut and pastes of Möbius strip.

Key-Words / Index Term :
Differential Topology, Differential geometry, Möbius strip, Orientable, Non-Orientable Manifold

References :
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