Some Properties of 'Bulky' Links, Generated by Generalised Möbius–Listing’s Bodies $$GML_m^n\{0\}$$
| Autor: | Paolo Ricci, Ilia Tavkhelidze |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Helicoid
Similarity (geometry) 010102 general mathematics Object (grammar) 020207 software engineering Listing (computer) Class (philosophy) Torus 02 engineering and technology 01 natural sciences Combinatorics symbols.namesake 0202 electrical engineering electronic engineering information engineering symbols Möbius strip 0101 mathematics Representation (mathematics) Mathematics |
| Zdroj: | Modeling in Mathematics ISBN: 9789462392601 |
| DOI: | 10.2991/978-94-6239-261-8_11 |
| Popis: | Natural forms affect all of us, not only for their beauty, but also for their diversity (see e.g. Fig. 1). It is still not known whether forms define the essence of the phenomena associated with them, or vice versa - that is, forms are natural consequences of the phenomena. The essence of one “unexpected” phenomenon is as follows: Usually after one “full cutting”, an object is split into two parts. The Mobius strip is a well-known exception, however, which still remains whole after cutting. The first author discovered a class of surfaces, which have following properties - after full cutting more than two surfaces appear, but this is a result for specific class of pure mathematical surfaces [1, 2]. It turns out that three-dimensional Mobius Listing bodies, \(GML_m^n\), which is a wide subclass of the Generalized Twisting and Rotated figures - shortly \(GTR_m^n\) - which, through their analytic representation, could yield more than two objects after only single cutting ([3] or [2]). These are not only theoretical results, as can be proved by real-life examples. Many classical objects (torus with different forms of radial cross sections, helicoid, helix, Mobius strip,... etc.) are elements of this wide class of \(GTR_m^n\) figures, so it is important to study the similarity and difference between these figures and surfaces. In this chapter we study some questions of similarity and difference in the cases of the “cut” of Generalized Mobius–Listing’s figures. |
| Databáze: | OpenAIRE |
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