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Author |
Gielis, J.; Tavkhelidze, I. |
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Title |
A note on Generalized Möbius-Listing Bodies |
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P1 Proceeding |
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Year  |
2023 |
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Pages |
31-39
T2 - Proceedings of the 1st International Sy |
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Keywords |
P1 Proceeding; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
Generalized Möbius-Listing surfaces and bodies generalize Möbius bands, and this research was motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin |
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Publication Date |
2023-11-29 |
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978-90-833839-0-3 |
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UA library record |
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no |
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Call Number |
UA @ admin @ c:irua:201047 |
Serial |
9063 |
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Author |
Gielis, J.; Tavkhelidze, I. |
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Title |
The general case of cutting of Generalized Möbius-Listing surfaces and bodies |
Type |
A1 Journal article |
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Year |
2020 |
Publication |
4Open |
Abbreviated Journal |
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Volume |
3 |
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Pages |
7-48 |
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Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
The original motivation to study Generalized Möbius-Listing GML surfaces and bodies was the observation that the solution of boundary value problems greatly depends on the domains. Since around 2010 GML’s were merged with (continuous) Gielis Transformations, which provide a unifying description of geometrical shapes, as a generalization of the Pythagorean Theorem. The resulting geometrical objects can be used for modeling a wide range of natural shapes and phenomena. The cutting of GML bodies and surfaces, with the Möbius strip as one special case, is related to the field of knots and links, and classifications were obtained for GML with cross sectional symmetry of 2, 3, 4, 5 and 6. The general case of cutting GML bodies and surfaces, in particular the number of ways of cutting, could be solved by reducing the 3D problem to planar geometry. This also unveiled a range of connections with topology, combinatorics, elasticity theory and theoretical physics. |
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Publication Date |
2020-08-31 |
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Edition |
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ISSN |
2557-0250 |
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UA library record |
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Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:174471 |
Serial |
7992 |
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Author |
Gielis, J.; Tavkhelidze, I. |
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Title |
The Mӧbius phenomenon in Generalized Mӧbius-Listing bodies with cross sections of odd and even polygons |
Type |
A3 Journal article |
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Year |
2020 |
Publication |
Sn – 1512-0066 |
Abbreviated Journal |
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Volume |
34 |
Issue |
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Pages |
23-26 |
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Keywords |
A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:174474 |
Serial |
8257 |
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