Volume 3, 2020
|Number of page(s)||48|
|Section||Mathematics - Applied Mathematics|
|Published online||31 August 2020|
The general case of cutting of Generalized Möbius-Listing surfaces and bodies
University of Antwerp, Department of Bioscience Engineering, 2020 Antwerpen, Belgium
2 Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, 0179 Tbilisi, Georgia
Accepted: 19 June 2020
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.
Key words: Generalized Möbius-Listing surfaces and bodies / Möbius phenomenon / Gielis Transformations / R-functions / Knots and Links / Projective geometry / Topology
© J. Gielis and I. Tavkhelidze, Published by EDP Sciences, 2020
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