The General Case of Cutting GML Bodies: The Geometrical Solution

Johan Gielis, Diego Caratelli, Ilia Tavkhelidze

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

The original motivation to study this class of geometrical objects of Generalized Möbius-Listing GML surfaces and bodies was the observation that the solution of boundary value problems greatly depends on the structure of the boundary of 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 [1]. This also unveiled a range of connections with topology, combinatorics, elasticity theory and theoretical physics.

Original languageEnglish
Title of host publicationDifferential and Difference Equations with Applications, ICDDEA 2019
EditorsSandra Pinelas, Sandra Pinelas, John R. Graef, Stefan Hilger, Peter Kloeden, Christos Schinas
PublisherSpringer
Pages397-411
Number of pages15
ISBN (Print)9783030563226
DOIs
Publication statusPublished - 2020
Event4th International Conference on Differential and Difference Equations with Applications, ICDDEA 2019 - Lisbon, Portugal
Duration: 1 Jul 20195 Jul 2019

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume333
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference4th International Conference on Differential and Difference Equations with Applications, ICDDEA 2019
CountryPortugal
CityLisbon
Period1/07/195/07/19

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