TY - GEN

T1 - The General Case of Cutting GML Bodies

T2 - 4th International Conference on Differential and Difference Equations with Applications, ICDDEA 2019

AU - Gielis, Johan

AU - Caratelli, Diego

AU - Tavkhelidze, Ilia

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85096572523&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-56323-3_31

DO - 10.1007/978-3-030-56323-3_31

M3 - Conference contribution

AN - SCOPUS:85096572523

SN - 978-3-030-56322-6

T3 - Springer Proceedings in Mathematics and Statistics (PROMS)

SP - 397

EP - 411

BT - Differential and Difference Equations with Applications

A2 - Pinelas, Sandra

A2 - Graef, John R.

A2 - Hilger, Stefan

A2 - Kloeden, Peter

A2 - Schinas, Christos

PB - Springer

CY - Cham

Y2 - 1 July 2019 through 5 July 2019

ER -