Complex Symmetries

This volume is a collection of essays on complex symmetries. It is curated, emphasizing the analysis of the symmetries, not the various phenomena that display those symmetries themselves. With this, the volume provides insight to nonspecialist readers into how individual simple symmetries constitute complex symmetry. The authors and the topics cover many different disciplines in various sciences and arts.

Simple symmetries, such as reflection, rotation, translation, similitude, and a few other simple manifestations of the phenomenon, are all around, and we are aware of them in our everyday lives. However, there are myriads of complex symmetries (composed of a bulk of simple symmetries) as well. For example, the well-known helix represents the combination of translational and rotational symmetry. Nature produces a great variety of such complex symmetries. So do the arts.

The contributions in this volume analyse selected examples (not limited to geometric symmetries).These include physical symmetries, functional (meaning not morphological) symmetries, such as symmetries in the construction of the genetic code, symmetries in human perception (e.g., in geometry education as well as in constructing physical theories), symmetries in fractal structures and structural morphology, including quasicrystal and fullerene structures in stable bindings and their applications in crystallography and architectural design, as well as color symmetries in the arts. The volume is rounded of with beautiful illustrations and presents a fascinating panorama of this interdisciplinary topic.

Existing books focus on objects (with symmetry properties) this book analyses the symmetry properties themselves Provides a wide scope on the application of composite symmetries in an iterdisciplinary aspect Explains the nature of the displayed symmetries

Autorentext
György Darvas, PhD, physicist, philosopher; director of Symmetrion (1991-); retired from the H. Academy of Sciences (1971-20119 and the R. Eötvös University (1998-2017), Budapest; editor, Symmetry: Culture and Science; founder (1989-), Intnl. Symmetry Association (2003-). Chairman and/or organiser: tens of symmetry related science-art events. Main fields of interest: symmetries in physics, the sciences and the arts.

György Darvas holds a MS degree in theoretical physics (1971, R. Eötvös University), a MS in philosophy of science (1974, R. Eötvös University), and a philosophical doctor (1985, R. Eötvös University). He is the author and editor of twenty seven volumes. His main 3 books: Symmetry, Basel: Birkhäuser, xi + 508 pp.; Hypersymmetry; Physics of the Isotopic Field-Charge Spin Conservation, de Gruyter: Berlin/Boston, ix + 219 pp.; (- with E. Agazzi, eds.) Philosophy of Mathematics Today, Episteme 22 (series ed., M. Bunge), Dordrecht/Boston/London: Kluwer Academic Publishers, xxix + 361 pp.

Inhalt
György Darvas: Complex Symmetries, Introduction.- Douglas Dunham: Complex Symmetries in Repeating Hyperbolic Patterns.- Paul Hertz: Ignotheory: A Compositional System for Intermedia Art Based on Tiling Patterns and Labelled Graphs.- Ashish Kumar Upadhyay: Symmetries of Maps on Surfaces.- Koji Miyazaki and Motonaga Ishii: Symmetry in Projection of 4-dimensional Regular Polychora.- Guy Inchbald: Morphic Polytopes and Symmetries.- Takeshi Sugimoto: Inducing the Symmetries out of the Complexity: The Kepler Triangle and its Kin as a Model Problem.- Jim Lehman: Synchronizing the Isotropic Vctor Matrix with the Stellated Vector Matrix.- András Recski: An Analogy and Several Symmetries.- Dmitriy Gurevich: Discrete Lattices on the Single Bearing Spiral: From Geometry to Botany.- Simone Brasili and Riccardo Piergallini: Symmetry and Invariance: Interdisciplinary teaching.- Eleonóra Stettner and György Emese: Dilative Rotation, Dilative Reflection in Mathematics, Nature, Art, and Education.- János Szász Saxon and Gábor Kis: Relationship of Symmetry and Combinatorics in the Poly-universe Game.- Marina Voinova: Symmetry in Arrow-like Salt Crystals.- László Szabados: Symmetries in Stellar, Galactic, and Extragalactic Astronomy.- Sergey V. Petoukhov, Elena S. Petukhova and Vladimir V. Verevkin: Symmetries and the Genetic, Code.- Kas Oosterhuis: Global Symmetry Local Asymmetry: In the Realized Buildings by the Innovation Studio ONL BV.- Katarzyna Szymaska-Stuka: Theme, Motive, Structure and Symmetry Pentasonata by Andrzej Panufnik.- FréIlgen: Fluid Symmetry: Logical to Artists, Mesmerizing to Viewers.- Paul B. Ré: Complex Symmetries in Réograms.- Patrice Jeener: Graphic Illustrations of Complex Symmetries.