Titlebook: A Guide to Penrose Tilings; Francesco D‘Andrea Book 2023 The Editor(s) (if applicable) and The Author(s), under exclusive license to Sprin

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Continuous Transformation Groups,elf-contained introduction to Bratteli diagrams, AF equivalence relations, AF algebras and their K-theory, and their use in the classification of minimal Cantor systems, such as the one parameterizing Penrose tilings. We will take for granted some basic results about K-theory and assume that the reader has some familiarity with C*-algebras.

Cacophonous

Book 2023in the ‘70s. Quasi-periodic tilings of the plane, of which Penrose tilings are the most famous example, started as recreational mathematics and soon attracted the interest of scientists for their possible application in the description of quasi-crystals. The purpose of this survey, illustrated with

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Book 2023more than 200 figures, is to introduce the curious reader to this beautiful topic and be a reference for some proofs that are not easy to find in the literature. The volume covers many aspects of Penrose tilings, including the study, from the point of view of Connes‘ Noncommutative Geometry, of the space parameterizing these tilings..

Common-Migraine

ns an overview of the tools from noncommutative geometry nee.This book provides an elementary introduction, complete with detailed proofs, to the celebrated tilings of the plane discovered by Sir Roger Penrose in the ‘70s. Quasi-periodic tilings of the plane, of which Penrose tilings are the most fa

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Mystic

Robinson Triangles,s and was more concerned with the measurement of material properties, such as eddy-current loss and permeability, than with what was then the very new concept of domain wall motion. A valuable review of the beginnings of a more microscopic approach to these problems has been given by Kittel (1946a)