From Kepler Tiling To Penrose Tiling To Cps Geometry
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From Kepler Tiling To Penrose Tiling To CPS Geometry
This book is a collection of my handwritten notes I took in the fall of 2021. They are presented the way they were created back then. I believe there is some values in publishing the raw notes, in the format they were taken, before the ideas contained in them were fully developed and have crystallized. To get the most of these notes an understanding of Penrose Tiling and the basic assumptions of the Close Packing of Spheres (CPS) Geometry, is a must. A lot has been written about Penrose Tiling over the years. Regarding the Geometry of Closed Packed Spheres, I highly recommend my book introducing the subject “From Riemann Hypothesis to CPS Geometry and Back: Volume 1” - please see https://www.amazon.com/dp/B08JG1DLCV Also, a lot more on this topic can be found here: http://platonicstructures.com/ Enjoy.
A Guide to Penrose Tilings
Author: Francesco D'Andrea
language: en
Publisher: Springer Nature
Release Date: 2023-08-19
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 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 more 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.
Connections
The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in OC Mathematics, Chemistry, and Astronomy OCo Professional and ReferenceOCO in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition. Contents: Proportion in Architecture; Similarity; The Golden Mean; Graphs; Tilings with Polygons; Two-Dimensional Networks and Lattices; Polyhedra: Platonic Solids; Transformation of the Platonic Solids I; Transformation of the Platonic Solids II; Polyhedra: Space Filling; Isometries and Mirrors; Symmetry of the Plane. Readership: Polytechnic students, architects, designers, mathematicians and general readers."