Polyhedra And Beyond

This volume collects papers based on talks given at the conference “Geometrias'19: Polyhedra and Beyond”, held in the Faculty of Sciences of the University of Porto between September 5-7, 2019 in Portugal. These papers explore the conference’s theme from an interdisciplinary standpoint, all the while emphasizing the relevance of polyhedral geometry in contemporary academic research and professional practice. They also investigate how this topic connects to mathematics, art, architecture, computer science, and the science of representation. Polyhedra and Beyond will help inspire scholars, researchers, professionals, and students of any of these disciplines to develop a more thorough understanding of polyhedra.

Diese Sammlung von Beitragen anerkannter Autoren zur Architektur, die uber den Quader hinausgeht, ist das einzige derzeit am Markt befindliche Referenzwerk auf diesem Gebiet. Theoretische und praktische Aspekte der Konstruktion von Vielflachnern und raumlichen Gebilden werden anhand von uber 480 Zeichnungen und zahlreichen Fotographien anschaulich erlautert. (02/98)

This volume collects papers based on talks given at the conference “Geometrias'19: Polyhedra and Beyond”, held in the Faculty of Sciences of the University of Porto between September 5-7, 2019 in Portugal. These papers explore the conference's theme from an interdisciplinary standpoint, all the while emphasizing the relevance of polyhedral geometry in contemporary academic research and professional practice. They also investigate how this topic connects to mathematics, art, architecture, computer science, and the science of representation. Polyhedra and Beyond will help inspire scholars, researchers, professionals, and students of any of these disciplines to develop a more thorough understanding of polyhedra.

The objective of this book is to present for the first time the complete algorithm for roots of the general quintic equation with enough background information to make the key ideas accessible to non-specialists and even to mathematically oriented readers who are not professional mathematicians. The book includes an initial introductory chapter on group theory and symmetry, Galois theory and Tschirnhausen transformations, and some elementary properties of elliptic function in order to make some of the key ideas more accessible to less sophisticated readers. The book also includes a discussion of the much simpler algorithms for roots of the general quadratic, cubic, and quartic equations before discussing the algorithm for the roots of the general quintic equation. A brief discussion of algorithms for roots of general equations of degrees higher than five is also included. "If you want something truly unusual, try [this book] by R. Bruce King, which revives some fascinating, long-lost ideas relating elliptic functions to polynomial equations." --New Scientist

This book includes the refereed Selected Papers of the 20th International Conference on Computer-Aided Architectural Design. INTERCONNECTIONS: Co-computing Beyond Boundaries, CAAD Futures 2023, held in Delft, The Netherlands, in July 5–7, 2023. The 43 full papers included in this book were carefully reviewed and selected from 144 submissions. They were organized in topical sections as follows: ​algorithmic architectural design; AI-powered architectural ideation; performance-based design, urban models and analysis; urban design; digital design, materials and fabrication; spatial information, data and semantics; building data analysis, visualisation, interaction; and building massing and layouts.

This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.