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)

Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics an d group theory. This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics. The author strikes a balance between covering the historical development of the theory surrounding polyhedra, and presenting a rigorous treatment of the mathematics involved. It is attractively illustrated with dozens of diagrams to illustrate ideas that might otherwise prove difficult to grasp. Historians of mathematics, as well as those more interested in the mathematics itself, will find this unique book fascinating.

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

Innovative Teaching: Best Practices from Business and Beyond for Mathematics Teachers provides educators with new and exciting ways to introduce material and methods to motivate and engage students by showing how some of the techniques commonly used in the business world — and beyond — are applicable to the world of education. It also offers educators practical advice with regard to the changing culture of education, keeping up with technology, navigating politics at work, interacting with colleagues, developing leadership skills, group behavior, and gender differences.Innovative Teaching demonstrates how the classroom environment is similar to the marketplace. Educators, like businesses, for example, must capture and hold the attention of their audience while competing with a constant stream of 'noise.' With the introduction of the Internet and the wide use of social media, promoters understand that they must not only engage their audience, but also incorporate audience feedback into the promotional work and product or service they offer. Innovative Teaching shows educators how to take the best practices from business — and beyond — and recombine these resources for appropriate use in the classroom.

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.