Includes "Commentariolus," Copernicus' hypotheses for heavenly motions; "Narratio Prima," popular introduction to Copernican theory; and "The Letter Against Werner," refutation of the views of a contemporary. Extensive editorial apparatus.

Praise for the previous edition [. . .] Dr. Popko’s elegant new book extends both the science and the art of spherical modeling to include Computer-Aided Design and applications, which I would never have imagined when I started down this fascinating and rewarding path. His lovely illustrations bring the subject to life for all readers, including those who are not drawn to the mathematics. This book demonstrates the scope, beauty, and utility of an art and science with roots in antiquity. [. . .] Anyone with an interest in the geometry of spheres, whether a professional engineer, an architect or product designer, a student, a teacher, or simply someone curious about the spectrum of topics to be found in this book, will find it helpful and rewarding. – Magnus Wenninger, Benedictine Monk and Polyhedral Modeler Ed Popko's comprehensive survey of the history, literature, geometric, and mathematical properties of the sphere is the definitive work on the subject. His masterful and thorough investigation of every aspect is covered with sensitivity and intelligence. This book should be in the library of anyone interested in the orderly subdivision of the sphere. – Shoji Sadao, Architect, Cartographer and lifelong business partner of Buckminster Fuller Edward Popko's Divided Spheres is a "thesaurus" must to those whose academic interest in the world of geometry looks to greater coverage of synonyms and antonyms of this beautiful shape we call a sphere. The late Buckminster Fuller might well place this manuscript as an all-reference for illumination to one of nature's most perfect inventions. – Thomas T. K. Zung, Senior Partner, Buckminster Fuller, Sadao, & Zung Architects. This first edition of this well-illustrated book presented a thorough introduction to the mathematics of Buckminster Fuller’s invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explained the principles of spherical design and the three classic methods of subdivision based on geometric solids (polyhedra). This thoroughly edited new edition does all that, while also introducing new techniques that extend the class concept by relaxing the triangulation constraint to develop two new forms of optimized hexagonal tessellations. The objective is to generate spherical grids where all edge (or arc) lengths or overlap ratios are equal. New to the Second Edition New Foreword by Joseph Clinton, lifelong Buckminster Fuller collaborator A new chapter by Chris Kitrick on the mathematical techniques for developing optimal single-edge hexagonal tessellations, of varying density, with the smallest edge possible for a particular topology, suggesting ways of comparing their levels of optimization An expanded history of the evolution of spherical subdivision New applications of spherical design in science, product design, architecture, and entertainment New geodesic algorithms for grid optimization New full-color spherical illustrations created using DisplaySphere to aid readers in visualizing and comparing the various tessellations presented in the book Updated Bibliography with references to the most recent advancements in spherical subdivision methods

Alliance politics is a regular headline grabber. When a possible military crisis involving Russia, North Korea, or China rears its head, leaders and citizens alike raise concerns over the willingness of US allies to stand together. As rival powers have tightened their security cooperation, the United States has stepped up demands that its allies increase their defense spending and contribute more to military operations in the Middle East and elsewhere. The prospect of former President Donald Trump unilaterally ending alliances alarmed longstanding partners, even as NATO was welcoming new members into its ranks. Military Alliances in the Twenty-First Century is the first book to explore fully the politics that shape these security arrangements – from their initial formation through the various challenges that test them and, sometimes, lead to their demise. Across six thematic chapters, Alexander Lanoszka challenges conventional wisdom that has dominated our understanding of how military alliances have operated historically and into the present. Although military alliances today may seem uniquely hobbled by their internal difficulties, Lanoszka argues that they are in fact, by their very nature, prone to dysfunction.

A page-turning novel that is also an exploration of the great philosophical concepts of Western thought, Jostein Gaarder's Sophie's World has fired the imagination of readers all over the world, with more than twenty million copies in print. One day fourteen-year-old Sophie Amundsen comes home from school to find in her mailbox two notes, with one question on each: "Who are you?" and "Where does the world come from?" From that irresistible beginning, Sophie becomes obsessed with questions that take her far beyond what she knows of her Norwegian village. Through those letters, she enrolls in a kind of correspondence course, covering Socrates to Sartre, with a mysterious philosopher, while receiving letters addressed to another girl. Who is Hilde? And why does her mail keep turning up? To unravel this riddle, Sophie must use the philosophy she is learning—but the truth turns out to be far more complicated than she could have imagined.

Sociology, as a discipline, was born at the height of global colonialism and imperialism. Over a century later, it is yet to shake off its commitment to colonial ways of thinking. This book explores why, and how, sociology needs to be decolonized. It analyses how sociology was integral in reproducing the colonial order, as dominant sociologists constructed theories either assuming or proving the supposed barbarity and backwardness of colonized people. Ali Meghji reveals how colonialism continues to shape the discipline today, dominating both social theory and the practice of sociology, how exporting the Eurocentric sociological canon erased social theories from the Global South, and how sociologists continue to ignore the relevance of coloniality in their work. This guide will be necessary reading for any student or proponent of sociology. In opening up the work of other decolonial advocates and under-represented thinkers to readers, Meghji offers key suggestions for what teachers and students can do to decolonize sociology. With curriculum reform, innovative teaching and a critical awareness of these issues, it is possible to make sociology more equitable on a global scale.