Wyniki wyszukiwania:

The focus of this monograph is converting-reshaping-one 3D convex polyhedron to another via an operation the authors call "tailoring." A convex polyhedron is a gem-like shape composed of flat facets, the focus of study since Plato and Euclid. The tailoring operation snips off a corner (a "vertex") of a polyhedron and sutures closed the hole. This is akin to Johannes Kepler's "vertex truncation," but differs in that the hole left by a truncated vertex is filled with new surface, whereas tailoring zips the hole closed. A powerful "gluing" theorem of A.D. Alexandrov from 1950...

Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.

This book covers traditional topics such as convex hulls, triangulations, and Voronoi...

Most philosophical explorations of responsibility discuss the topic solely in terms of metaphysics and the "free will" problem. By contrast, these essays by leading philosophers view responsibility from a variety of perspectives -- metaphysics, ethics, action theory, and the philosophy of law. After a broad, framing introduction by the volume's editors, the contributors consider such subjects as responsibility as it relates to the "free will" problem; the relation between responsibility and knowledge or ignorance; the relation between causal and moral responsibility; the difference, if...

The concepts of time and identity seem at once unproblematic and frustratingly difficult. Time is an intricate part of our experience -- it would seem that the passage of time is a prerequisite for having any experience at all -- and yet recalcitrant questions about time remain. Is time real? Does time flow? Do past and future moments exist? Philosophers face similarly stubborn questions about identity, particularly about the persistence of identical entities through change. Indeed, questions about the metaphysics of persistence take on many of the complexities inherent in philosophical...