Polyhedra - Shopping2000.com

Modeling of Curves and Surfaces with MATLAB®

This concise text on geometry with applications in a variety of disciplines is devoted to three main geometrical topics: curves, surfaces, and polyhedra. It presents elementary methods for analytical modeling and their visualization, as well as demonstrating the potential of symbolic computational tools to support the development of analytical solutions.The author systematically examines powerful tools including 2D and 3D animation of geometric images, transformations, shadows and colors, and then further studies more complex geometrical modeling problems related to analysis and differential equations. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. The book is also well-illustrated, with over 300 figures reproducible using Matlab programs.This text greatly extends the author's previous title, "Geometry of Curves and Surfaces with Maple" (Birkhauser, 2000), and has a different focus. In addition to being applications-driven and motivated by numerous examples and exercises from real-world fields such as physics, engineering, biology, computer science, and IT, the book also contains more than 60 percent new material, including new sections with a geometric view of dynamical systems and PDEs, fractals, and surfaces-splines.This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines, engineers, computer scientists, and instructors of applied mathematics.

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Price: 40.99 EUR excl. shipping

Geometry Revealed

Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended...In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is very much alive and at the very heart of the work of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concepts to be created. The book is visually rich and inviting, so that readers may open it at random places and find much pleasure throughout according their own intuitions and inclinations.Marcel Berger is the author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with an affinity for geometry.

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Price: 49.99 EUR excl. shipping

The Polyhedrists: Art and Geometry in the Long Sixteenth Century

A history of the relationship between art and geometry in the early modern period. In The Polyhedrists, Noam Andrews unfolds a history of the relationship between art and geometry in early modern Europe, told largely through a collective of ground-breaking artisan-artists (among them, Luca Pacioli, Albrecht Dürer, Wenzel Jamnitzer, and Lorentz Stöer) and by detailed analysis of a rich visual panoply of their work, featuring paintings, prints, decorative arts, cabinetry, and lavishly illustrated treatises. But this is also an art history of the polyhedra themselves, emblems of an evolving artistic intelligence, which include a varied set of geometrical figures-both Platonic, or regular, like the simple tetrahedron, and Archimedean, or irregular, like the complex yet beguiling rhombicosidodecahedron. Moreover, The Polyhedrists argues that the geometrical depictions of Dürer, Jamnitzer et al. were far more than mere follies from the dawn of perspective, at odds with a contemporary view of the Renaissance, and destined to be superseded by later developments in higher level mathematics. In fact, the evolution of the solids into innumerable "irregular bodies" constituted a sustained moment in the formulation of Renaissance mathematical knowledge and its engagement with materiality. This intense field of experimentation would birth a new language of geometrical abstraction that would ignite a century of novel form-making strategies, ultimately paving the way for developments in geometry and topology in the nineteenth and early twentieth centuries, and even prefiguring the more recent digital turn. The book, in this sense, is not just an applied history of geometry, nor a particular geometric reading of early modern art through some of its more celebrated practitioners, but a manifesto of sorts into the hitherto unexplored wilds of art and science.

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Price: 35.99 EUR excl. shipping