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Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.
Polyhedra --- Polyèdres --- Models --- Data processing --- Modèles --- Geometrical models --- Polyhedral figures --- Polyhedrons --- Geometry, Solid --- Shapes --- Data processing. --- Models.
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This much-anticipated textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. Because there is no other book that puts together all of these ideas in one place, this text is truly a service to the mathematical community. We encounter here a friendly invitation to the field of "counting integer points in polytopes," also known as Ehrhart theory, and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant, and the authors' engaging style encourages such participation. The many compelling pictures that accompany the proofs and examples add to the inviting style. For teachers, this text is ideally suited as a capstone course for undergraduate students or as a compelling text in discrete mathematical topics for beginning graduate students. For scientists, this text can be utilized as a quick tooling device, especially for those who want a self-contained, easy-to-read introduction to these topics. .
Mathematics. --- Discrete geometry. --- Polyhedra. --- Computer science --- Geometry --- Combinatorial geometry --- Math --- Science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Polyhedral figures --- Polyhedrons --- Geometry, Solid --- Shapes --- Mathematics --- Combinatorics. --- Geometry. --- Number theory. --- Discrete groups. --- Computer science. --- Discrete Mathematics. --- Number Theory. --- Convex and Discrete Geometry. --- Computational Science and Engineering. --- Informatics --- Groups, Discrete --- Infinite groups --- Number study --- Numbers, Theory of --- Algebra --- Euclid's Elements --- Combinatorics --- Mathematical analysis --- Discrete mathematics. --- Convex geometry . --- Computer mathematics. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis
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