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Opt Art

From Mathematical Optimization to Visual Design

Robert Bosch

PDF
ca. 28,99
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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

A fun and stunningly illustrated introduction to the art of linear optimization

Linear optimization is a powerful modeling method for discovering the best solution to a problem among a set of available alternatives. It is one of today’s most important branches of mathematics and computer science—and also a surprisingly rich medium for creating breathtaking works of art. Opt Art takes readers on an entertaining tour of linear optimization and its applications, showing along the way how it can be used to design visual art.

Robert Bosch provides a lively and accessible introduction to the geometric, algebraic, and algorithmic foundations of optimization. He presents classical applications, such as the legendary Traveling Salesman Problem, and shows how to adapt them to make optimization art—opt art. Each chapter in this marvelously illustrated book begins with a problem or puzzle and demonstrates how the solution can be derived using a host of artistic methods and media, including 3D printing, laser cutting, and computer-controlled machining. Bosch focuses on mathematical modeling throughout—converting a problem into a workable mathematical form, solving it using optimization techniques, and examining the results, which can take the form of mosaics, line drawings, and even sculpture. All you need is some high-school algebra, geometry, and calculus to follow along.

Featuring more than a hundred illustrations and photos of Bosch’s own art, Opt Art demonstrates how mathematics and computing can be used to create beauty and express emotion through amazing works of art.

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Schlagwörter

Diagram (category theory), Rotational symmetry, Scientific notation, Bézier curve, Linear programming, Great stellated dodecahedron, Interlacing (bitmaps), RGB color model, Complete graph, Jordan curve theorem, Optimization problem, Binary number, Diagonal, Variable (mathematics), Diagram, Applied mathematics, Linear equation, Computation, Checkerboard, Mathematical optimization, Assignment problem, Exhaustion, Iteration, Equation, Pure mathematics, Pointillism, Algorithm, Error, Restriction (mathematics), Mathematics, Laptop, Rectangle, Summation, Marquetry, Grayscale, Simplex algorithm, Celtic knot, Sandro Botticelli, Branch and bound, Subset, Rendering (computer graphics), Integer programming, Equilateral triangle, Martin Gardner, Analogy, Loss function, Rubik's Cube, Black string, PostScript, Emoji, Integer, Feasible region, Addition, Fair coin, Modularity (networks), Quantity, Knight's tour, Mathematician, Tree (data structure), Line segment, Parity (mathematics), Mathematical problem, Function (mathematics), Notation, Mathemagician, Solver, Duotone, Gustave Courbet, Ken Knowlton, Half-space (geometry), Bit, Small stellated dodecahedron, Donald Knuth, John Horton Conway, Weighted arithmetic mean, William Rowan Hamilton, Instance (computer science), Chessboard, Computer performance, Mirror symmetry (string theory), Smoothing, Polyhedron, Mirror symmetry, Pixel, Line (geometry), Travelling salesman problem, Combination, Regular polygon, Linear function, Contour line, Brendan McKay, Local optimum, Truchet tiles, Linear inequality, Ariadne's thread (logic), Gurobi, M. C. Escher, Variable (computer science), Big O notation, George Dantzig