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. . . one should not be too ready to erect a wall of separation between nature and the human mind. d'Alembert [Dugas (1955)] It is possible to present mathematics in a purely fonnal way, that is to say, without any reference to the physical world. Indeed, in the more advanced parts of abstract algebra and mathematical logic, one can pro ceed only in this manner. In other parts of mathematics, especially in Euclidean geometry, calculus, differential equations, and surface ge ometry, intimate connections exist between the mathematical ideas and physical things. In such cases, a deeper (and sometimes quicker) under standing can be gained by taking advantage of these connections. I am not, of course, suggesting that one should appeal to physical intuition whenever one gets stuck in a mathematical proof: in proofs, there is no substitute for rigor. Rather, the connections with physical reality should be made either to motivate mathematical assumptions, or to introduce questions out of which theorems arise, or to illustrate the results of an analysis. Such interconnections are especially important in the teaching of mathematics to science and engineering students. But, mathematics students too have much to gain by familiarizing themselves with the interconnections between ideas and real things. The present book explores the geometry of curves and surfaces in a physical way. Taschenbuch, 01.11.1996.

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This introductory text is exploratory in nature, and is intended as a bridge between Euclid's geometry and the modern geometry of curved spaces. It is organized around a collection of simple experiments which the reader can perform at home or in a classroom setting. Methods for physically exploring the intrinsic geometry of commonplace curved objects (such as bowls, balls and watermelons) are described. The concepts of Gaussian curvature, parallel transport and geodesics are treated. The book also contains biographical chapters on Gauss, Riemann and Levi-Civita. Paperback, Издание: Softcover reprint of the original 1st ed. 1996, Этикетка: Vieweg+Teubner Verlag, Vieweg+Teubner Verlag, Группа продуктов: Book, Опубликовано: 1996-01-01, Дата выпуска: 1996-01-01, Студия: Vieweg+Teubner Verlag, Продажи звание: 3232081.

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Einfache Experimente: Veranschaulichung differentialgeometrischer Begriffe Diese Einführung ist als Brücke zwischen der euklidischen und der modernen Geometrie gekrümmter Räume gedacht. Durch eine Sammlung einfacher Experimente, die der Leser zu Hause oder im Unterricht ausführen kann, bietet es einen intuitiven Einstieg. Beschrieben werden physikalische Methoden zur Untersuchung der intrinsischen Geometrie gewöhnlicher gekrümmter Objekte wie Schalen, Bälle und Wassermelonen. Die Begriff, . . . one should not be too ready to erect a wall of separation between nature and the human mind. d´Alembert [Dugas (1955)] It is possible to present mathematics in a purely fonnal way, that is to say, without any reference to the physical world. Indeed, in the more advanced parts of abstract algebra and mathematical logic, one can pro­ ceed only in this manner. In other parts of mathematics, especially in Euclidean geometry, calculus, differential equations, and surface ge­ ometry, intimate connections exist between the mathematical ideas and physical things. In such cases, a deeper (and sometimes quicker) under­ standing can be gained by taking advantage of these connections. I am not, of course, suggesting that one should appeal to physical intuition whenever one gets stuck in a mathematical proof: in proofs, there is no substitute for rigor. Rather, the connections with physical reality should be made either to motivate mathematical assumptions, or to introduce questions out of which theorems arise, or to illustrate the results of an analysis. Such interconnections are especially important in the teaching of mathematics to science and engineering students. But, mathematics students too have much to gain by familiarizing themselves with the interconnections between ideas and real things. The present book explores the geometry of curves and surfaces in a physical way. Taschenbuch, 01.11.1996.

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