Titlebook: Exploring Curvature; James Casey Textbook 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1996 Gaussian curvatu

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Keeping Track of Magnitude, Direction and Sense: Vectors,quantities can be represented mathematically by .. It turns out that vectors are also very useful in geometry, and you will have ample opportunity to see this when we study curves and surfaces. In the present chapter, the basic properties of vectors are described.

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Curvature of Curves,inly, the curvature of a straight line should be considered zero. Perhaps then, we can regard a curve as a deviation from a straight line? Let us explore how this idea can be given quantitative meaning.

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Gaussian Curvature,r. We learned that this variation is governed by Euler’s formula (15.30). In the present chapter, a completely different approach is taken, which is not based at all on the curvature of curves. Here, we study a brilliant idea of Gauss’s, which will enable us to define a unique value of . at each point on a smooth surface.

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,Levi-Civita (1873–1941), Christoffel (1829–1901), Beltrami (1835–1900), and others. During the closing decades of the 19th century, a powerful school of mathematics developed at the University of Padua. It was here that Levi-Civita came into contact with modern geometry.

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978-3-528-06475-4Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1996

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Studies of Phase Transformations,es give rise. Modem geometry is an extremely active field of research by pure and applied mathematicians, and it also has significant applications in physics and engineering. In the present book, we will explore in a physical manner the geometrical properties of curves and surfaces, and will discuss

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