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

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Normal Sections,One way of exploring curved surfaces is to examine the curvature of curves lying on them. In the present chapter, we will use planes to cut a surface in a specific way, and we will study the resulting curves to gain some insight into the nature of surface curvature.

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,Riemann (1826–1866),Like Mozart’s, Bernhard Riemann’s life was short but marvelously creative. He solved several of the most difficult problems in pure and applied mathematics, introduced entirely new concepts and techniques, and profoundly changed the way in which mathematicians, physicists, and philosophers view space.

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Parallel Transport of a Vector on a Surface,In this chapter, we describe a particular way of moving a vector along a given curve on a surface. It provides an especially revealing means of exploring the non-Euclideanness of the surface.

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Materialflu?gestaltung in Fertigungssystemen, and Beethoven (1770–1827) seem to possess almost superhuman powers. In literature, we have Shakespeare (1564–1616), Milton (1608–1674), Goethe (1749–1832), and several others. In mathematics, Archimedes (287–212 B.C.), Newton (1642–1727), and Gauss are ranked at the top, but magnificent contributi

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Textbook 1996lity 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 stu

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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.