Surfaces in Space

Vladimir Rovenski
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Vladimir Rovenski: University of Haifa and Technion, Department of Mathematics

Chapter 19 in Geometry of Curves and Surfaces with MAPLE, 2000, pp 231-264 from Springer

Abstract: Abstract In Sections 19.1 and 19.2 we consider some basic notions of a parametrized surface and a regular surface (analogous definitions for curves were studied in Section 5.1). In Section 19.3 we use a number of MAPLE commands to produce surfaces by various methods. In Section 19.4 we calculate and plot tangent planes and normal vectors of a surface. As an application we solve the conditional extremum problems in space (see the two-dimensional case in Section 5.6). In Section 19.5 we use changes in coordinates and linear transformations in space to calculate and plot an osculating paraboloid at the point of a surface. This elementary approach is given only for methodical reasons. In Section 19.6 we consider parametrized and implicitly defined surfaces with singularities.

Keywords: Singular Point; Tangent Plane; Smooth Point; Klein Bottle; Level Curf (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2128-9_20

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DOI: 10.1007/978-1-4612-2128-9_20

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