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Surfaces in Space

In: Geometry of Curves and Surfaces with MAPLE

Author

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  • Vladimir Rovenski

    (University of Haifa and Technion, Department of Mathematics)

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.

Suggested Citation

  • Vladimir Rovenski, 2000. "Surfaces in Space," Springer Books, in: Geometry of Curves and Surfaces with MAPLE, chapter 19, pages 231-264, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2128-9_20
    DOI: 10.1007/978-1-4612-2128-9_20
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