Plane Curves in Rectangular Coordinates

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

Chapter 5 in Geometry of Curves and Surfaces with MAPLE, 2000, pp 47-60 from Springer

Abstract: Abstract There are many ways to classify curves. One of them is to think of curves as either algebraic or transcendental. An algebraic (plane) curve is given by a polynomial equation P(x, y) = 0. Its degree n = deg P is called the order of the curve. Curves of order n = 2 are studied in analytic geometry. The first classification of curves of order n = 3 was obtained by Newton. The case n > 3 is more difficult. But among easily obtained curves, there are many that are nonalgebraic, for example, the cycloid and spiral of Archimedes; we study them using parametrized or implicit equations (Chapter 5) or polar coordinates (see Chapter 6).

Keywords: Vector Field; Plane Curf; Level Curf; Logarithmic Spiral; Happy Face (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-1-4612-2128-9_6

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