152 CHAPTER 2. CURVES θ = 0 θ = 2 π Figure 2.21: Cycloid pair of equations. By contrast, the dynamic view of a curve as the path of a moving point—especially when we use the language of vectors—extends very naturally to curves in space. We shall adopt this latter approach to specifying a curve in space. The position vector of a point in space has three components, so the (changing) position of a moving point is speci±ed by a function whose values are vectors in R 3 , which we denote by −→ p : R → R 3 ; this can be regarded as a triple of functions: x = x ( t ) y = y ( t ) z = z ( t ) or −→ p ( t ) = ( x ( t ) ,y ( t ) ,z ( t )) . As before, it is important to distinguish the vector-valued function
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.