152CHAPTER 2. CURVESθ= 0θ= 2πFigure 2.21: Cycloidpairof equations. By contrast, the dynamic view of a curve as the path ofa moving point—especially when we use the language of vectors—extendsvery naturally to curves in space. We shall adopt this latter approach tospecifying a curve in space.The position vector of a point in space has three components, so the(changing) position of a moving point is specified by a function whosevalues are vectors inR3, which we denote by−→p:R→R3; this can beregarded as atripleof 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 thevector-valued function
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