C is the intersection of the surfaces (Figure 12) x + y = z, y = z

C is the intersection of the surfaces (Figure 12)

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x + y = z, y = z (a) Separately parametrize each of the two parts of C corresponding to x > 0 and x 0, taking t = z as the parameter. (b) Describe the projection of C onto the xy-plane. (c) Show that C lies on the sphere of radius 1 with its center (0, 1,0). This curve looks like a figure eight lying on a sphere [Figure 12(B)]. Viviani's curve (A) x + y =z y=z 8 (B) Viviani's curve viewed from the negative y-axis