(a) Show that any point on x 2 + y 2 = z 2 can be written...
Question:
(a) Show that any point on x2 + y2 = z2 can be written in the form (z cos θ, z sin θ, z) for some θ.
(b) Use this to find a parametrization of Viviani’s curve (Exercise 31) with θ as the parameter.
Data From Exercise 31
C is the intersection of the surfaces (Figure 12)
Transcribed Image Text:
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
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We first verify that x z cos 0 y z sin 0 and z z satisfy the equation of the surface x y 2 cos0 2 si...View the full answer
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