Viviani's Curve C is the intersection of the surfaces x2 + y2 = z2, y = z2
Question:
x2 + y2 = z2, y = z2
(a) Parametrize each of the two parts of C corresponding to x ¥ 0 and x ¤ 0, taking t = z as parameter.
(b) Describe the projection of C onto the xy-plane.
(c) Show that C lies on the sphere of radius 1 with center (0, 1, 0). This curve looks like a figure eight lying on a sphere
Transcribed Image Text:
Viviani's curve y=2" (B) Viviami's curve viewed from the negative y-axis.
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a We must solve for y and x in terms of z which is a parameterWe get Here the from x z 2 z 4 represe...View the full answer
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