Consider the torus of revolution generated by rotating the circle (x − a)² + z² = r², y = 0, - about the z axis (a > r > 0). The parallels generated by the points (a +r, 0), (a −r, 0), (a, r) are called the maximum parallel, the mini- mum parallel, and the upper parallel, respectively. Check which of these parallels is a. A geodesic. b. An asymptotic curve. c. A line of curvature.
Consider the torus of revolution generated by rotating the circle (x − a)² + z² = r², y = 0, - about the z axis (a > r > 0). The parallels generated by the points (a +r, 0), (a −r, 0), (a, r) are called the maximum parallel, the mini- mum parallel, and the upper parallel, respectively. Check which of these parallels is a. A geodesic. b. An asymptotic curve. c. A line of curvature.
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter13: Conic Sections
Section13.1: Circles
Problem 47PS
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![5. Consider the torus of revolution generated by rotating the circle
(x − a)² + z² = r², y = 0,
about the z axis (a > r > 0). The parallels generated by the points
(a +r, 0), (ar, 0), (a, r) are called the maximum parallel, the mini-
mum parallel, and the upper parallel, respectively. Check which of these
parallels is
a. A geodesic.
b. An asymptotic curve.
c. A line of curvature.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F882ce437-6984-48a2-b1c1-0c70a26630a5%2F02ae2b00-8c72-4a69-9cc9-26ef9796c555%2Fmdymqw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Consider the torus of revolution generated by rotating the circle
(x − a)² + z² = r², y = 0,
about the z axis (a > r > 0). The parallels generated by the points
(a +r, 0), (ar, 0), (a, r) are called the maximum parallel, the mini-
mum parallel, and the upper parallel, respectively. Check which of these
parallels is
a. A geodesic.
b. An asymptotic curve.
c. A line of curvature.
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