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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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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