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Prove that the surface of revolution = (u cos e)e, + (u sin e)e, + f(v)ez where u = C, cos (v/a) + C2 sin (v/a) and f(v) = | V1- (du/dv)² dv is a surface of constant positive Gaussian curvature K= 1/a² for all C1, C2. For what values of C, and C2 is the surface a sphere? Ans. C, = a, C2 = 0 or C, = 0, C2 = a.

Prove that the surface of revolution = (u cos e)e, + (u sin e)e, + f(v)ez where u = C, cos (v/a) + C2 sin (v/a) and f(v) = | V1- (du/dv)² dv is a surface of constant positive Gaussian curvature K= 1/a² for all C1, C2. For what values of C, and C2 is the surface a sphere? Ans. C, = a, C2 = 0 or C, = 0, C2 = a.

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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Prove that the surface of revolution = (u cos e)e, + (u sin e)e, + f(v)ez where u = C, cos (v/a) + C2 sin (v/a) and f(v) = | V1- (du/dv)² dv is a surface of constant positive Gaussian curvature K= 1/a² for all C1, C2. For what values of C, and C2 is the surface a sphere? Ans. C, = a, C2 = 0 or C, = 0, C2 = a.
Transcribed Image Text:Prove that the surface of revolution = (u cos e)e, + (u sin e)e, + f(v)ez where u = C, cos (v/a) + C2 sin (v/a) and f(v) = | V1- (du/dv)² dv is a surface of constant positive Gaussian curvature K= 1/a² for all C1, C2. For what values of C, and C2 is the surface a sphere? Ans. C, = a, C2 = 0 or C, = 0, C2 = a.
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