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Subject:
Parametrization of surface S
Category: Science > Math Asked by: chuvak2k-ga List Price: $10.00 |
Posted:
02 Feb 2005 17:26 PST
Expires: 04 Mar 2005 17:26 PST Question ID: 467832 |
x = a*u*cos(2Pi*v), y= a*u*sin(2Pi*v), z= b*v Describe the parametrized surface S, where a,b are positive constant 0<= u <=1 and 0<= v<= 1 Compute the area of S. |
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There is no answer at this time. |
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Subject:
Re: Parametrization of surface S
From: alcatraz28-ga on 08 Feb 2005 21:05 PST |
OK, here is my answer: the surface is the trace of a stick of length a, which is being lifted up with velocity b for one second and at the same time rotated about the z-axis with angular velocity 2Pi. The surface area can be computed by the standard fomula http://ltcconline.net/greenl/courses/202/vectorIntegration/parametricSurfaces.htm and equals (if I didn't make any mistakes) (b^2/2Pi) * ln(1+sqrt{2}) + \sqrt{ a^2 * b^2 + 4 * Pi^2 * a^4 * b^2} Keep the 10 bucks. |
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