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Given
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Surface in 3D space (torus):
x = (a+b*cos(u))*cos(v)
y = (a+b*cos(u))*sin(v)
z = b*sin(v)
in rectangular coordinate system | | - surface metric (first fundamental form)
- second fundamental form
- mean curvature vector
- connection, Christoffel symbols, curvature
- Riemann and Ricci tensors
- Gauss curvature
- Laplace operator
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Solution
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Start | Run atlas 2D/3D Wizard and press NEXT button |
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Dimension 2D/3D | Choose 3D - space and press NEXT button |
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Coordinate System | Select rectangular coordinate system and press NEXT button |
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Curve or Surface | Select surface and press NEXT button |
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Enter Equations | Enter the surface equations and press NEXT button (u, v are surface coordinates) |
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Final Check-Out | Press Check-Out button or just skip this step and press NEXT button |
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Save as Worksheet | Specify a worksheet to save the Maple™ code (output.mws by default). |
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Finish | Press FINISH button and execute in Maple™ the generated file |
Result of the execution
| You will see the results of the execution in the worksheet: surface metric, second fundamental form, mean curvature vector, connection, Christoffel symbols, curvature, Riemann and Ricci tensors, Gauss curvature, Laplace operator.
It takes 40 seconds to solve this problem from the beginning to the end! Just try it. |
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