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July 15th, 2019, 09:16 AM   #1
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Computing volume of fiber bundle

I am trying to compute the 3d-area of the 3d-sphere (embedded in 4d space) by treating it as a bundle of circles over a 2d-sphere. I assume the following:

1. The base is a 2d-sphere having the same radius as the total 3d-sphere.
2. Each fiber is a circle, also having the same radius.
3. Each fiber is perpendicular to the base at the point where it intersects the base.
4. Each fiber is parallel (equidistant) to its neighboring fibers.

When I multiply the circumference of the circle fiber with the area of the 2d-sphere base, I'd think I should get the 3d-area of the 3d-sphere, but I get something different. What am I doing wrong?
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