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Topic: unification of Green, Stokes, Divergence and keep the manifold #-107
Uni-textbook 7th ed.: TRUE CALCULUS; without the phony limit concept

Replies: 7   Last Post: Jul 26, 2013 2:07 AM

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 plutonium.archimedes@gmail.com Posts: 7,939 Registered: 3/31/08
a new way of finding volume and surface via the Cell theory #-109
Uni-textbook 7th ed.: TRUE CALCULUS; without the phony limit concept

Posted: Jul 25, 2013 5:33 AM

Perhaps I found a new way of doing volume and surfaces in mathematics.

Perhaps I found an equivalent method of the triple integral.

Two functions in 2nd dimension allows us to obtain area of closed figures such as those found in Green, Stokes and Divergence theorems. But then to get to surfaces and volume as in Stokes or Divergence theorem, we use the z-axis to stack planes.

For a surface with area, the z axis stacks planes containing graphed function curves in the x and y axis and the stacking of those curves turns them into a surface with area. We can work backwards also. We start with a closed surface with area in 3rd dimension and we take a fancy saw that cuts the 3 dimensional space into planes. Our curved surface is still there only contained in a multitude of planes containing a line segments of the surface and when we stack those planes we retrieve our surface.

For a volume, the graphed functions in the x and y axis are closed loops and the stacking of planes of these closed loops builds a 3 dimensional object of volume. Here again we can work backwards and starting with the sphere in 3rd dimension we take the fancy saw that cuts 3 D into planes and the planes contain various sizes of circles and when stacking all those planes we retrieve the original sphere inside.

So when we do a triple integral, are we in fact doing a double integral of a closed surface and by stacking planes of these surfaces we end up with volume.

I am trying to think of how a z component refers to the proper plane that contains either a line-curve or a surface, or a point (tangent point). For the z axis would be the putting in sequental order the proper planes to build the figure.

So the z axis would be a function of sequential order of planes.

AP