A three-dimensional (3-D, nonplanar) geometrical configuration of astrophysical fluids could be conveniently visualized.
What is a justified way to visualize one-dimensional (1-D, planar) geometrical configuration of dust molecular cloud fluids in astrophysics?
What is well represented by the single spatial variable, x, in this context?
In continuation, it is well known that a spherical (3-D) problem (with total degree of freedom # 3) could be reduced into a radial (1-D) problem (with total degree of freedom # 1) at the backdrop of spherically symmetric geometry. In both the cases (3-D + 1-D), the radial coordinate, r, can be well visualized in a sphere.
The same problem for analytic simplicity can also be worked out in a planar cartesian geometry (1-D). In this case, what does the cartesian position coordinate, x, represent? Is it possible to draw a crystal clear pictorial visualization of the latter in reference with the former under the condition that r=x if and only if (1/r)~0?
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