A geometric analogy for understanding emptiness. Is it a valid one?

Segments in a straight line have non-zero lengths but all of them have zero area i.e. they are "empty" when viewed as embedded in 2-dimensional plane. Similarly, all 2-dimensional shapes viewed as embedded in 3 dimensions appear as zero-volume entities, although in their own plane of 2 dimensions they do have intrinsic substance (area).
So my first question is: is this a valid analogy for the buddhist concept of "emptiness"? Naturally, the analogy can be continued to infinity: at each step, objects are "substantial" within their own plane but "empty" as regards the higher planes. This urges us to think that in infinite dimensions we have finally arrived at perfect substantiality, as no higher plane can exist to destroy it. But we can move further on, to spaces with uncountably infinite dimensions, where "orders of infinity" can indeed provide new dimensions to our enquiry, to a point where our human thinking begins to be at a loss as to what is going on...
So my second question is: has this extension to infinite dimensions caught the attention of buddhist philosophers?