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On Sat, 26 Jan 2002, Paul O. Johnson wrote:
I'm hoping you will finally reveal (1) why my "impossible stairway" is half
of an arch, and (2) why the location of its CG is not crucial. Surely, if
the CG of each group of blocks extends beyond the edge of the supporting
block the entire stack will fall.
I'm with Paul.
Jack Uretsky wrote:
It's part of the correct statement of the problem which was omitted in
the version you wrote down (and which was originally given to me). When
I first heard the problem I thought that I was being kidded.
I'm completely mystified by this talk of "half an arch".
I've built arches. I've build logarithmic cantilevers of
the type Paul is asking about. Except for the obvious
fact that they solve somewhat similar problems (extending
beyond their base) they have remarkably little in common.
The physics is different. The ability to span large
distances is tremennnndously different.
The cantilever problem is well-posed without saying
anything about half an arch. The solution that Paul
outlined is the well-known optimal solution.
However an optimal cantilever is not very good from
an engineering standpoint. Nobody in his right mind
would span any significant distance with this techique.
The technique appeals mainly to mad scientists and
mathematicians. Arches, in contrast, can span a
distance of 10x or 100x or 1000x the block-size,
and have been used in this way for thousands of years.