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Karl Trappe wrote:
....
Regarding the cantilever/arch issue. Two such "cantilever-like"
structures placed as mirror images of each other result in the classical
architectural arch, or the bridge without pillars in the water.
I am astonished to read this.
Is there any evidence for this claim whatsoever?
Here are some classical architectural arches:
http://207.228.125.45/France/reims_france_arch.htm
http://www.people.virginia.edu/~dhm1h/images/RomanRuins/orage-arch1-700_JPG
.html
http://www.goldenboughmusic.com/news/Roman_arch.jpg
http://nrich.maths.org/~smt32/album/10_morroco/3_mouley/Morocco2001_0310_11
5833AA_Med.jpg
http://nrich.maths.org/~smt32/album/10_morroco/3_mouley/Morocco2001_0310_12
1241AA_Lg.jpg
http://nrich.maths.org/~smt32/album/10_morroco/3_mouley/Morocco2001_0310_12
2013AA_Lg.jpg
I assert each such arch doesn't _look_ anything like a pair of
one-sided cantilevers. I further assert that physically, it
doesn't _work_ anything like a pair of one-sided cantilevers.
Observable fact: Look at the ratio of the span to blocksize
in this arch:
http://nrich.maths.org/~smt32/album/10_morroco/3_mouley/Morocco2001_0310_11
5833AA_Med.jpg
then calculate the number of blocks it would take to do
this using the one-sided cantilever principle. This is
not my opinion; this is plain high-school physics.
I'm willing to listen if anybody has any real evidence
(i.e. something beyond mere opinion) to support the
"arch=cantilever" notion. But so far I haven't seen any.
====
BTW a useful reference on cantilevers is:
http://mathworld.wolfram.com/BookStackingProblem.html
including a closed-form expression for how far
you can reach using N blocks.