we cannot describe the location of any place on a smooth surface
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Mathematically, the contact area is zero, and so if the ball had any mass, it would apply infinite pressure to the flat surface...
Staying mathematical, but bringing some equilibrium theory into play, tells us that the ball could only be statically at rest, if there were 3 points of contact. So still playing games with arbitrarily simple modeling, you would say that your sphere would need 3 atoms in contact with your surface. So the smallest possible area would be of the order of the Bohr radius squared.
Getting even more real requires that you take into account non-rigid body mechanics, which, as a physicist, I never do! :-)
Staying mathematical, but bringing some equilibrium theory into play, tells us that the ball could only be statically at rest, if there were 3 points of contact. So still playing games with arbitrarily simple modeling, you would say that your sphere would need 3 atoms in contact with your surface. So the smallest possible area would be of the order of the Bohr radius squared.
Getting even more real requires that you take into account non-rigid body mechanics, which, as a physicist, I never do! :-)
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We cannot describe the location of any place on a smooth surface because some places has a lot of big plates and plateau. There are not definite surface of a earth plane.
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