Mineralogy
"Hardness" is determined by comparison with other minerals. In the Mohs scale, a standard set of minerals are numbered in order of increasing hardness from 1 (talc) to 10 (diamond). A harder mineral will scratch a softer, so an unknown mineral can be placed in this scale by which minerals it scratches and which scratch it. A few minerals such as calcite and kyanite have a hardness that depends significantly on direction. Hardness can also be measured on an absolute scale using a sclerometer; compared to the absolute scale, the Mohs scale is nonlinear.
Flatness problem
Since the constant formula_7 is known and the expansion rate formula_2 can be measured by observing the speed at which distant galaxies are receding from us,
formula_9 can be determined. Its value is currently around . The ratio of the actual density to this critical value is called Ω, and its difference from 1 determines the geometry of the universe: corresponds to a greater than critical density, , and hence a closed universe. gives a low density open universe, and Ω equal to exactly 1 gives a flat universe.