Mohs scale of mineral hardness integrity, they are not considered "scratches" for the determination of a Mohs scale number. The Mohs scale is a purely ordinal scale. For example, corundum (9) is twice as hard as topaz (8), but diamond (10) is four times as hard as corundum. The table below shows the comparison with the absolute hardness measured by a sclerometer, with pictorial examples. On the Mohs scale, a streak plate (unglazed porcelain) has a hardness of approximately 7.0. Using these ordinary materials of known hardness can be a simple way to approximate the position of a mineral on the scale. The table below
Hardness of approximation polynomial time. In the early 1990s, with the development of PCP theory, it became clear that many more approximation problems were hard to approximate, and that (unless P = NP) many known approximation algorithms achieved the best possible approximation ratio. Hardness of approximation theory deals with studying the approximation threshold of such problems. For an example of an NP-hard optimization problem that is hard to approximate, see set cover. Hardness of approximation In computer science, hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems. Hardness of approximation complements the study of