Mohs scale of mineral hardness incorporates additional substances that may fall between levels: Comparison between hardness (Mohs) and hardness (Vickers): Mohs scale of mineral hardness The Mohs scale of mineral hardness is a qualitative ordinal scale characterizing scratch resistance of various minerals through the ability of harder material to scratch softer material. Created in 1812 by German geologist and mineralogist Friedrich Mohs, it is one of several definitions of hardness in materials science, some of which are more quantitative. The method of comparing hardness by seeing which minerals can visibly scratch others is, however, of great antiquity, having been mentioned by Theophrastus in his treatise
Hardness of approximation 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 approximation algorithms by proving, for certain problems, a limit on the factors with which their solution can be efficiently approximated. Typically such limits show a factor of approximation beyond which a problem becomes NP-hard, implying that finding a polynomial time approximation for the problem is impossible unless NP=P. Some hardness of approximation results, however, are based on other hypotheses, a notable one among which is the unique games conjecture.