Irrational number number to ratios of continuous magnitude. In his commentary on Book 10 of the "Elements", the Persian mathematician Al-Mahani (d. 874/884) examined and classified quadratic irrationals and cubic irrationals. He provided definitions for rational and irrational magnitudes, which he treated as irrational numbers. He dealt with them freely but explains them in geometric terms as follows: In contrast to Euclid's concept of magnitudes as lines, Al-Mahani considered integers and fractions as rational magnitudes, and square roots and cube roots as irrational magnitudes. He also introduced an arithmetical approach to the concept of irrationality, as he attributes the following to irrational
Women's fear of crime and victimization rates. A 1998 study in Glasgow, Scotland, found a gender disparity in fear of crime levels smaller than what is generally accepted. The study also found that men and women with similar fear levels tended to use similar reasoning to explain their fear of crime or lack of fear, although men's and women's fear appeared in different situations (men tended to be more often fearful about property crime, whereas women were more fearful about violent crime). A 2010 Turkish study using a large nationwide sample confirmed that women expressed significantly higher levels of fear of crime than men.