In this paper, we study the extraction of roots as presented by Al-Kashi in his 1427 book “Key to Arithmetic” and Stevin in his 1585 book “Arithmetic”. In analyzing their methods, we note that Stevin’s technique contains some flaws that we amend to present a coherent algorithm. We then show that the underlying algorithm for the methods of both Al-Kashi and Stevin is the same.

This study analyzes how the board’s characteristics could be associated with globally corporate social responsibility CSR and specific areas of CSR. It is drawn on all listed firms, in 2016, on the SBF120 between 2003 and 2016. Our results provide strong evidence that diversity in boards and diversity of boards globally are positively associated with corporate social performance. However, they influence differently specific dimensions of CSR performance. First, we show that large boards are positively associated with all areas of CSR (...) performance, while specific and overall CSR scores are negatively associated with CEO-chair structures. Second, board gender diversity is positively associated with human rights and corporate governance dimensions. Third, age diversity is positively associated with corporate governance, human resources, human rights, and environmental activities. Also, our results provide evidence that outside directors care about CSR performance. Specifically, the presence of foreign directors is positively associated with environmental performance and community involvement, whereas CSR-Governance dimension is positively associated with the presence of independent directors. Regarding the director’s educational level, post-graduated directors are positively and significantly associated with overall CSR score and all CSR sub-scores, except the corporate governance one. When directors have multiple directorships, they are more concerned about human resources, environmental performance, and business ethics. Finally, our findings are robust only in non-family firms. In fact, family boards are less diverse than non-family ones; specifically, they have a lower number of independent, foreign, and high-educated directors. (shrink)