The Babylonian Method and Higher Order Approximations to Square Roots

It may have been Chebyshev who said that in the olden days the mathematical problems were posed by the gods, later by the demi-gods (Gauss, etc.) and nowadays by the technician. Modern demands by technology are growing and often (paradoxically) lamented by designers of courses and syllabi. Arguments that fundamentals have to be established rst, leave the fear that applications and philosophical implications are then relegated to occasional spin-o s. On the other hand the play and discovery motivated courses seem to lead to catastrophic skill gaps and lack of breadth in knowledge. Mathematical skills are required with su cient knowledge, also of the basic sciences, in order to tackle the problems that are faced. The challenge of diversity is upon us.