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Extending the work of Wilf and Zeilberger on WZ-pairs, we describe how new terminating hypergeometric series identities can be derived by duality from known identities. A large number of such identities are obtained by a Maple program that applies this method systematically. I consider the Diophantine approximation Buy Beats For Cheap problem of sup-norm simultaneous rational approximation with common denominator of a pair of irrational numbers, and compute explicitly some pairs with large approximation constant. One of these pairs is the most badly approximable pair yet computed. The present note explores the structure of the interior of Julia sets and of the Mandelbrot set of quadratic maps. These sets usually appear as ‘dark’ regions in the computer generated graphics of iterations Beats Sale Canada of the quadratic map. Two different ways of coloring and probing into these sets are provided. In 1994 the author, who had no experience or training in librarianship, was hired as a paraprofessional to plan and implement library tours and a basic instruction program at a large public library. This column reviews the development of her successful program, describes the procedures that worked well, and offers advice for persons implementing similar programs.