History of Catalan numbers

We give a brief history of Catalan numbers, from their first discovery in the 18th century to modern times. This note will appear as an appendix in Richard Stanley's forthcoming book on Catalan numbers.Comment: 10 page

The area of cyclic polygons: Recent progress on Robbins' Conjectures

In his works [R1,R2] David Robbins proposed several interrelated conjectures on the area of the polygons inscribed in a circle as an algebraic function of its sides. Most recently, these conjectures have been established in the course of several independent investigations. In this note we give an informal outline of these developments.Comment: To appear in Advances Applied Math. (special issue in memory of David Robbins

Exploring the City in the Cinema of Bahram Beyzaie

This article explores five of Bahram Beyzaie's urban films over the last four decades to study their critique of the process of modernization and social changes that have taken place in Iran. These include The Journey (Safar, 1972), The Crow (Kalagh, 1977), Maybe Some Other Time (Shayad Vaqti Digar, 1987), Killing Mad Dogs (Sag Koshi, 2001) and When We Are All Asleep (Vaqti Hame Khabim, 2009). It examines the impact of modernization on the architecture and landscape of the city and consequently on the local community. It then studies the increasing complexity of ascertaining the real and unreal within the city. Finally, it looks at the changing values, the fears and threats within the city and the impact these have on its inhabitants, particularly women and their movement within the city.</jats:p

A short proof of rigidity of convex polytopes

We present a much simplified proof of Dehn's theorem on the infinitesimal rigidity of convex polytopes. Our approach is based on the ideas of Trushkina and Schramm.Comment: to appear in Siberian Journal of Mathematics; 5 pages 2 figure