24,831 research outputs found
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
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