Discrete & Computational Geometry, Oct 2007

Jacob E. Goodman, János Pach, Richard Pollack

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Discrete Comput Geom Jacob E. Goodman · János Pach · Richard Pollack - This special issue of Discrete & Computational Geometry commemorates two events that took place during 2006. The first was the twentieth anniversary of the journal, whose first issue appeared in January, 1986, and the second was the AMS-IMS-SIAM Joint Summer Research Conference that took place during June, 2006 in Snowbird, Utah, under the title “Discrete and Computational Geometry—Twenty Years Later.” These events, of course, were not unrelated. In the summer of 1986, as a means of calling attention to the new journal, the first and third of its present editors organized a Joint Summer Research Conference in Santa Cruz, to which we invited outstanding researchers in the areas of discrete geometry and computational geometry (as well as a number of young people, including the second of DCG’s current editors), with the aim of encouraging communication between the two fields, which we thought would benefit each, and in fact of fostering collaboration between researchers in the two areas. Discrete geometry, an old branch of mathematics that had flowered in the late nineteenth and early twentieth centuries, had settled down to a steady flow of results on polytopes, packings, geometry of numbers, and arrangements, spurred mostly by the efforts of a few people (among them Hadwiger, Delone, Fejes Tóth, Erdo˝s, Rogers, Cassels, Lekkerkerker, Klee, and Grünbaum), while computational geometry was a brand new field that had only begun to emerge in the 1970s and 80s. As can be judged by the explosion of work that followed in the next two decades, and by the (now) frequent collaboration among researchers in both areas, our hopes were realized. The journal itself burgeoned (from its original 400 pages a year to its current 1440), two additional journals were started to cover the field of computational geometry, numerous conferences were organized all over the world, and more and more young researchers now list their primary area of interest as “discrete and computational geometry.” Not only has the field itself grown immensely, but as it has, surprising connections with other branches of mathematics and computer science have opened up, to the mutual enrichment of both. It has given us immense pleasure to help spur this development to its present peak of activity, and we dedicate the present issue of DCG, which, as the reader will see, covers a wide swath of mathematics and theoretical computer science, to the large body of researchers who have taken part in the development of the field during the past two decades; many of them are represented in its pages.

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Jacob E. Goodman, János Pach, Richard Pollack. Foreword, Discrete & Computational Geometry, 2007, 1-2, DOI: 10.1007/s00454-007-9036-8