Welcome to the webpage of the Chair of Combinatorial Geometry of Prof. János Pach
How many objects of a given shape and size can be packed into a large box of fixed volume? Can one plant n trees in an orchard, not all along the same line, so that every line determined by two trees will pass through a third? These questions, raised by Hilbert and Sylvester roughly one hundred years ago, have generated a lot of interest among professional and amateur mathematicians and scientists. They have led to the birth of a new mathematical discipline with close ties to classical geometry and number theory, and with many applications in coding theory, potential theory, computational geometry, computer graphics, robotics, etc.
This is a relatively new field, starting with M. I. Shamos’s thesis (1978), concerned with algorithms for solving geometric problems. See “Computational Geometry, Algorithms and Applications” by M. de Berg, M. van Kreveld, M. Overmars and O. Schwarzkopf for a textbook (Springer).