TY - BOOK ID - 7987872 TI - Polygons, Polyominoes and Polycubes PY - 2009 SN - 1402099266 1402099274 PB - Dordrecht : Springer Netherlands : Imprint: Springer, DB - UniCat KW - Polygons KW - Polyominoes KW - Physics - General KW - Geometry KW - Physics KW - Mathematics KW - Physical Sciences & Mathematics KW - Polygons. KW - Polyominoes. KW - Polygonal figures KW - Physics. KW - Chemometrics. KW - Numerical analysis. KW - Algorithms. KW - Combinatorics. KW - Statistical physics. KW - Dynamical systems. KW - Mathematical Methods in Physics. KW - Numeric Computing. KW - Statistical Physics, Dynamical Systems and Complexity. KW - Math. Applications in Chemistry. KW - Combinatorial designs and configurations KW - Geometry, Plane KW - Shapes KW - Mathematical physics. KW - Electronic data processing. KW - Chemistry KW - Complex Systems. KW - Mathematics. KW - Combinatorics KW - Algebra KW - Mathematical analysis KW - Algorism KW - Arithmetic KW - Physical mathematics KW - ADP (Data processing) KW - Automatic data processing KW - Data processing KW - EDP (Data processing) KW - IDP (Data processing) KW - Integrated data processing KW - Computers KW - Office practice KW - Foundations KW - Automation KW - Chemistry, Analytic KW - Analytical chemistry KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Statics KW - Mathematical statistics KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics KW - Measurement KW - Statistical methods UR - https://www.unicat.be/uniCat?func=search&query=sysid:7987872 AB - This unique book gives a comprehensive account of new mathematical tools used to solve polygon problems. In the 20th and 21st centuries, many problems in mathematics, theoretical physics and theoretical chemistry – and more recently in molecular biology and bio-informatics – can be expressed as counting problems, in which specified graphs, or shapes, are counted. One very special class of shapes is that of polygons. These are closed, connected paths in space. We usually sketch them in two-dimensions, but they can exist in any dimension. The typical questions asked include "how many are there of a given perimeter?", "how big is the average polygon of given perimeter?", and corresponding questions about the area or volume enclosed. That is to say "how many enclosing a given area?" and "how large is an average polygon of given area?" Simple though these questions are to pose, they are extraordinarily difficult to answer. They are important questions because of the application of polygon, and the related problems of polyomino and polycube counting, to phenomena occurring in the natural world, and also because the study of these problems has been responsible for the development of powerful new techniques in mathematics and mathematical physics, as well as in computer science. These new techniques then find application more broadly. The book brings together chapters from many of the major contributors in the field. An introductory chapter giving the history of the problem is followed by fourteen further chapters describing particular aspects of the problem, and applications to biology, to surface phenomena and to computer enumeration methods. ER -