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Introduction To Circle Packing
''Introduction to Circle Packing: The Theory of Discrete Analytic Functions'' is a mathematical monograph concerning systems of tangent circles and the circle packing theorem. It was written by Kenneth Stephenson and published in 2005 by the Cambridge University Press. Topics Circle packings, as studied in this book, are systems of circles that touch at tangent points but do not overlap, according to a combinatorial pattern of adjacencies specifying which pairs of circles should touch. The circle packing theorem states that a circle packing exists if and only if the pattern of adjacencies forms a planar graph; it was originally proved by Paul Koebe in the 1930s, and popularized by William Thurston, who rediscovered it in the 1970s and connected it with the theory of conformal maps and conformal geometry. As a topic, this should be distinguished from sphere packing, which considers higher dimensions (here, everything is two dimensional) and is more focused on packing density than on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Monograph
A monograph is generally a long-form work on one (usually scholarly) subject, or one aspect of a subject, typically created by a single author or artist (or, sometimes, by two or more authors). Traditionally it is in written form and published as a book, but it may be an artwork, audiovisual work, or exhibition made up of visual artworks. In library cataloguing, the word has a specific and broader meaning, while in the United States, the Food and Drug Administration uses the term to mean a set of published standards. Written works Academic works The English term ''monograph'' is derived from modern Latin , which has its root in Greek. In the English word, ''mono-'' means and ''-graph'' means . Unlike a textbook, which surveys the state of knowledge in a field, the main purpose of a monograph is to present primary research and original scholarship. This research is presented at length, distinguishing a monograph from an article. For these reasons, publication of a monograph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |