Anatolij T. Fomenko – författare

Geometry and topology are strongly motivated by thevisualization of ideal objects that have certain specialcharacteristics. A clear formulation of a specific propertyor a logically consistent proof of a theorem often comesonly after the mathematician has correctly "seen" what isgoing on. These pictures which are meant to serve assignposts leading to mathematical understanding, frequentlyalso contain a beauty of their own.The principal aim of this book is to narrate, in anaccessible and fairly visual language, about some classicaland modern achievements of geometry and topology in bothintrinsic mathematical problems and applications tomathematical physics. The book starts from classical notionsof topology and ends with remarkable new results inHamiltonian geometry. Fomenko lays special emphasis uponvisual explanations of the problems and results anddownplays the abstract logical aspects of calculations. Asan example, readers can very quickly penetrate into the newtheory of topological descriptions of integrable Hamiltoniandifferential equations. The book includes numerous graphicalsheets drawn by the author, which are presented in specialsections of "Visual material". These pictures illustrate themathematical ideas and results contained in the book. Usingthese pictures, the reader can understand many modernmathematical ideas and methods.Although "Visual Geometry and Topology" is aboutmathematics, Fomenko has written and illustrated this bookso that students and researchers from all the naturalsciences and also artists and art students will findsomething of interest within its pages.

Geometry and topology are strongly motivated by thevisualization of ideal objects that have certain specialcharacteristics. A clear formulation of a specific propertyor a logically consistent proof of a theorem often comesonly after the mathematician has correctly "seen" what isgoing on. These pictures which are meant to serve assignposts leading to mathematical understanding, frequentlyalso contain a beauty of their own.The principal aim of this book is to narrate, in anaccessible and fairly visual language, about some classicaland modern achievements of geometry and topology in bothintrinsic mathematical problems and applications tomathematical physics. The book starts from classical notionsof topology and ends with remarkable new results inHamiltonian geometry. Fomenko lays special emphasis uponvisual explanations of the problems and results anddownplays the abstract logical aspects of calculations. Asan example, readers can very quickly penetrate into the newtheory of topological descriptions of integrable Hamiltoniandifferential equations. The book includes numerous graphicalsheets drawn by the author, which are presented in specialsections of "Visual material". These pictures illustrate themathematical ideas and results contained in the book. Usingthese pictures, the reader can understand many modernmathematical ideas and methods.Although "Visual Geometry and Topology" is aboutmathematics, Fomenko has written and illustrated this bookso that students and researchers from all the naturalsciences and also artists and art students will findsomething of interest within its pages.

The flood of information through various computer networks such as the In­ ternet characterizes the world situation in which we live. Information worlds, often called virtual spaces and cyberspaces, have been formed on computer networks. The complexity of information worlds has been increasing almost exponentially through the exponential growth of computer networks. Such nonlinearity in growth and in scope characterizes information worlds. In other words, the characterization of nonlinearity is the key to understanding, utiliz­ ing and living with the flood of information. The characterization approach is by characteristic points such as peaks, pits, and passes, according to the Morse theory. Another approach is by singularity signs such as folds and cusps. Atoms and molecules are the other fundamental characterization ap­ proach. Topology and geometry, including differential topology, serve as the framework for the characterization. Topological Modeling for Visualization is a textbook for those interested in this characterization, to understand what it is and how to do it. Understanding is the key to utilizing information worlds and to living with the changes in the real world. Writing this textbook required careful preparation by the authors. There are complex mathematical concepts that require designing a writing style that facilitates understanding and appeals to the reader. To evolve a style, we set as a main goal of this book the establishment of a link between the theoretical aspects of modern geometry and topology, on the one hand, and experimental computer geometry, on the other.