Geometry and topology are strongly motivated by the visualization of
ideal objects that have certain special characteristics. A clear
formulation of a specific property or a logically consistent proof of a
theorem often comes only after the mathematician has correctly "seen"
what is going on. These pictures which are meant to serve as signposts
leading to mathematical understanding, frequently also contain a beauty
of their own. The principal aim of this book is to narrate, in an
accessible and fairly visual language, about some classical and modern
achievements of geometry and topology in both intrinsic mathematical
problems and applications to mathematical physics. The book starts from
classical notions of topology and ends with remarkable new results in
Hamiltonian geometry. Fomenko lays special emphasis upon visual
explanations of the problems and results and downplays the abstract
logical aspects of calculations. As an example, readers can very quickly
penetrate into the new theory of topological descriptions of integrable
Hamiltonian differential equations. The book includes numerous graphical
sheets drawn by the author, which are presented in special sections of
"Visual material". These pictures illustrate the mathematical ideas and
results contained in the book. Using these pictures, the reader can
understand many modern mathematical ideas and methods. Although "Visual
Geometry and Topology" is about mathematics, Fomenko has written and
illustrated this book so that students and researchers from all the
natural sciences and also artists and art students will find something
of interest within its pages.
