Visual Geometry and Topology by Anatolij T. Fomenko | (PDF) Free Download

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is a classic. Granted, it is not a classic in the sense of Munkres, because it takes a special kind of math student to appreciate the awe-inspiring drawings that it contains. Namely, a student who has been curious about the supposed mind-expanding effects of LSD, but worried that it could damage their brain, will probably reckon that this is the closest they will ever get to a crazy, enlightening trip. Sadly, there are not many textbooks like this that appeal to the nonstandard, nonconformist, future artist-mathematicians. Mathematics needs more people who think in different, creative, unusual ways and more different, creative books like this one could appeal to them. Granted, I shudder to think what kinds of nightmares a calculus book by Fomenko could give me, but Visual Geometry and Topology has earned a special place on my shelf.

⭐Unique survey of Topology presented in a very attractive format. There are no exercises here, just presentation with many great pictures, diagrams and related theorems and concepts that serve to show the range and applicability of the subjects springing from topology. Wonderful addition to the Geometry library. The great algebraic topology text has yet to be written complete with diagrams exercises and solutions.

⭐This book should be purchased by the library of any university. Topology and geometry could be treated at many levels of rigor. Because of this, it is easy to obscure the subject to the extent that people who are not professional mathematicians will be instantly scared away by terminology and details. Fomenko’s book is absolutely different. It deliberately avoids many words which are being used in other books and replaces them with images of stunning clarity and simplicity.There are no difficult issues for Fomenko. All subjects are being treated at the level of conversation between friends. This makes this book to stay in the class by itself. As Albert Einstein used to say: It is essential to present things in the simplest possible way, but not too simple still.” Fomenko apparently was following Einstein’s advise when he was writing this book.

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