Visual Geometry and Topology

Więcej o książce

Geometry and topology are driven by the visualization of ideal objects with unique characteristics. A clear understanding of specific properties or proofs often emerges when mathematicians can "see" the concepts at play. These visualizations serve as signposts to mathematical comprehension and possess their own inherent beauty. This book aims to narrate, in an accessible and visual manner, classical and modern achievements in geometry and topology, addressing both intrinsic mathematical problems and their applications in mathematical physics. It begins with classical topology and progresses to notable advancements in Hamiltonian geometry. Fomenko emphasizes visual explanations over abstract calculations, allowing readers to quickly grasp the new theory of topological descriptions of integrable Hamiltonian differential equations. The book features numerous graphical illustrations created by the author, presented in dedicated "Visual material" sections, which elucidate the mathematical ideas and results discussed. These visuals enable readers to engage with contemporary mathematical concepts and methods. Although focused on mathematics, the book is crafted to appeal to students and researchers across the natural sciences, as well as artists and art students, ensuring a wide range of interest.