El. knyga: "e;Golden"e; Non-euclidean Geometry, The: Hilbert's Fourth Problem, "e;Golden"e; Dynamical Systems, And The Fine-structure Constant

Stakhov and Aranson trace the connection of the golden ratio, Fibonacci numbers, Lucas sequences, and Binets formulas with the golden hyperbolic Fibonacci and Lucas functions, Fibonacci -numbers, and metallic proportions. The primary result of their collaboration led to an unusual solution of Hilberts Forth Problems and ultimately to the justification of recursive, or golden non-Euclidean geometry. This challenges theorists in the natural scientists to discover these recursive non-Euclidean geometries in nature. Annotation ©2017 Ringgold, Inc., Portland, OR (protoview.com) This unique book overturns our ideas about non-Euclidean geometry and explains the role of the "golden ratio" in Euclids Elements. It highlights a new view on Euclids Elements and the history of mathematics based on Proclus hypothesis. It describes a general theory of "recursive" hyperbolic functions based on the "golden," "silver," and other "metallic" proportions. The book contains an original solution of Hilberts Fourth Problem for hyperbolic and spherical geometries, and puts forward a problem searching for new hyperbolic and spherical worlds of nature based on this solution. For the first time, the book describes the "golden" qualitative theory of dynamical systems based on the mathematics of harmony. It is intended for a wide range of readers, who are interested in the history of mathematics, non-Euclidean geometry, Hilberts mathematical problems and dynamical systems.