A History, the Main Mathematical Results and Applications for the Mathematics of Harmony

• 作者: A. P. Stakhov
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Golden Ratio Pascal’s Triangle and FIBONACCI NUMBERS Binet’s FORMULAS Gazale’s FORMULAS HYPERBOLIC FIBONACCI Functions Number Systems with IRRATIONAL Bases FIBONACCI λ-Numbers “Metallic Proportions” Hilbert’s Fourth Problem
• 年，卷（期）: 2014,（3）
• 页码范围: 363-386
• 页数: 24页
• 分类号: O1

摘要

We give a survey on the history, the main mathematical results and applications of the Mathematics of Harmony as a new interdisciplinary direction of modern science. In its origins, this direction goes back to Euclid’s “Elements”. According to “Proclus hypothesis”, the main goal of Euclid was to create a full geometric theory of Platonic solids, associated with the ancient conception of the “Universe Harmony”. We consider the main periods in the development of the “Mathematics of Harmony” and its main mathematical results: algorithmic measurement theory, number systems with irrational bases and their applications in computer science, the hyperbolic Fibonacci functions, following from Binet’s formulas, and the hyperbolic Fibonacci l-functions (l = 1, 2, 3, …), following from Gazale’s formulas, and their applications for hyperbolic geometry, in particular, for the solution of Hilbert’s Fourth Problem.