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Alexey Stakhov
Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science
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Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science
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Contents
Preface to the Three-Volume Book
Continuity in the Development of Science
Pythagoreanism and Pythagorean MATHEM’s
Proclus Hypothesis
The Statements by Alexey Losev and Johannes Kepler
Ancient Greeks Mathematical Doctrine of Nature
Introduction of the Term Mathematics of Harmony
Fibonacci Numbers
Sources of the Present Three-Volume Book
Structure and the Main Goal of the Three-Volume Book
Introduction
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Chapter 1
The Golden Section: History and Applications
1.1. The Idea of the Universal Harmony in Ancient Greek Science
1.1.1. What is Harmony?
1.1.2. Numerical harmony of Pythagoreans
1.1.3. The contribution of Heraclitus to the development of the doctrine of Harmony
1.1.4. The musical harmony of Pythagoras and the music of the spheres
1.1.5. Once again about the term of the Mathematics of Harmony
1.2. The Golden Section in Euclid’s Elements
1.2.1. Proposition II.11 of Euclid’s Elements
1.2.2. The second form of the task of the division of segment in the extreme and mean ratio
1.2.3. Comments of Mordukhai-Boltovsky, concerning the golden section
1.2.4. The origin of the term of the golden section
1.3. Proclus Hypothesis and New View on Classic Mathematics and Mathematics of Harmony
1.3.1. For what purpose did Euclid write his Elements?
1.3.2. The significance of the Proclus hypothesis for the development of mathematics
1.3.3. The Proclus hypothesis and “key” problems of ancient mathematics
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