Volume I is the first part of the 3-volume book "Mathematics of Harmony as a new interdisciplinary direction of modern science". "Mathematics of Harmony" rises in its origin to the "harmonic ideas" of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the "Universe Harmony, " the main conception of ancient Greek science, and implementation of this conception to modern science and education. Volume I is a result of the authors’ research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the "Mathematics of Harmony, " a new interdisciplinary direction of modern science. This direction has its origins in Euclid’s Elements and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet’s formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic). The 3-volume book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Key Features: ○Development of the original historical and mathematical view on Euclid’s "Elements", based on the hypothesis of Proclus (411–485) ○Generalization of Fibonacci numbers and golden section, following from the diagonal sums of Pascal triangle (mathematical discovery of the outstanding American mathematician George Polya) ○A new view on the role of the Fibonacci numbers theory in modern mathematics

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