Geodesic
The Mathematics of Harmony: Clarifying the Origins and Development of Mathematics
This study develops a new approach to the origins and history of mathematics. We analyze ?strategic mistakes? in the development of mathematics and mathematical education (including severance of the relationship between mathematics and the theoretical natural sciences, neglect of the ?golden section,? the one - sided interpretation of Euclid�s Elements, and the distorted approach to the origins of mathematics). We develop the Mathematics of Harmony as a new interdisciplinary direction for modern science by applying to it Dirac?s �Principle of Mathematical Beauty� and discussing its role in overcoming these ?strategic mistakes.? The main conclusion is that Euclid�s Elements are a source of two mathematical doctrines � the Classical Mathematics based on axiomatic approach and the Mathematics of Harmony based on the Golden Section (Theorem II.11 of Euclid�s Elements) and Platonic Solids (Book XIII of Euclid�s Elements)
Classification : 20H15
Keywords: golden mean, Fibonacci and Lucas numbers, Binet formulas, Gazale formulas, hyperbolic Fibonacci and Lucas functions, Fibonacci matrices, Bergman's number system, Fibonacci codes, Fibonacci computers, ternary mirror, symmetrical arithmetic, a coding theory based on Fibonacci matrices, "golden" cryptography, mathematics of harmony 
@article{VM_2013_15_2_a1,
     author = {A. P. Stakhov},
     title = {The {Mathematics} of {Harmony:} {Clarifying} the {Origins} and {Development} of {Mathematics}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2013_15_2_a1/}
}
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A. P. Stakhov. The Mathematics of Harmony: Clarifying the Origins and Development of Mathematics. Visual Mathematics, Tome 15 (2013) no. 2. http://geodesic.mathdoc.fr/item/VM_2013_15_2_a1/