Mathematics

2009-01-10

The International Club of the Golden Section

6 McCreary Trail, Bolton, ON, L7E 2C8, Canada

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__Contents__

Preface

- Introduction: Dirac’s Principle of Mathematical Beauty and “beautiful” mathematical objects
- A new approach to the mathematics origins
- The Mathematics of Harmony as a “beautiful” mathematical theory
- The “Golden” Fibonacci goniometry: a revolution in the theory of hyperbolic functions
- The “Golden” Fibonacci goniometry and Hilbert’s Fourth Problem: revolution in hyperbolic geometry
- Fibonacci and “golden” matrices: a unique class of square matrices
- New scientific principles based on the Golden Section
- The Mathematics of Harmony: a renaissance of the oldest mathematical theories
- The “Golden” information technology: a revolution in computer science
- The important “golden” discoveries in botany, biology and genetics
- The revolutionary “golden” discoveries in crystallography, chemistry, theoretical physics and cosmology
- Conclusion

**2005-09-04**

**O.N. Grinbaum**

*Poetry is, in essence, the articulated expression of perception…*

J. Brodsky

This study is an attempt to understand the processes of perception of a poetic text, including the role of rhythm as a portent of emotional and semantic modulation in speech. The point of departure of this study harks back to S.M. Bondi, who wrote: "The artist (musician, poet, actor) arrests our attention by means of rhythm, forcing our hearts to beat faster or more slowly, to breathe more evenly or to catch our breath, to feel the flow of time with our whole bodies…When we are saturated by the effects of rhythm, we achieve a particular state of consciousness in which our bodies **resonate **to it, and we become extraordinarily alert and responsive to all the details of the rhythmically organized process affecting us in this way."[1]

**2004-06-01 **

Looking back into my young days only now I begin to realize why in 1949 when I was about to enter the Mathematical and Mechanical Faculty of the Leningrad University I had chosen, solely by intuition, the Mechanical Department. My bent to pure mathematics was then impeded by a maturing question: why the mathematical exactness goes further than it is needed for life. Examples of miraculous revival of mathematical abstractions carried away but did not soothe. The value of extrapolations also caused no doubt. However, there was a presentiment of some border line separating the infinity from the ontological reality.

**2004-03-01 **

Later 2 500 years after ancient Greeks three "eternal" problems (accounting, measurement and harmony of systems), which stood at sources of creation of mathematics and exact sciences, put forward again on the foreground of modern science. The author has tried to unit new mathematical theories that were created for the solution of these problems in the harmonious mathematical theory named "Mathematics of Harmony".