The mechanics of an orientable point (point with ”spin”) based on 3D and 4D Frenet equations is considered. In such mechanics there is an opportunity to describe formally any physical trajectory of a particle with own rotation. We use anholonomic rotational coordinates (Euler angles) as elements of internal space of the mechanics which generate a rotational relativity.

We should understand, according to the academic’s logic, that while the Slavs wandered among other, cultured nations in search of an appropriate name for their favourite national dish – which is nothing else than living in poverty – all of the tribes fell into the possession of a German overlord to whom apparently also belonged the Duleb river in Serbia and the town of Dulyovo near Moscow. All they had to do was to wait until the Germans found the legal inheritors of this property and then present a complaint according to the latest scholarly findings.

An important idea in contemporary linguistics is the notion of a former parent or proto-language common to all Indo-European peoples.

Modern sources of generally accessible information (Wikipedia) contain propaganda that Russian writing is adopted.

In general, this is the accepted opinion of academic institutes and orthodox specialists about Russian writing.

The numerous political and public discussions related to events on Caucasus in August, 2008 with all clearness have shown sharp necessity of a substantiation of correctness of our political rate not only arguments of force, clear to all opponents without exception, but also more thin tools from an arsenal of scientific, philosophical and spiritual concepts.

The superficial knowledge of events of domestic history allows noticing, that attempts of creation of positive state ideology were undertaken repeatedly. Not entering into critical analysis of details, we shall remind, that one of the most "powerful" arguments from opponents of such attempts was groundless denying, aversion, demonstrative ignorance of the positive facts and circumstances of Russian history which can serve as the base of creative ideological activity.

Strictly speaking, the followers of Nikon's reform, who finally has won, are dissenters as reformers were the reason of split of Orthodoxy on some conflicting doctrines. Before Nikon's reform all orthodox was made by church services how those it made, whom we know under an abusive name of dissenters subsequently.

To look after names - reference points on a Slavic orthodox inner world before the next ideological reform of the Russian outlook, known to us as acceptance of Christianity in Russia, we shall address to works of the Russian historian, member-correspondent of the Academy of sciences, director of the Armory Museum, Alexander Veltman.

Petoukhov has shown that a family of bisymmetric 2ⁿ x 2ⁿ matrices encode the structure of the four RNA and DNA bases and 64 codons that make up the 20 amino acids in all living structures. He discovered that the elements of the square roots of these matrices are all powers of the golden mean. We have generalized his matrices and shown that the square roots of general bisymmetric matrices are generalizations of the golden mean including a subclass that correspond to the family of silver means. Powers of these matrices are also shown to generate all Pythagorean triples. The integers in these matrices are identical to the set of integers in a table attributed to the second century Syrian mathematician, Nicomachus, who used them to describe the ancient musical scale of Pythagoras.

All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold.

A method is presented for generation of a subwavelength (0.43λ) longitudinally polarized beam, which propagates without divergence over lengths of about 4X in free space. This is achieved by controlling the amplitude, phase and polarization property of the Bessel-Gaussian field on the aperture of a high numerical aperture focusing lens.

In the beginning of the last century K. Tsiolkovskiy has shown how the mankind can go out behind boundary of Earth in Space. Half-century went and the first man saw our Earth from Space. Today in practice over in a hundred years after K. Tsiolkovskiy was drew a way to stars, our compatriot M.V. Smelov has experimentally proved an opportunity of making gravilets in near future and developed the basic diagram of near-earth, circumsolar and galactic transport network in a future.

We consider the Gazale formulas, which are a wide generalization of the Binet and Pell formulas, and a new class of the «golden» hyperbolic functions, which a wide generalization of the symmetric hyperbolic Fibonacci and Lucas functions (Stakhov and Rozin, 2005). Also we consider a new class of the «golden» matrices being a wide generalization of the «golden» matrices (Stakhov, 2006). The improved cryptographic method, which is a generalization of Stakhov’s «golden» cryptographic method, follows from the new «golden» matrices.

Concept: Use the golden section as a unifying theme in the WTC site design and include a Museum of Harmony in the site plans. Our proposal for the rebuilding of the World Trade Center is to create overall harmony in the design of the WTC site through use of the timeless and universal principle of design known as the Golden Section or, as it was called by Leonardo Da Vinci, the Divine Proportion.

In the article we consider a concept of the Museum of Harmony and the Golden Section as unique history-nature-science-art museum, collection of the Nature, Science and Art works based on the Golden Section

A survey of new mathematical models of Nature is presented based on the golden section and using a class of hyperbolic Fibonacci and Lucas functions, and a surface referred to as the Golden Shofar. Also considered are generalized Fibonacci numbers, generalized golden proportions, a Generalized Principle of the Golden Section, golden algebraic equations, generalized Binet formulas, generalized Lucas numbers, continuous functions for the generalized Fibonacci and Lucas numbers, Fibonacci matrices, and golden matrices.

We give in the article a survey of the new results in the «Mathematics of the Golden Section», going back in its origin to Euclid’s Elements, namely, a new class of hyperbolic functions, a generalization of Euclid’s Theorem II,11, a new class of hyperbolic functions — hyperbolic Fibonacci and Lucas functions, the generalized Fibonacci numbers, the generalized golden proportions, the generalized principle of the golden section, the golden algebraic equations, the generalized Binet formulas, the generalized Lucas numbers, Fibonacci matrices, the «golden» matrices. We consider applications of these mathematical results in number theory, measurement theory, computer arithmetic, coding theory and cryptography.

In the beginning of twentieth century classical natural philosophy ( classical physics ) was destroyed and replaced by so called non classic mathematical physics consisting of theor y of relativ ity and quantum mechanics. New non classic physics is based on postulates and faith, so it is more religion , than a scienc e. This article is a fragment of a new book in which development of natural ideas classical physics is presented.

We consider a new class of square matrices called the «golden» matrices. They are a generalization of the classical Fibonacci Q-matrix for continuous domain. The «golden» matrices can be used for creation of a new kind of cryptography called the «golden» cryptography. The method is very fast and simple for technical realization and can be used for the cryptographic protection of different telecommunication systems (including Internet) functioning in real scale of time.

SEVENTY-FIVE years ago this month, The New York Times reported that Albert Einstein had completed his unified field theory — a theory that promised to stitch all of nature's forces into a single, tightly woven mathematical tapestry. But as had happened before and would happen again, closer scrutiny revealed flaws that sent Einstein back to the drawing board. Nevertheless, Einstein's belief that he'd one day complete the unified theory rarely faltered. Even on his deathbed he scribbled equations in the desperate but fading hope that the theory would finally materialize. It didn't.

Based on the PhD thesis of Anne Bulckens, the proportional system of the Parthenon is examined. With the appropriate choice of a module and the length of a «Parthenon foot», all dimensions are shown to be integers. These integer values are shown to be related to the musical scale of Pythagoras. Among the many musical relationships expressed by this structure, this paper focuses on a pentatonic scale made up of lengths, widths and heights of the outer temple and the inner temple or cella.

The logic by which the creator of the Nefertiti statuette was guided is clear and simple. Harmony is the prerogative of the divine order which dominates the Universe, and geometry is a means of its expression. The Queen is given to people by God. Hence, her image, personifyng the world’s wise tranquillity must be full of geometrical perfection to bear the stamp of high and irreproachable harmony, beauty and clearness. Such is, in fact, the whole philosophy of ancient Egyptian art, which glorified the eternal, the measured, the perfect in the ever changing being.

Before starting, I offer the following overview, the details of which will be discussed in the rest of the article. An application of abductive reasoning to Plato's puzzles in the dialogues leads to the solution that the Divided Line in the Republic is constructed using a series of Golden Cuts (i.e., divisions in extreme and mean ratio). This leads to the discovery that there is a more primitive form than the √2 and √3 ratios (the roots inherent in the elementary triangles of the Timaeus), and that this form is based in the Golden Section.

The main goal of the present article is to consider the harmony mathematics from the point of view of the sacral geometry and to show how it can be used in this field. We also consider some secrets of the Egyptian civilization that have relation to the golden section and platonic solids. Briefly, this is considered to be the main concepts involved in harmony mathematics and its application to the sacral geometry.

We consider two important generalizations of the golden proportion: golden p-proportions [Stakhov A.P.] and «metallic means» [Spinadel V.W.]. We develop a constructive approach to the theory of real numbers that is based on the number systems with irrational radices (Bergman's number system and Stakhov's codes of the golden p-proportions). It follows from this approach ternary mirror-symmetrical arithmetic that is the basis of new computer projects.

This article presents the results of some new research on a new class of hyperbolic functions that unite the characteristics of the classical hyperbolic functions and the recurring Fibonacci and Lucas series. The hyperbolic Fibonacci and Lucas functions, which are the being extension of Binet's formulas for the Fibonacci and Lucas numbers in continuous domain, transform the Fibonacci numbers theory into «continuous» theory because every identity for the hyperbolic Fibonacci and Lucas functions has its discrete analogy in the framework of the Fibonacci and Lucas numbers.

The goal of the present article is to develop the «continues» approach to the recurrent Fibonacci sequence. The main result of the article is new mathematical model of a curve-linear space based on a special second-degree function named «The Golden Shofar».

The special case of the (p+1)th degree algebraic equations of the kind x^p+1 = x^p + 1 (p = 1,2,3,...) is researched in the present article. For the case p = 1, the given equation is reduced to the well-known Golden Proportion equation x² = x + 1. These equations are called the golden algebraic equations because the golden p-proportions τ_p, special irrational numbers that follow from Pascal's triangle, are their roots. A research on the general properties of the roots of the golden algebraic equations is carried out in this article.

We consider a new class of square Fibonacci (p + 1) × (p + 1)-matrices, which are based on the Fibonacci p-numbers (p = 0,1,2,3,...), with a determinant equal to +1 or — 1. This unique property leads to a generalization of the «Cassini formula» for Fibonacci numbers. An original Fibonacci coding/decoding method follows from the Fibonacci matrices. In contrast to classical redundant codes a basic peculiarity of the method is that it allows to correct matrix elements that can be theoretically unlimited integers. For the simplest case the correct ability of the method is equal 93.33% which exceeds essentially all well-known correcting codes.

The new continuous functions for the Fibonacci and Lucas p-numbers using Binet formulas are introduced. The article is of a fundamental interest for Fibonacci numbers theory and theoretical physics.

There have been obtained experimental results on remote effects of rotating objects on readings of semiconductor gamma – ray spectrometric equipment and devices. It is shown that the trace shift of statistic distribution is the function of velocity changes in semiconductor detector’s charges accumulation. In its turn, the accumulation rate is subject to a physical field of non-electromagnetic origin created in the result of rotation.

Modern natural science requires the development of new mathematical apparatus. The generalized Fibonacci numbers or Fibonacci p-numbers (p = 0,1,2,3,...), which appear in the "diagonal sums" of Pascal's triangle and are assigned in the recurrent form, are a new mathematical discovery. The purpose of the present article is to derive analytical formulas for the Fibonacci p-numbers. We show that these formulas are similar to the Binet formulas for the classical Fibonacci numbers. Moreover, in this article, there is derived one more class of the recurrent sequences, which is defined to be a generalization of the Lucas numbers (Lucas p-numbers).

The «Dichotomy Principle» and the classical «Golden Section Principle» are two of the most important principles of Nature, Science and also Art. The Generalized Principle of the Golden Section that follows from studying the diagonal sums of the Pascal triangle is a sweeping generalization of these important principles. This underlies the foundation of «Harmony Mathematics», a new proposed mathematical direction. Harmony Mathematics includes a number of new mathematical theories: an algorithmic measurement theory, a new number theory, a new theory of hyperbolic functions based on Fibonacci and Lucas numbers, and a theory of the Fibonacci and «Golden» matrices.

As is well known, mathematics is one of the outstanding creations of the human intellect; a result of centuries of intensive and continuous creative work of man's geniuses. What is the goal of mathematics? The answer is not simple. Probably, the goal of mathematics is to discover «mathematical laws of the Universe» and to construct models of the physical world. It is clear that the progress of the human society depends on the knowledge of these laws.