Golden Section in Secondary School

Dear reader! For each of you, who had enough patience to reach this page of our Museum, there is a question instinctively: why I had not possibility to get such interesting information in secondary school? You know that the knowledge about the "golden section" and its numerous applications in the Nature, Science and Art could enrich doubtlessly of each of us. And hardly someone from the recognized pedagogical scientists can give the intelligible answer to this question. Frankly speaking, and we, the authors of the present Museum, cannot answer this question too.

Possibly, the point is in tradition. Traditionally the classic science, and consequently, the classic pedagogic, treated to the "golden section" with some prejudice. The point is in the broad usage of the "golden section" in the astrology and so-called "esoteric sciences". In this respect the book by Bob Frissell "Nothing in this book is true, but it's exactly how things are" translated to the Russian in 1998 is rather interesting.

The book by Bob Frissell 'Nothing in this book is true, but it's exactly how things are' (1998)

From this book, for example, we can learn about the "golden" equiangular spiral on the plateau in Gizeh, on which the ancient Egyptians located their famous pyramids.

The 'golden' equiangular spiral on the plateau in Gizeh
The "golden" equiangular spiral on the plateau in Gizeh.

From this book we can learn also that the main geometrical symbols of the "sacral geometry" such, as the "Flower of life", the "Seed of life", the "Tree of life", the "Fetus of life" are connected through the "Cube of Metatron" to the "Platonic Solids", each of which can be extracted from the "Cube of Metatron".

Flower of lifeFetus of life
Flower of lifeFetus of life
Cube of MetatronPlatonic Solids
Cube of MetatronPlatonic Solids

Certainly, we can not accept the " esoteric " philosophy based on the Fibonacci numbers, the golden section, "golden" spiral and "Platonic Solids", but we should recognize the botanic phenomenon of phyllotaxis, Shechtman's quasi-crystals, Fibonacci computers, which use the same Fibonacci numbers, the golden section and the "Platonic Solids". And it follows from here that the classic "materialistic" science moves now to embraces of the "esoteric" science!

So from what to start reforming school education? Let's begin from the saying of the ingenious astronomer Johannes Kepler:

"In geometry there are two treasures: Pythagorean theorem and division of a line segment in extreme and mean ratio. The former can be compared to value of gold, the latter can be name as a gemstone".

But if each schoolboy knows the Pythagorean theorem, in Kepler's opinion, he should also well know and the "golden section". And our first step is to enter into the school "Geometry" the section of the "Golden Section". In this section it will be interesting to the schoolboys to learn about the geometric definition of the "golden section, about the "golden" rectangle, about the pentagram, about the "Platonic Solids", in particular, about the regular icosahedron and dodecahedron.

Let's go to the "Algebra". Here schoolboys study algebraic equations and methods of their solution. But for the schoolboys it is interesting to learn about the special class of the algebraic equations, the "golden proportion equation". And we have a full right to enter the small section "The golden proportion equations" into the "Algebra".

In that part of the school mathematics where "The theory of numbers" is studied it is reasonable to enter the special section "Fibonacci numbers".

Let's go now to the Nature sciences namely, physics, chemistry, astronomy, botanic, biology. In the "Physics" at the crystallography statement it is desirable to enter the section "Quasi-crystals" based on the "icosahedral" symmetry. But our schoolboys already know about the regular icosahedron from the "Geometry".

In the "Chemistry" it is expedient to pay schoolboy's attention to the chemical compounds constructed "on Fibonacci". And in the "Astronomy" it is necessary to tell about the "resonant theory of the Solar system". Only by such way the schoolboys can understand the causes of the Solar system stability.

Let's go now to the alive nature sciences. The "Phyllotaxis Laws" based on the Fibonacci numbers and the golden section could become by embellishment of the "Botanic". The Nature gives a huge number of this Laws manifestation and this circumstance is the main argument for the benefit of this section. The similar sections would be desirable and in the "Biology" or "Anatomy".

Let's consider now the school courses on art. The principles of the "golden section" usage in the art works ("golden" rectangle, "golden" spiral, "two-adjacent square", etc.) are rather simple and also the examples of their usage in the architecture, painting and sculpture are interesting to the schoolboys.

One could continue these examples. But the introduction of the special discipline "Harmony of systems", which could be esteemed as the completing discipline of the physical, mathematical and aesthetic pupil's formation is the radical decision in this field of the school education. The formation of the new scientific world outlook based on the principles of Harmony and Golden Section is the main purpose of such discipline. The program of this discipline depends on a specialization of the schoolboys. And we can help to you to elaborate such program and to perform such course on the ground of materials set up on the pages of our Museum. Address to us!