The Golden Mean and self-similar structures in optics

Modeling of Atomic Systems and Positioning of Elements of Noble Gases of the Periodic Table by Proportional Division Method

“…and shifted right by a unity 1  q . Along the direction (4) modules , k q p   (5) coincide, so in the second 0 , 0   q p and the third 0 , 0   q p quadrants the roots of a square threeterm , 0 2    q px x (6) are quadratically irrational and exhibit the GS properties (Fig. 1).…”

“…The method of golden section (GS) of the whole system divided into two unequal parts was applied for various modeling problems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], including problems related to the modeling of atomic [1][2]9,11] and quantum [15,16] systems. Thus, in [1,[17][18][19], by means of the Cartesian axis system scaling, it was illustrated that by partial reconstruction of the periodic system, the elements of noble gases can be arranged along lines whose slope tangents in the coordinate system 'the atomic number -the relative atomic mass' are in close agreement with the sequence of inverse Fibonacci numbers: .…”