The periodic law requires obviousness

There are three basic modes of functional associations representation known in science: a) analytical, b) graphic, c) tabular.

From the moment of its statement the periodic law required tools of expression. The table was chosen as the basic tool.

There were many attempts to find an adequate form, visual representation of the law. More than 500 modifications of the periodic system are known today. Tables (> 400) predominate among them; the remaining images are various geometrical figures, analytical curves and so on. [2] [See, for example, [10].

The great variety is explained, obviously, not only by supplement of the system with new elements, but also by the objective difficulties of quasiperiodic structure representation.

In most of periodic objects and events observed in nature, (for example, segmented worms, striated  muscle, oscillation of a pendulum, rhythm of heart muscle contraction, change of time of day, seasons of year and so forth), the length of periods is constant or it increases in regular intervals in an arithmetical or geometrical progression, (some patterns on plants or spiral shells of some chambered mollusks). In the periodic law modification of period length is a variable value. The length of periods in the system composes neither a geometrical nor an arithmetical progression. This variable submits to the more complicated nonlinear association based on the electronic configuration of an atom.

The difficulties at construction of the periodic system of elements remind, from my point of view, of a packing problem. How to pack the things - periods (for example, books of a different format) on shelfs of afixed length? Hydrogen (H) and helium (He) cannot fill a line of the first period of the traditional table (even if hydrogen is written twice). With magnification of the period number the arrangement of elements in its lines becomes tighter. The lanthanides and the actinides cannot be laid (squeezed) at all into standard formats and are born outside of the table. If we speak about theoretically predicted superheavy elements, the problem of their arrangement is even more aggravated (complicated).

# Extended Periodic Table

 IA 0 1 1 H IIA IIIA IVA VA VIA VIIA 2 He 2 3 Li 4 Be 5 B 6 C 7 N 8 O 9 F 10 Ne 3 11 Na 12 Mg IIIB IVB VB VIB VIIB VIII IB IB 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 4 19 K 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 30 Zn 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr 5 37 Rb 38 Sr 39 Y 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe 6 55 Cs 56 Ba 57 La 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn 7 87 Fr 88 Ra 89 Ac 104 Rf 105 Ha 106 Sg 107 Ns 108 Hs 109 Mt 110 Uun 111 Uuu 112 Uub 113 Uut 114 Uuq 115 Uup 116 Uuh 117 Uus 118 Uuo 8 119 Uue 120 Ubn 121 Ubu 154 Upq 155 Upp 156 Uph 157 Ups 158 Upo 159 Upe 160 Uhn 161 Uhu 162 Uhb 163 Uht 164 Uhq 165 Uhp 166 Uhh 167 Uhs 168 Uho 6 58 Ce 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu 7 90 Th 91 Pa 92 U 93 Np 94 Pu 95 Am 96 Cm 97 Bk 98 Cf 99 Es 100 Fm 101 Md 102 No 103 Lr 8 122 Ubb 123 Ubt 124 Ubq 125 Ubp 126 Ubh 127 Ubs 128 Ubo 129 Ube 130 Utn 131 Utu 132 Utb 133 Utt 134 Utq 153 Upt 8 135 Utp 136 Uth 137 Uts 138 Uto 139 Ute 140 Uqn 141 Uqu 142 Uqb 143 Uqt 144 Uqq 145 Uqp 146 Uqh 147 Uqs 148 Uqo 149 Uqe 150 Upn 151 Upu 152 Upb

Figure 1.This periodic table is extended to include element 168.
The elements 113, 115, 117, and above 118 have not yet been
proven to exist, they have only generic names and symbols.

Materials of the site [10] are used (adapted) by creation of the table. The length of periods  - is not a simply nonconstant magnitude - this magnitude itself varies periodically. In each even period one observes its integration on the progressively growing magnitude equal to double odd number {6, 10, 14..., 2 (2n-1)...); n = 2, 3, 4...}.

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