Hopefully some advanced mathematicians will find this file on the
web and get provoked enough to search for explanations!
Geometrical relations in the two 12groups:
385 x √2 is
~ 544. Through this factor √2
and inversions (/\ ) the codon
groups 385 and 367 in the ESseries become related, figure 81 below..
How to interpret such relations? They are very likely only one example
among many similar dimensional relations on a deeper underlying
level that remains to investigate. (√2
should probably not be regarded as a relation diagonal/side
in a square, sooner in its serial development?)
Fig 81: Geometrical
relations through √2:
Two notes:
1) A rightangled triangle with the sides 176 and 209 (the number division of 385 within mixed codon groups) gives the hypotenuse 273.23.; 273 the mean number of two ams R + B unbound.
2) Cf peraps the relations between Znumbers of ATP and NADPH(+H) around 258  387, a 2/3relation, 6 x 43  9 x 43. see Biochemistry.
Intervals in the ESchain with exponents 3/2 and 4/3:
Intervals 404484 in the ESchain with exponent 3/2 gives numbers 253 292, and 770, as a kind of feed back (?) or mutual references , reestablishing the ESnumbers 5' and 4' (+1):
403/2 = 252.98. = 253.
443/2 = 291.86. = 292. ........Sum 544 +1.
(Third number 208?: 84  49 = 35, →
353/2 = 207.06. = 208 1)
843/2 = [292  208]3/2 = 770. = Cross plus Formcoded ams.
Compare with 42, 1/2 times the interval 84, divided and whole number:
Fig. 81b
Intervals in the three middle steps of the ESchain, sum 152:
443/2 = 291.9. 493/2 = 343 593/2 = 453.2.......sum 1088.15. = 2 x 544.

Exponent 4/3 ?
Testing this exponent  as related to a higher ddegree step 4  3 (?)  shows up to be another way to reestablish the starting number 292:
404/3 + 444/3 → 292.13. (Cf. 52/3 = 2.924.)
Note that 404/3 is about 136 +1 and 444/3 about 156 1: 136 mass of Inosine, 156 mass of Orotate, the parents of the bases in the codons
844/3 = 367.9. = 208 + 159, +1; x 2 = 736. = RNA + Paircoded ams +2.
The golden section:
The golden section (gs) as Fibonacci series appears also in this
ESchain and mass relations within groups of ams. Following series,
figure 82, leads from 2' in the ESseries to total sum R + B of
the 24 bound ams through steps as times gs:
The ESnumbers 208 and 367 gives for instance the groups G+C 544 and U+A 960 approximately.
Fig 82: Golden
section (gs) steps in the ESseries:
Higher numbers abridged. Number 257. = 208 + middle
interval 49. In 7th step we get 2848, x gs = 2 x 2304 = 2 x 48^{2}.(24
= number of codons, ams.)
Forms of Rchains:
Elementary structure of Rchains as basis for grouping of ams may
give three elementary groups: vary roughly ringformed, "straight"
and "branched":
Ringformed ams 292 + 159 (a loop 5'  2'.) = 451,
three aromatic ams 328, + His + Pro 123.
"Straight" ams = 2 x 159 (2') = 318,
Ala, 2 Ser, Thr, Cys, Lys, Meth = 317, + Gly 1.
Ringformed + "straight" = 770
1.
Branched = 734 +1 (as at middle of the ESchain):
CHxgroups = 271; OOH + ONHx = 262; 2 Arg NHxNHx = 202.
π and √2 , an arithmetical curiosity:
Reading and adding 2 x 5 twofigurenumbers (31 + 41 + 59..., 14
+ 15 + 92...) from first eleven figures in these transcendent celebrities
gives both whole and partial sums of the codon grouped amino acids
as well as vertically numbers from the exponent series, see the
figure below.
No motivation for the operation is offered here.
Should there exist any sense in the operation, it's left to more
advanced mathematicians to find it.
Fig 83: π and √2:
*Cf. fig.
41.
Sums of numbers from π = 431
and from √2 = 321; cf. triplet
numbers 432321.
A note:
If √2 is seen connected to ddegree step 21 and π to step 32, the number 321 from √2 could be thought of as displaced, here one 10power step:
Fig. 83x. Sum 431 + 321 with displaced 321 number
[Cheops pyramid:
½ x 292 = 146 ~ the height of this
pyramid  in meters!
½ x 460 = 230 ~ side of this pyramid
 in meters!
If the old Egyptians were acquainted with cubic roots and exponents
2/3 is probably uncertain. The Pharaoh measure "ell" is
said to have been about half a meter.
That the circumference of the base is approximately
2π times its height is a wellknown
fact.
460/292, x 2 = 3.15068, differs from π 3.1415... with ~ 3 pro mille.
π and √ 2 in figure 83: the 2figure numbers summed in another way:
One example:
π 31 14 41 15 59 92 26 65 53 35
√ 2 14 41 14 42 21 13 35 56 62 23
210+2 367 1752
 
385
[212 x 173 = 366,76 x 10^2. 3' + 2' = 366,74.)
What kind of relation could exist, which closely couples π and √ 2?
π represents 1/2 of a unity circle, but √ 2 only 1/4, if illustrated as in the figure
below? Could we interpret it in terms of a step or displacement in dimension
degree 3 to 2: (431 →
321 as sums of the 2figure numbers above)? π related to a 3dimensional world, √ 2 to a 2dimensional one.
Fig. 84 Bell's theorem
a. b.
Assuming the definition of a dimension as characterized by two complementary “endpoles” (0  00 in figure a), the shortest step between the poles in an 1dimensional world would be 2 r and the shortest step in a 2dimensisonal world could be only √2. In a 3dimensional world, the shortest way could be the circular one (with reference to Einstein)?
(There is an association here to Bell's theorem and Aspect's experiments with photons in quantum physics: measurements in two dimensions (directions) as φ
a branched way for two possible outcomes. If there were no coupling between the photons, the maximum result of Bell’s formula should be +/ 2. But the experiments showed on a maximum of +/ 2√2 showing that the photons were entangled.
The question arises: what would be the result if such measurements were carried out in three dimensions?)
√2 representing the tangent of an angle, a direction?
Arc tan √2 = φ 54.736.
Sin
φ = √2/3,
Cos
φ = √1/3
Treating these numbers
sin  cos in the same way as π and √2 above gives these results:
Fig. 85. Sin  Cos for arc tan √2
Taking each other 2figure number from the cosine series and each other from sine numbers, the upper ten first, gives sums of the ESchain:
Fig. 86. SinCosseries with sum 1011 of the ESseries
*
To Glycolysis
 Citrate cycle.
