Picture



π(0) = 1 = r = "Lenght" = "1" "Dim"
"Length" of a "3/2" torus knot = 4 :









Picture

3-dimensional cubic hyperarea of a 3-sphere


Multiple fractions and negation of fractions of numerical dimensions:

-1.-1.-1.-1

π(2|>1) = 3.14"'

Theorem: Autogeometrization :
Lemma: "...every section is divisible into infinite subsections..."
Therefore there are neither lenght nor even any "end" - "point" in the real science and real structure of the Universe.
There are only:
Operational rotation after infinitie"s", hence numerical autogeometry bending:

1 π (/2) = 2 Dim (Abs .+ .- <-> ./ .* )
2 π (/2) = 1 Dim (Rel ./ .* <-> .+ .-)

π(3|>2) = 4

Dim (Abs .+ .- <-> ./ .* <-> ./ .* )
Dim (Rel ./ .* <-> .+ .- <-> ./ .*)
Dim (Tar ./ .* <-> ./ .* <-> .+ .-)

pi(4|>3) = 3/2 π = 4.71"'

3 π (/2) = 4 Dim (Abs .+ .- <-> ./ .* )
4 π (/2) = 3 Dim (Rel ./ .* <-> .+ .-)

Picture

5-4 ; 4-3 "π":

Picture
4-3 ; 3-2 "π":

Picture
Initial number (multiple fractured value) of absolute (sub)dimension(s) : 1.1.1.1
Initial amount of (sub)dimension(s): 4.0

Subtransform View : 4.0 -> 3.0 -> 2.x -> 3.0
[Traditional translation of values by meaning of dimension]:
4D-> [Orthogonal projection] 3D-> [Perspective projection] 2D

Target number of absolute (sub)dimension(s): 1.1.1.0
Target amount of (sub)dimension(s): 3.0

Asymmetric - dual shift :
1.1.1.x -> x.x.x.1
(Fotonical <- > Hadronical)

Important ! :

4.0 <> 3+1 <> 4/1
3.0 <> 4-1 <> 3/1
<> = +/+/ Opposite shift /+/+ of (π's) dimensions' operand = The Reality



When you call something's "lenght", you have just now truncated -in your head- an infinite dimension into not only two , but exactly >3< parts:

there are two parts beyond the "lenght", - with different polarities-, and an inside the area you have just created: sliced / polarized ... is also infinite.

But what happens with these forgotten parts of these dimensions you called until this :flat / linear ?!

Both of them will become a curve in infinity !!! They explicitly MUST to do so in infinity !

Same way when you bend and truncate into itself .. a "1/3" into 0."33" often in just the second (!) iteration of infinite iterations.

Let see now the very same dimension from "opposite direction" , outside :

the whole case happening reverse: the curve , as you called until this, will become a flat !

This is the only property of infinities, which makes geometry and algebra impartible from now, with a very "simple" , but the most important logical algrebraic modification, without

which impossible to understand mathematics, thus write formulas of dimensions and its "physics" right , called: multiple negated fractions
as a completely new science of mathematics and the physics of dimensions, use negative expressions after fractions,
this is the only simple trick to understand how the things are working exactly.
Without the realization of these things above, like the behaviour of numbers in infinities like dimensions and without
multiple negated fractions, we can not speak about mathematics, especially not science. Furthermore:
without this kind of symmetry in algebra i just can't understand what the hell are physicists looking for in physics??!!

±1.±1.±1.±1 [ π3[Target] ±F0 ]



PI lower/middle/upper hook segment MEAN:



3

3



4

4



4

4


3/1


3


4/1


4


4/1


4

4

4



4

4



4

4


7/2


3,5


8/2


4


8/2


4

19/6

3,1”66”



2

2



2

2


61/18


3,3”88”


10/3


3,”33”


10/3


3,”33”

46/15

3,0”66”



8/3

2,”66”



3

3


397/120


3,308”33”


19/6


3,1”66”


13/4


3,25

47/15

3,1”33”



11/3

3,”66”



7/2

3,5


491/150


3,27”33”


49/15


3,2”66”


33/10


3,3

616/195

3,1”589743”



52/15

3,4”66”



19/6

3,1”66”


1523/468


3,25”427350”


33/10


3,3


59/18


3,2”77”

1321/420

3,14”523809”



14/5

2,8



46/15

3,0”66”




3,238”697017268445839874411302982731554160125588”


113/35


3,2”285714”


341/105


3,2”476190”



πn / πn-1 ratio:

π0/π-1 = 1/0 = = 1 |(*π-1)

π10 = 2/1 |(*π0) = 2

π21 = π2/2 = 1.57"' |(*π1) = 3.14"'

π32 = 4/π2 = 1.27"' |(*π2) = 4

π43 = ( 2π22/(4/3 π2) / 4) = (3/8) π2 = 1.17"' |(*π3) = 3/2 π2 = 4.71"'

π54 = ( (8/3π22) / (π22 /2) ) / (3/2 π2) = 32/(9π2) = 1.13"' |(*π4) = 16/3 = 5.33"'

π65 = ( π23 ) / ( (8/15) π22 ) / ( 16/3 ) = 45/(128π2) = 1.10'" |(*π5) = 15/8 π2 = 5.89"'

π76 = ( (16/15) π23 ) / ( (1/6) π23 ) / ( 15/8 π2 ) = 768/(225π2) = 1.08"' |(*π6) = 32/5 = 6.4