THE AXIAL NETWORK OF THE IBOZOO UU

 
A summary definition of the final definition of the IBOZOO UU that we will give to you at the end is this one:

An IBOZOO UU is a elementary cosmic entity integrated by a beam of oriented axes WHICH CANNOT CROSS EACH OTHER, bound to a whole of IBOZOO UU independent one from the other in relation to their angularity.

You can see that we are gradually adjusting each time more accurately the authentic concept of IBOZOO UU defined by our specialists on UMMO. We thought that to bring you an exact definition from the outset would have been excessively confusing, especially taking into consideration that no theory approaching ours in its formalism exists on the planet EARTH.

Observe also that through the translation of this definition, we expressed that the IBOZOO UU integrate a beam of oriented axes which cannot cross each other.

This is very difficult to understand if you to continue to maintain the mental image of Euclidian space with its points and lines. Naturally if the IBOZOO UU were like a sphere or a hypersphere (D59_FG10), in its centre the different axes could CROSS EACH OTHER at a point. (For example the radius vectors would cross in the center). Therefore this mathematical model does not accurately represent the IBOZOO UU.

 If we chose the model of a sphere in our description, it was only to obtain a more faithful translation of the concepts by using mathematical algorithms, notations and geometrical concepts very familiar to Earth people. (It is a little like what you do when, for the purposes of simplification, you consider the Earth to be an ideal sphere whereas you know that it is an deformed ellipsoid. (isosceles Ellipsoid with three axes)).

Let us then suppose a sphere (D59_FG10) which would constitute one of the infinite hyperplane meridians of a hypersphere of order N = 4.

  If you are not familiar with this concept, imagine that if we give the name "meridian plane" to the section of a sphere which passes through its center, a sphere of order N = 3, for a hypersphere of dimension 4, its section will be precisely a figure of N - I dimensions, i.e. a sphere. It is necessary to remember the concept of the ANGLE in a HYPERSPACE.
Q = Q (P,Q)

Let P and Q be two HYPERPLANES defined by the co-ordinates U = (U0 U1 U2... Un) and V = (V0 V1 V2 .....Vn)

These two HYPERPLANES determine a beam G.

Thus in this beam G there are TWO HYPERPLANES P¥ and Q¥ which are tangent with the fundamental quadratic S .

 

The angle Q= Q(P,Q) (in which 0<Q<P) between these two HYPERPLANES P and Q is defined by:
Q = Q(P,Q) = 1/2ì Log R (P, Q, P ¥, Q ¥)
 

This angle is defined by the equations: (we cannot represent Q on an image. We reproduce only the projection of Qp of Q. Qp will be expressed by two meridian planes in the case of Q for an N-space of the order N = 4.)

 

D59_FG18 and D59_FG19

 

D59_FG20

In that which e = +1 since we suppose a HYPERSPHERE of positive curvature.

Let us remember the difference between SPHERE of positive curvature and a spherical surface of negative curvature, which helps us to understand the concepts of HYPERSPHERE of curve e = +1 and e = -1 (D59_FIG 19).

Therefore: when R (P Q, P¥, Q¥) = -1 we consider that the two HYPERPLANES are orthogonal.

If you replace the concept of linear OOWAOO (radius vector) linear of our former simplified model, by that of the HYPERPLANE of the order N = 4 and if you imagine these HYPERPLANES of reference not in the IBOZOO UU studied, but in another that is dependent on it, we can imagine three directing cosines which we will call cosY, cosX , cosW which define other angles for us (Y, X , W ) which we call IOAWOO (dimensional angles) . The angles will define each one the respective values of three-dimensional space such as we conceive it. It is supposed that an infinitesimal variation in the values of these directing cosines brings about a dependent pair of IBOZOO UU.
 
 

 
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