# Visualization

VISUALIZATION

• Of the rank, follows Theta Math, and utilized Theta Math nomenclature for the plot of a 3D/9D solid. (Matrix 9+)

SET SCORE LINES (SL)

• Choose the score lines you would like to utilize for the chart, assessment or solid representation of a rank.
• The score lines are the matrix dimensions.

SET SEQUENCE OF DIMENSIONS / PRIORITY Θ

• Set the sequence according to Prime Master design, assigned to a unique training program as for a unique student type.
• Right hand direction, set spin upwards, through thomb.
• Score lines are equidistant from each other, placed at the circle line, according to this priority pre set.
• The Wisdom of this priority is the wisdom of the primes.

SET SCORE LINES RANK (SLR)

• At each score line, assessment, relative rank assignment. ( 0 up to 9+ rank points, equidistant from each other)

SET RANK DEGREE

Use coordinates as for rank degree:  + elevation from the  fundamental point (vector origin) to the score rank (vector destination).

• 0° = no rank
• 1° = rank status 1
• 2° = rank status 2
• 3° = rank status 3
• 4° = rank status 4
• 5° = rank status 5
• 6° = rank status 6
• 7° = rank status 7
• 8° = rank status 8
• 9° = rank status 9
• 9+° = rank status 9+

• The magnitude is set as for equivalent of that one of the score line rank assigned.
• For example: Kung Fu Panda Rank 4, will have a R4 as result.
• As the Solid Radious may change for purpose of visualization, the Vector Radious, which signs magnitude will never change as for the agreement set here.
• The result is that any radious choosen for a solid, will bring the same visualization, and cyphers, as a result. While geometrically will look differently, will create the same message, content.

From axis fundamental origin point, distance to the score line rank point

• R0 = 0
• R1 = 1
• R2 = 2
• R3 = 3
• R4 = 4
• R5 = 5
• R6 = 6
• R7 = 7
• R8 = 8
• R9 = 9
• R9+ = 9+

• SR= Between 0 and 9+

SOLID DIAMETER

• SD = 2*SR

SET SOLID VERTICAL LIMIT (SV)

• SV = Theta Variable: (9,..,9**)

SOLID RANK POINT

• Vector result of the addition of all vectors.

EXAMPLE:

SOLID RANK :

• SR = 9
• SV = 27
• SD = 18
• SL Set = (Kung Fu Panda, 9 Belts, 9 Stages of Love )  It is a 3D Matrix9+
• SLR =  (Kung Fu Panda(3), 9 Belts(5), 9 Stages of Love(4) ) Prioirity Θ assigned here are for right hand spin: 1.) Kung fu panda score line, 2.) 9 belts score line, 3.) 9 stages of love score line) as Θ=3 (3 score lines, 360/3=120 degress between each other)
• Now plot the coordinates in the space, by placing the Score Lines at equal distances from each other on the circle line, and marking a dot at the score line rank, result of the assessment.
• Set the vectors for each score line.
• Calculate the SOLID RANK POINT (SRP): (3°, 5°, 4° ) by vector addition math/transformation
• Calculate for each assessment the angle of approximation as for Alpha = Phi ( a) when a= RADIUS (R) reduced down to zero
• Coordinates in Prime Tech Matrix 9+ nomenclature for Θ = 3
• V1 = (9,9,3, Θ) = (9,9,3, 3) = (9,9,3, 120)
• V2 = (9,9,5, Θ) = (9,9,5, 3) = (9,9,5, 120)
• V3 = (9,9,4, Θ) = (9,9,4, 3) = (9,9,4, 120)
• Transformation to cartesian : Radius = 9,  then : 9= a2 + b2 = c2
• Calculate: http://www.cleavebooks.co.uk/scol/calrtri.htm
• http://hotmath.com/learning_activities/interactivities/3dplotter.swf (useful for visualization) http://illuminations.nctm.org/activity.aspx?id=4182
• V1 = ( 9;0 ;3; Θ) = ( , ,3, 3) = ( , ,3, 0)
• V2 = ( -4,5; 7,79 ; 5; Θ) = ( , ,5, 3) = ( , ,5, 120)
• V3 = (-4,5 ; -7,79 ; 4;  Θ) = ( , ,4, 3) = ( , ,4, 240)
• ADDITION: ( 0; 0 ; 12; 0) Solid Rank Point Vector

RANK SOLID – PATTERN OF EVOLUTION – RANK TRACE (in time)

• As for any given point in time the solid rank will be a SOLID, the transformation of solids along time will create a 3D shape/pattern, which describes the nature of change along time.
• Consider now the time line as an additional axis utilized for the purpose of creating a solid shape. Take the axis of each solid created at particular time point, place it at its associated  time point on the time line axis: then, we will be able to visualize the transformation in time (in the time line) of the solid.
• As many assessments you do in time, more solids you will generate, more accurate the transformation pattern, shape.
• By adjusting the time line scale unit from seconds, to months or years, according to case (students change/transformation-ability), a shape would be easy to visualize as well
• A study on patterns and nature of the TRACE the individual creates while developing on self along the training (ranking, career) will give to the trainer as well as to the student mirror information, meaningful for self-perfecting own self along the path of action.

REF: Calculations, systems and nomenclatures

(r, θ, z) is given in cartesian coordinates by:

$\begin{bmatrix} r \\ \theta \\ z \end{bmatrix} = \begin{bmatrix} \sqrt{x^2 + y^2} \\ \operatorname{arctan}(y / x) \\ z \end{bmatrix},\ \ \ 0 \le \theta < 2\pi,$

or inversely by:

$\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} r\cos\theta \\ r\sin\theta \\ z \end{bmatrix}.$

Any vector field can be written in terms of the unit vectors as:

$\mathbf A = A_x \mathbf{\hat x} + A_y \mathbf{\hat y} + A_z \mathbf{\hat z} = A_r \mathbf{\hat r} + A_\theta \boldsymbol{\hat \theta} + A_z \mathbf{\hat z}$

The cylindrical unit vectors are related to the cartesian unit vectors by:

$\begin{bmatrix}\mathbf{\hat r} \\ \boldsymbol{\hat\theta} \\ \mathbf{\hat z}\end{bmatrix} = \begin{bmatrix} \cos\theta & \sin\theta & 0 \\ -\sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} \mathbf{\hat x} \\ \mathbf{\hat y} \\ \mathbf{\hat z} \end{bmatrix}$

Vectors are defined in spherical coordinates by (ρ,θ,φ), where

• ρ is the length of the vector,
• θ is the angle between the positive Z-axis and the vector in question (0 ≤ θ ≤ π), and
• φ is the angle between the projection of the vector onto the X-Y-plane and the positive X-axis (0 ≤ φ < 2π).

(ρ,θ,φ) is given in Cartesian coordinates by:

$\begin{bmatrix}\rho \\ \theta \\ \phi \end{bmatrix} = \begin{bmatrix} \sqrt{x^2 + y^2 + z^2} \\ \arccos(z / \rho) \\ \arctan(y / x) \end{bmatrix},\ \ \ 0 \le \theta \le \pi,\ \ \ 0 \le \phi < 2\pi,$

or inversely by:

$\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} \rho\sin\theta\cos\phi \\ \rho\sin\theta\sin\phi \\ \rho\cos\theta\end{bmatrix}.$

Any vector field can be written in terms of the unit vectors as:

$\mathbf A = A_x\mathbf{\hat x} + A_y\mathbf{\hat y} + A_z\mathbf{\hat z} = A_\rho\boldsymbol{\hat \rho} + A_\theta\boldsymbol{\hat \theta} + A_\phi\boldsymbol{\hat \phi}$

The spherical unit vectors are related to the cartesian unit vectors by:

$\begin{bmatrix}\boldsymbol{\hat\rho} \\ \boldsymbol{\hat\theta} \\ \boldsymbol{\hat\phi} \end{bmatrix} = \begin{bmatrix} \sin\theta\cos\phi & \sin\theta\sin\phi & \cos\theta \\ \cos\theta\cos\phi & \cos\theta\sin\phi & -\sin\theta \\ -\sin\phi & \cos\phi & 0 \end{bmatrix} \begin{bmatrix} \mathbf{\hat x} \\ \mathbf{\hat y} \\ \mathbf{\hat z} \end{bmatrix}$

So the cartesian unit vectors are related to the spherical unit vectors by:

$\begin{bmatrix}\mathbf{\hat x} \\ \mathbf{\hat y} \\ \mathbf{\hat z} \end{bmatrix} = \begin{bmatrix} \sin\theta\cos\phi & \cos\theta\cos\phi & -\sin\phi \\ \sin\theta\sin\phi & \cos\theta\sin\phi & \cos\phi \\ \cos\theta & -\sin\theta & 0 \end{bmatrix} \begin{bmatrix} \boldsymbol{\hat\rho} \\ \boldsymbol{\hat\theta} \\ \boldsymbol{\hat\phi} \end{bmatrix}$

WISDOM

• In space and time, 2 parallel score lines (dimensions)  may meet at any given point.
• The solid rank point indicates the vector/arrow destination, and magnitude.
• The Set of score lines (Matrix 9+) used, defines a Perception Model (perception standing point or auxiliary view, like in geometry 3D description ) of the RANK SOLID.
• The Sequence of sets of score lines, the THETA Degree (sequence priority) of each score line within the foundation circle projection of the rank at the XY dimension of the solid, suggest a training program complexity.
• The art of design of training programs, is that of the Prime Masters, and Grand Masters. The art of design of  a prime Rank training program is that one of a prime master. The art of providing a training program is that one of a prime master, grand master and master. The art of learning and self learning is that one of a white belt. For example why the  (Kung Fu Panda(3), 9 Belts(5), 9 Stages of Love(4) ) score lines are used to design a training for a student TYPE THETA 3 ? and why it wouldnt be used for a students type THETA 5 ? This knowledge is the knowledge of the Primes, and prime masters.

VECTORS MATH

• Vector = Score Line Rank (var) = the vector radious, degree and magnitude.
• The Theta  priority (in sequence set on the circle projection of the solid on the foundation plane))
• For an addition, utilize transformation to cartesian coordinates.

REF:

• http://math.stackexchange.com/questions/17517/vector-sum-in-spherical-coordinates
• http://mathinsight.org/vectors_cartesian_coordinates_2d_3d