Appendix-1 The growing spiral of the Cosmos
The spira mirabilis of Bernoulli is the result of the straight line
movement from which the velocity increases with the covered distance and the
rotating movement with a displacement angle proportional with time.
If the
distance covered by the movement of the straight line is represented by h, then
the velocity on a arbitrary instant t is given by :
dh / dt
= k(1).h where k(1) is a constant
and dh / dt is the velocity
For the
rotating movement, with displacement triangle
T(thau) we then have T
= k(2).t where: k(2) is the constant
and dependent of the number of revolutions, that also is a constant.
So there
are 2 expressions with which every point of the spira mirabilis must correspond
:
dh / dt = k(1).h and T = k(2).t ,
which on rearranging give :
dh / h = k(1).dt ……….. {1}and dt = dT
/ k(2) ……… {2} ; substituting {2} in {1} gives
dh / h = k(1).dT / k(2)
Or: log h = k(1).T / k(2) = K.T
with K constant.
We see
here that the logarithm of the carrying radii
h are proportional with the angles T between the carrying angles
(see definition of logarithm further).
With
S(1), S(2), S(3) and S(4) spiral points we have for each distance h the relation:
log h = K.T and consequently :
log h(2) - log h(1) =
log h(3) – log h(2) = log h(4) – log h(3).
The
logarithm of the carrying radii are a mathematical series, while the carrying
radii themselves a geometrical,
Because
the relations h(2)/h(1) , h(3)/h(2), h(4)/h(3) are identical,
And so :
h(2) = square root (h(1).h(3)) and h(3) = square root (h(2).h(4)).
When 3
carrying radii are giving an angle T , then
the middle one is the geometrical average of the two outer ones.
In
figure A1-1 above the triangles OS(1)S(2), OS(2)S(3), OS(3)S(4) are all
similar:
Because:
OS(1)/OS(2) = OS(2)/S(3) = OS(3)/S(4)
And so:
S(1)S(2)/S(2)S(3) = S(2)S(3)/S(3)/S(4).
The relation between the carrying radii is equal to the relation of the lines closing the successive carrying radii.
The same
relation is found between the arcs above the carrying radii.
The
triangles (or the sectors limiting the carrying radii) “ are generated from themselves
“ by a similarity of
tranformation.
This procedure of “own similarity” , of
“perfect analogy”, is continued in the
spiral of evolution.
The spira mirabilis is the only spiral with the
property of reproducing himself in
similar lines.
It is
the only curve with always similar arcs. They are changing in size not in form.
Every
part of the curve is a “gnomon” of the whole previous curve.
Due to
the this logarithmic growing process , similar lines, arcs, triangles and
sectors are generated.
Logarithmic Definition
The
number row 1, 10, 100, 1000, 10000 is the same as 10 power 0, 10 exp 1, 10 exp
2, 10 exp 3, 10 exp 4 ….
Instead
of using big numbers it is easier to use exponents of a base.
Instead of a base of 10 the spiral of evolution
is based on logarithms of base Phi.
+
See also
translation of Phi and the process triangle of book 3 Hidden Analogic , click
to Triangle 36
+
For links to the website of Prof. Michael Joyce , chemistry , UK,
Website on ancient and new
metaphysical geometry and numerology ,
With extended studies and comments on
the works of Prof. Kris Thijs :
click on : Website of Prof. Michael
Joyce :
for The Biblical book of Nummbers
click on Cheops Covenant Codes
for The
Universal Pyramid structure
click on PYRAMID-the UNIVERSAL
STRUCTURE
for The
Solar System
click on Thijs on The Universal
Pyramidal Structure
for
Bifurcation and constant
"e"
click on Thijs on The Universal
Pyramidal Structure (continued)
for
Saturn and Planck's constant
click on Ark of the Covenant, Saturn
Effect, Precession and Planck's constant
For
next appendix click appendix 2
For
appendix overview click Appendix 1 – 32
The Secret Language of God
Use
BACK arrow to return, or click to :
HOME PAGE TOPIC INDEX BASIC LINKS EXTENDED
LINKS E-MAIL - PERSONALIA
Explanations
are taken over in translated form from Het Geheimschrift van God ( The Sacred
Language of God)
of
Professor Kris Thijs, with the written authorization of Editor Guido Maes
Millennium Productions Belgium, documents still under copy rights.