Below: Mathematician Ted Small..

accurately plotted the Golden Mean spiral in independant computer graphics from pure equation to create origin of the Alphabet..

reproducing work earlier done by Dan Winter, showing indeed that the correct alphabet graphic animations were and are based on a pure equation for the Golden Spiral.

click here to play pinwheels

Origin of symbol: embedding yourself into the center of psychokinesis by tornado steering..

(physics is no-thing if not wormholes)

These pages are legal because in US Federal Law, the material in US Federal Court (Here in the US District Court in Rochester NY Case : Winter vs. Tenen)

are absolutely in the public domain and shareable as such. Also see the file: danside.pdf below, explaining the legal background.

BELOW EXAMPLE OF U.S. LAW ENFORCEMENT EQUALS IN
ABSURDITY THE CLAIM OF A HOUSEWIFE WHO SUED THE
MANUFACTURER BECAUSE HER PUPPY DOG DIED IN THE
WASHING MACHINE...

... a message in defence of Science...

Dear all,

everytime that Stan says, that Dan's equations are a fraud, he
makes it strong with court testimonies. Dan's equation is NOT
a fraud, it is a pure interprojection of excuisitely straightforward
equations. This is what we understand from the message on Ted
Small's website. As long as people refuse to look at the actual
mathematic contents, rather than the "social" form of what's the
issue, either because of dogmatism or simply for lacking brains,
Stan's false allegations will never be dismantled. Stan's claim is
just as absurd as making the number Pi (3.141) out of clay, asking
copyright on it and sueing every scientist who says it is a really a
mathematical formula. If a mouse wins in court, that does not make
him an elephant. And, if lawsmen do not understand mathematics,
that does not mean that the rest of society does not understand it
either. Unfortunately, Dan himself may have be lacking the time
and the exact detailed mathematical presentation to make his case
sound under legal pressure. But the truth is simple, like every truth.

This is what Stan did not discover himself, and which he now apparently
wants to hide for the world, helped by lawsman who do understand
law because they studied it, but do not understand mathematics simply
because they did NOT study it.

So NOW follows the never-before published (also not by Dan)
MATHEMATICAL FORMULA FOR PRODUCING A 3D FORM THAT
HAPPENS TO LOOKS VERY SIMILAR E.G. TO HEBREW LETTER
FORMS. THIS IS A CREATION OF NATURE, NOT A CREATION OF
DAN WINTER...


... SHOWING US THE ARCHETYPAL TRACE OF HOW HETERODYNING
WAVES SELF-ORGANISE TO FORM MATTER AND CONSCIOUSNESS,
WHICH IS A COMBINATION OF PHI-BASED SYMMETRY PLUS THE ONLY
POSSIBLE WAY NATURE REMEMBERS SHAPE: THE UNIVERSAL
PRINCIPLE OF "INSIDE-OUTNESS" WHICH WE KNOW AS A "DONUT"
(TORUS). HENCE, THE COMBINATION OF THE PHI-SPIRAL AND THE
DONUT DOES RENDER THIS ANCIENT FORM, THE SHAPE OF ALL
SHAPES, THE HEART OF OUR HEARTS, AND OF ALL CREATION.

First, PHI-SPIRAL only:

Basic formula for natural Phi Spiral: radius = Phi ^ ( 2 * a / Pi )

Explanation: A by angle "a" rotating vector's length "radius" is determined
as a power of Phi, such that by each quarter circle, it's length is "Phi" times
longer. This traces the Phi spiral in a flat plane.

As an algorithm, it could look as follows:

c=1
For a = 0 * Pi To 4000 * Pi ' for alpha in radians, go round a few times
alpha = a / 1000 'make high resolution
radius = Phi ^ (2 * alpha / Pi)
PhiSpiral(c).x= spiralScale * radius * Cos(alpha)Delta)) 'Phi-spiral's X-coordinates
PhiSpiral(c).y= spiralScale * radius * Sin(alpha)Delta)) 'Phi-spiral's Y-coordinates
c=c+1 'counting the steps
Next a

DONUT only:

Basic formula: simply a "fanned" group of composing circles, the radius of the donut surface at any point is
the cosine of the angle of a composing circle, it x, y coordinates this radius time the cos resp. sine angle of the
donut, its z coordinate the sine of the composing circle.

As an algorith:

c = 1
For i = 1 To 20 'choosen nr. of composing circles building the Donut
For j = 1 To 20 'choosen nr. of segments making up one composing circle
radius = donutScale * Cos(j / 20 * 2 * Pi) 'Effective radius of one composing circle
Donut(c).x = radius * Cos(i / 20 * 2 * Pi) 'Donut's X-coordinates, unimportant for flame-form
Donut(c).y = radius * Sin(i / 20 * 2 * Pi) 'Donut's Y-coordinates, unimportant for flame-form
Donut(c).z = Phi * donutScale * Sin(j / 20 * 2 * Pi) 'Donut's Z-coordinates, USED FOR THE 3D Phi Spiral, or flame-form
c = c + 1'counting the steps
Next j
Next i

PHI-SPIRAL + DONUT = FLAME-FORM, IT'S SHADOW LOOKING E.G. LIKE HEBREW LETTERS
using the x and y coordinates of the phi-spiral, and the z coordinate of the donut.

For i = 1 to 40 'this one is for the spiral
j=i 'this one is for the donut
if j > 20 then j = j - 20 'after 20 steps next round, projection will naturally "fall of the edge"
FlameForm(i).x = PhiSpiral(i).x
FlameForm(i).y = PhiSpiral(i).y
FlameForm(i).z = Donut(j).z
next i

(This is one single trace, a full letter form is created by repeating above e.g. over 36 degrees)

THAT - IS - ALL (NO tinkering needed, despite Dan's own bit clumsy "efforts" to make it look
different...). Again: the Flame Letter is a simple, natural mathematical form.

Ted Small shows how Dan's too low resulution created the suggestion of tinkering.


The mutual scales (sizes) of Phi-spiral and Donut are irrelevant, as long as the spiral is evolved
from the centre upto the circumference. THIS NATURALLY RESULTS IN A 1.5 TURN. Where the
projection of the Phi-spiral reaches the edge of the Donut, it "falls straight off", naturally resulting
in a straigth angular approach
to the equator of the Donut, and hence, a parallel letter shape.

Hence, moreover, the Flame Form is a natural phenomenon, and thus everyone who defends
a person who wants to copyright it, should also defend a person who copyrights a clay model of
the number Pi (3.14)...



THIS EXAMPLE OF U.S. LAW ENFORCEMENT EQUALS IN ABSURDITY THE CLAIM OF A
HOUSEWIFE WHO SUED THE MANUFACTURER BECAUSE HER PUPPY DOG DIED IN THE WASHING MACHINE...
_____


This is what's really going on. Any attorney or prosecutor who cannot or will not understand this,
or at least it's implications, yet appreciates the validity of other sports than plain lawenforcment,
should seriously consider not to advise in this case.


friendly, - Shared_Science

 

Flame letter registered in Tetra

Samples below are created by the author using a pure Phi-spiral projection on a toroidal
shape, revolving it about 10 degrees to create a filled font. The software is written in
Visual Basic, using general formula's to create the spiral and toroid, as well as the 3D
functions. The result are the Hebrew alphabet letters registered inside the Tetrahedron.

 

 

The Source: the pure Phi Spiral R=Phi^2a/Pi

 

How the projection is done

Graph showing the result of projecting pure Phi Spiral R=Phi^2a/Pi onto a toroid.
The points where the projection touches the surface are encircled, together tracing
the shape of the 3D Flame Letter:

 

Tenen claimed Dan Winter 'cheated' on his accurate Phi Golden Spiral math plots, because he saw the tail end of Winter's 'Flame Letter' equation appear to 'tilt backwards'. In the below, we see this was the natural result of the original lower resolution in which Winter did his plot, and was not a distortion of the accurate placement of the plot points themselves. In effect this is evidence, Winter used only equation mathematics for Golden Mean in his graphic originals on alphabet origins.

Samples below showing effect of resolution, both are the same pure R=Phi^2a/Pi
(here as single line) projected onto the same toroid:

LO-RES: the steep projection angle creates a sharp bent trajectory,
the dotted line LOOKS like the normal progression, but is not.

 

HI-RES: the projection is now a smooth curve, naturally bending
toward a more perpendicular approach of the equatorial plane,
evolving into the proper form for the flame alphabet.

 

This example from Meru Foundation seems to demonstrate a more
oblique approach of the equator, suggesting that a perpendicular
approach would be unnatural, but this sculpture does not apply a
pure Phi spiral (it looks pretty much like an early tryout of mine,
where the path around the circumference is a mere linear function
of the path around the cross circle).

early tryout, using no spiral projection at all.

 

Detail of the meru sculpture, plus a pure Phi spiral inserted.
The green circle is drawn to check the aspect ratio of the print,
it is clear this cannot account for the difference.

 

 

Attachment: Dan Winters original work on the Flame Letter