
Home  Contact  Credos [ˈkɾeːd̪oː]):
Sacred/Natural
Geometry  Ancient
Ratios  Great
Pyramid  Links 
A mathematical, yet, 2D artistic approach
Towards explorations
[2008, 2009] into our ancient past,
world of mystery,
Prime & Pattern
Numbers , sacred and/or “natural”
geometry, plus more…All seeking..:
Forgotten knowledge and or
evidence of advanced knowledge lost in our past; yet, buried in 2D plane
sites!!
Introduction:
This research is focused on explorations and
analysis of the mathematical systems employed via
the ancients
as evidenced, via texts, symbols, art and or structures in order to
extract lost
knowledge and join cross culture metrology paving a connection through our
past.
Currently, with the help of University of Cairo
Professor Assem Deif,
2DCode has introduced two foundational
Geometrical models (“Tri2Pi” & “Square2Pi”) that
bind shape with number for a pure mathematical “natural” harmony….
These relational models (2:1 & sqrt2:1) have a trail of metrology through our
past via Masonic symbols
and structures {ex:
Grand Lodge, Rosslyn Chapel};Paul MartynSmith finds evidence within areas of his
study of
the IChing & Tao and their symbols, We find
evidence within Euclid’s Prop 47, Pythagorean Theorem,
the
Aztec/Maya Art , AE’s EMP/RMP, Integral units of GP, GP overhead view along
with the 2:1 GP KC seked.
These sekeds were sacred to the AE... Why?
This site will
endeavor to explain why as well as introduce both 2:1 pure mathematical models
demonstrated via applied mathematics using metrology ratios of the cultures in
focus.
These mathematical models could have real
world application within the fields of engineering, mathematics in general,
physics and more.
Additionally, this
research builds off of past pioneers evidenced data and through current
collaboration and analysis of the “GHMB Flow Gang”, will endeavor to explore
These natural shape
concepts through geometry and pure math to correlate with reverse engineered
evidence left behind.
Buckle up and
prepare to gain mathematical insight to forgotten knowledge.
2DCoderpast.com conveys no conclusions be made on
anything unless provable through solid evidence and or math..
Discussions of material have been linked where possible and when
time has permitted to actually “find” material posted…
**The term
“Pi” is used quite often in place of the term “circle” within this data. BASE
CIRCLE [D] of unit 1 will equate a circumference [C] of Pi.
Additionally,
2Dcode will endeavor to prove the ancients reconciled the circle via the
square. We can gauge both circle and square from one tangent [D].
All Hyperbolic theorems, methodology and foundational techniques
are defined on the geometry page:
REF: Foundational
SQRT2/1:1:1/SQRT2 “Square2Pi” & SQRT3/2:1:1/SQRT3 “Tri2Pi” Hyperbolic
Geometry.
Theorems have been formulated and presented as a direct result via
these observations and explorations:
 [BASE]x(Pi/SQRT8) = SQRT2 PARENT (Square2Pi) “natural”
Hyperbolic Side … [D]:[S]
=(SQRT2:1)
 [BASE]x(2/SQRT3)x(Pi/3) =
2/SQRT3 PARENT (Tri2Pi) “natural” Hyperbolic Side … [D]:[TS] =(2/SQRT3:1)
 [BASE]x(Pi/3) =
2:1 PARENT:PARENT or “2:1 natural”
Hyperbolic Side … [D]:[S]
=(2:1)(applies to both Tri2Pi & Square2Pi Geom Models)
 [BASE]
x(Pi/4)
= Hyperbolic Squared
(CIRCLE PERIMETER) Side
 [BASE]
xSQRT(Pi/4) =
Hyperbolic Squared (CIRCLE AREA) Side
1/2[BASE]x(Phi^2) = Phyperbolic
Side
Rational
2:1 Geom Model Evidenced within EMP/RMP [AE’s rational
sqrt2/1:1:1/sqrt2 model]Discussion…: GHMB
 Ma’at
“The Rosetta Stone” to the Ancient Egyptian’s Geometry skills (AE 1^{st}
Dynasty Hemaka Disks).
(Fall ’09)
Photos provided by and copyright Jon Bodsworth
2009 ("The Egypt Archive": http://www.egyptarchive.co.uk
)
(many thanks to Jon B. for the best AE
pictures available on the web.)
Correlating
metrology cross culture(AE:Aztec&Maya)
Aztec/Maya
World Picture Geometry {joining metrology systems and linking the GP}[May/June 2009]
Expanded EMP/RMP study binding the integral units of the GP
structure…
Ancient
Egyptian Metrology through analysis of Hieroglyphs, GP, Royal Cubit &
EMP/RMP or Ahmes Papyrus [summer ‘09]
Exploring Ancient Egyptian
Metrology through analysis of the Royal Cubit [early ‘09]
Attempting
to bridge the gap towards a new foundation; joining camps via proof the ancients
not only knew, but, embedded sacred knowledge within their structures.
Theorem to Square the Circle’s AREA
& PERIMETER. [June ‘09][Posted @ GHMB]
The GP Khufu stands at the hyperbolic arc of the [D] diameter
... which splits the circle into two mirrored halves or hemispheres.
hence Pi/2 is the hyperbolic arc formula for a diameter of a circle creating
the hyperbolic length unit of one hemisphere... x2 completes the
circle or circumference and relates the diameter via Pi/2 or to the
ancients, 11/7 & 7/11, evidenced via
EMP/RMP and confirmed via GP BASE : GP
Height ratio with a slope angle
Or 14/11 seked equal to the rational
approximation for the Pi/4 hyperbolic arc theorem that squares the circle.
Confirmed via GP Height [S]x(14/11)…x4=PERIM that
squares GP Apothem [D]x[Pi]=[C]. Additionally, ½ GP BASE SIDE [S] Squares PERIM
with GP Height [D]…etc..etc.
Exploration of the “Canon” through Harmony of the spheres:
Detailed Demonstration
of the “Star of Ishtar” using the natural Harmony of spheres. [Sept 2009 Research]
REF LINK:
Giza Explorations: (GHMB
Discussion) [April / May 2008]
Sacred and or Natural Geometry Page: Here (Defines
hyperbolic theorems and current techniques)
Convergence:
{August/Sept
2008 } Converging
Pi, SQRT’s and
more with potential output pattern in an approximation of the same input…[Posted
@ GHMB]
[July/August 2008] How much knowledge did the Ancients really have? And, how much
did they “intend” to convey or even hide in “plane” site 4 that matter?
For
example…let's take the Giza Plateau that John Legon
and others convey a root2 x root3 GizaRectangle with a root5 diagonal!
But, as
an “approximation” to what we currently call true SQRT2 & SQRT3.
If these roots were intended and can be proven; then, how could the Architects
not also have known the combined approximation of Pi?
SQRT2
(99/70)+SQRT3 (97/56) approximates to Pi!
Below, is the geometry / ["art"]
that binds the two "roots" of the square into one dual harmony of BASE 360
geometry....! :)
posted
[GHMB Aug 2008]
Could
the Architect of the GP’s have known SQRT2/1:1:1/SQRT & SQRT3/2:1:1/SQRT3
via approximations?
Furthermore,
could Ahmes have used a BASE 360 degree system
similar to the above root2 & root3 diagram? And, can we find signs in the
RMP?
The
AE used
fractions and could easily approximate these root approximations.
(99/70)+*(97/56) =
3.1464285714 =~ an approximation of Pi {true Pi= 4xATAN(1)
using radians}.
[Dec
2009] After two years of exhausting research, I came upon the 1st Dynasty Hemaka Geometry Disk excavated by Emery published in 1938.
Hence,
It would appear the answer to “if” the ancients
understood basic shape models and root approximations can be concluded “yes”.
Please
observe:
Posted
[GHMB
Dec 2009]
Plato also mentions: “…. root 2 as the irrational and rational diagonals of 5”
5*sqrt(2) = 7.0710678118... = [10/SQRT(2)]
therefore,
1/(sqrt(2)*5) = 0.14142135623 = [SQRT(2)/10]
hence,
10/(sqrt(2)*5) = 1.414213562373095 = [SQRT(2)]
And, can be broken down algebraically by dividing the 10 by 5
Therefore,
2/SQRT(2) = 1.414213562373095 OR, 2/SQRT(2)=SQRT(2).
hence,
x/SQRT(x) = SQRT(x) = “The underlying math from Plato as it
was processed ([via post by Ariston])
Furthermore, if we apply those SQRT2 approximations; used most notably
by John Michell, and mentioned many times throughout
this site.
99/70 = 1.4142857 cyclic "142857"
140/99 = 1.4141 cyclic "41"
They actually switch values upon
2 as the numerator using (AE style) AE 2/PrimeN fraction table.[Exploration 
Expanded study to 999]
2/(140/99) = 1.4142857 cyclic
"142857"
2/(99/70) = 1.4141 cyclic "41"
And, if we dig a little deeper into the [Wiki]Rhind Mathematical Papyrus
We can
observe indication of intention via these very units in the company of diagonals.
If a square
measures 70 by 70 royal cubits, the diagonals measure practically 99 royal
cubits,
and if a square
measures 99 by 99 royal cubits, the diagonals measure practically 140 royal
cubits
[Exploration  RMP#1 SQRT1/1:1:1/SQRT2 Exploration];
Discussion…:
GHMB
 Ma’at
SQRT2/1:1:1/SQRT2 (…through rotating root approximation)
Proof the AE understood convergence within the Rhind?
Further evidence of SQRT2 convergence
within the Rhind.
Proof of SQRT5 convergence within the Rhind?
If nothing else; the data appears compelling enough to pursue further investigations.
Visit the explorations
page for:
Exploration
 Base 9 geometry layer to represent
Ahmes 9 unit start area. [posted:
GHMB  Ma’at]
Exploration  Base 16 geometry layer to break the RMP50 down to 256. [posted: GHMB  Ma’at]
“If the edge of a cube
measures 10 royal cubits or 70 palms or 280 fingers = 5 x 56 fingers,
the diagonal of a face measures
practically 99 palms,
the cubic diagonal measures
practically 5 x 97 = 485
fingers.
SQRT2 APPRX = 99/70 = 1.4142857
SQRT3 APPRX = 97/56 = 1.732142857
…If we “just”
take the current orthodox understandings, and accept the “AE seked” ratio of [14:11]
and employ the inverse or reciprocal (1/14:11) or (11:14) per
side angle.
All 4 angles of
that Khufu GP, then add up to “exact” 22/7 “natural”… cyclic Old School Pi!
Were potentially more advanced then current mainstream accepts…
**....given any
remain in thousands of years from now?
….much much more
scattered throughout this site.
 Additional Explorations of the GP’s, Giza and AE Math…
Additional Explorations & Research documented and or
noted for 2008…
Additional Explorations & Research documented and or
noted for 2009…