Embed Size (px)
Citation preview
T
R
F
Rediscover Egypt—
The Ancient Future
T
R
F
The Sacred Geometry of the Giza Pyramids
Moustafa Gadalla
T
R
F
Introduction
1. The meaning of sacred geometry and its AE applications.
2. The sacred geometry of the 3 Giza pyramids.
T
R
F
What is Sacred Geometry
• Herodotus, stated in 500 BCE:• Now, let me talk more of Egypt for it has a
lot of admirable things and what one sees there is superior to any other country.
• Plato stated,• That the pictures and statues made ten
thousand years ago, are in no one particular better or worse than what they now make.
T
R
F
T
R
F
The Tool
• a cord consisting of 12 equally spaced distances
1 cubit = 1.72 ft.= 0.5236 m
T
R
F
The Sacred Cord
• When the cord is looped as a full circle, radius is 1.91 cubits = 1 meter exactly (1.91 x 0.5236).
• 1 meter = 1/100,000th part of the quarter of the earth’s meridian
T
R
F
Design Parameters of Egyptian buildings
• unification of two systems:• arithmetic (significant numbers).• graphic (square, rectangles, and a few
triangles).• This union follows the elements described
below:• 1 - The Active Axes• 2 - Significant Points (Along the Axis)• 3 - The Telescopic Triangles• 4 - The Rectangular Perimeters
T
R
F
Pyramid Temple of Khafra
T
R
F
II. Progression of Growth and Proportion
235 (3+2)8 (5+3)13 (8+5)21 (13+8)34 (21+13)55 (34+21)89, 144, 233, 377, 610, . . .
T
R
F
3:2 = 1.55:3 = 1.6678:5 = 1.6013:8 = 1.62521:13 = 1.61534:21 = 1.61955:34 = 1.61889:55 = 1.618144:89 = 1.618 , . . .
T
R
F
General Layout of Geometric Shapes
• Equilateral triangle
T
R
F
Circular Curves
T
R
F
Square EBCF
T
R
F
The Neb (Golden) Triangle or Rectangle
T
R
F
T
R
F
A logarithmic spiral indicated by “whirling squares”
T
R
F
The Root Rectangles
T
R
F
Map of 10 pyramids
T
R
F
The Collapsed Pyramid of Meidum
T
R
F
The Meidum Pyramid of Snefru
Height (original): 306’ (93m)Mass (original?): 1.5 million tonsBase (original): 482’ (147m) squareAngle: 51o 50’ 35”
T
R
F
The Giza Plateau
T
R
F
The harmonic proportion of Khufu’s pyramid
Height (Original): 280 cubits (481', 147m)Base: 440 cubits square (757' sq,
229m sq)Mass: 6.5 mil tons limestoneArea of base: 13 acres (5.3 hectares)Inclination: 51o 50' 35"
T
R
F
The harmonic proportion of Khufu’s pyramid
Height = 280 = 14 = 1.272727½ Base 220 11
= 1.619 = Golden Ratio
2 Base = 880 = 3.1429Height 280 = Circle Index
3.14159 – 3.1429 = 0.0013 Diff = 0.04%
T
R
F
T
R
F
T
R
F
“King Khufu’s” Room
T
R
F
Khafra Pyramid
Height: 471' (143.5m)Base: 708' square (214.5m)
[error from true north 5’-30”]Mass: 5.3 million tonsInclination Angle: 53o 07' 48"
T
R
F
The Ausar (Union) Triangle
T
R
F
Menkaura’s Pyramid
T
R
F
Menkaura
Base: 356' square (108m) [error from true north = 14”]
Height: 218' (67m)Mass: 0.6 million tonsSlope: (face to base) 51o 20' 25" (5/4) (edge to base) 51o 29' 53" (8/9)
T
R
F
Rediscover Egypt—
The Ancient Future
