TRFTRF Rediscover Egypt— The Ancient Future. TRFTRF The Sacred Geometry of the Giza Pyramids Moustafa Gadalla.

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Presentation transcript:

TRFTRF Rediscover Egypt— The Ancient Future

TRFTRF The Sacred Geometry of the Giza Pyramids Moustafa Gadalla

TRFTRF Introduction 1. The meaning of sacred geometry and its AE applications. 2. The sacred geometry of the 3 Giza pyramids.

TRFTRF 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.

TRFTRF

TRFTRF The Tool a cord consisting of 12 equally spaced distances 1 cubit= 1.72 ft. = m

TRFTRF The Sacred Cord When the cord is looped as a full circle, radius is 1.91 cubits = 1 meter exactly (1.91 x ). 1 meter = 1/100,000th part of the quarter of the earth’s meridian

TRFTRF 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

TRFTRF Pyramid Temple of Khafra

TRFTRF II. Progression of Growth and Proportion (3+2) 8 (5+3) 13 (8+5) 21 (13+8) 34 (21+13) 55 (34+21) 89, 144, 233, 377, 610,...

TRFTRF 3:2 = 1.5 5:3 = :5 = :8 = :13 = :21 = :34 = :55 = :89 = 1.618,...

TRFTRF General Layout of Geometric Shapes Equilateral triangle

TRFTRF Circular Curves

TRFTRF Square EBCF

TRFTRF The Neb (Golden) Triangle or Rectangle

TRFTRF

TRFTRF A logarithmic spiral indicated by “whirling squares”

TRFTRF The Root Rectangles

TRFTRF Map of 10 pyramids

TRFTRF The Collapsed Pyramid of Meidum

TRFTRF The Meidum Pyramid of Snefru Height (original): 306’ (93m) Mass (original?): 1.5 million tons Base (original): 482’ (147m) square Angle: 51 o 50’ 35”

TRFTRF The Giza Plateau

TRFTRF 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 limestone Area of base:13 acres (5.3 hectares) Inclination:51 o 50' 35"

TRFTRF The harmonic proportion of Khufu’s pyramid Height = 280 = 14 = ½ Base = = Golden Ratio 2 Base = 880= Height 280= Circle Index – = Diff = 0.04%

TRFTRF

TRFTRF

TRFTRF “King Khufu’s” Room

TRFTRF Khafra Pyramid Height:471' (143.5m) Base:708' square (214.5m) [error from true north 5’-30”] Mass:5.3 million tons Inclination Angle:53 o 07' 48"

TRFTRF The Ausar (Union) Triangle

TRFTRF Menkaura’s Pyramid

TRFTRF Menkaura Base:356' square (108m) [error from true north = 14”] Height:218' (67m) Mass:0.6 million tons Slope: (face to base) 51 o 20' 25" (5/4) (edge to base) 51 o 29' 53" (8/9)

TRFTRF Rediscover Egypt— The Ancient Future