Pyramid Angles, Slopes (Giza, Nubian)
Before we discuss pyramid angles and slopes, let us revisit what is required to form a pyramid. For a pyramid, we need a square base and four triangular sides (equal in shape), slanting upward to meet at the top. This is all that is required for a pyramid. Experiment by trying an exercise we demonstrate with rubber bands on pyramid shapes.
Let us remember that a pyramid is not the same as a tetrahedron. A tetrahedron is made of four triangles with no square. Another exercise is to build your own pyramid out of cardboard. First draw a square, then draw equally shaped triangles facing outward from each side. Cut it out, then fold the triangles upward to have them meet at the top.
In the design (upper left), each triangular side is an equilateral triangle (all three sides of each of the four triangles have the same length). When you fold the tabs upward to meet at the top, you will have an equilateral pyramid. Equilateral pyramids have an edge slope of forty-five degrees (see reference, below). By "edge" we are referring to one of the four corners of the pyramid. If you were to elongate the length (upper right), the slope would change. It would be closer to the Nubian pyramid slope.
The Great Pyramid of Giza Slope
Understanding these basics or pyramids and slopes, we now move on to examine the special slope present in both the Great Pyramid of Giza and Nubian Pyramids of Meroe. To do this, we must differentiate between edge slope and face slope. Using the Great Pyramid as an example, there are two perspectives from which to examine the slopes of pyramids. The first perspective is with a corner facing us. This will allow us to observe the edge slope (below, left). Viewed from this perspective, the Great Pyramid has a slope of 42 degrees (41 degrees, 59 minutes, etc.). The second perspective is with a pyramid face directly in front of us (lower, right). Viewed from this perspective, the Great Pyramid slope is 51.83 degrees (51 degrees, 50 minutes, etc.). When we speak about the special slope of the Giza pyramid, we are referring to 51.83.
When we build copper pyramids, we are careful to reflect the specific slopes in both Giza and Nubian models. We do this by carefully duplicating the relationships between the length of the base on a given side (for us, the length of insulated copper wire) and the length of the angled pyramid edge (for us, the length of copper pipe). The duplication of this relationship of base and side (adhereing to the math of the Golden Ratio) allows us to duplicate the slopes of these pyramid. When our portable pyramids are set up with wire at the base made taught, the dimensions of the pyramid should be correct to within 1/8 inch.
The Golden Section (Golden Ratio)
Although the math (expressed in the Miranda Lundy quote below) may be difficult to wrap our heads around, it is apparent (see image above) that each subsequent square (moving outward in the spiral) is proportionately related to those previous. Hence, "the ratio of the lesser part to the greater part is the same as the ratio of the greater part to the whole." The Phi (Φ) ratio occurs organically in nature. Both Giza and Nubian pyramids celebrate this naturally-occuring proportion.
"1:Φ, where Φ, or phi, can be either 0.618 or 1.618 (more exactly .61803399.. .). Importantly, Φ divides a line so that the ratio of the lesser part to the greater part is the same as the ratio of the greater part to the whole. No other proportion behaves so elegantly around unity. Φ appears predominantly in organic life."
To unpack the math just a bit, we will look closely at the ratio 1:1.618. Take note (for example) in the image of the Golden Ratio above, how the two dominant squares in the upper part of the image are (in width) 1 (left-most square) and 1.618 (right-most square). This ratio continues for each set of squares, moving inward or outward.
The Golden Ratio and the Great Pyramid of Giza
Expressed in the Great Pyramid of Giza and resulting in the 51.83 face slope is this same ratio (see image below). Proportionately, a line drawn from the center of the square to the center of the left-most base line, equals 1. The length of a line drawn from that same point to the apex equals 1.618. This proportion is Phi (the symbol is Φ).
The Golden Ratio and the Nubian Pyramids of Meroe
What represented 1 in the Giza slope (half the base) now represents the full length of the base, with Phi (Φ) again representing the slope of each face. One easy way to appreciate the Nubian shape is inside an image of a pentagram (see below). Phi (Φ) naturally occurs within this five-sided form. The shape below criss-crosses a Nubian's center point.
How the Golden Ratio Pyramids Impact Us
Pyramids modeled after both the Great Pyramid of Giza and The Nubian Pyramids of Meroe have been recognized as having a positive impact on organic life. They have been used to extend the life of fruit, sharpen raxor blades, and so on. Those in the alternative healing community have explored its impact on the human body and psyche. Active throughout organic life, this proportional value 1:1.618 (Φ) is likely what causes these pyramid shapes to be so compelling. The Golden Ratio spiral is both organic and perpetual. This can offer some insight into why our experiences inside these pyramids modeled after the Giza and Nubian slopes tend to feel so encouraging and uplifting. We experience enhanced meditation (contact with source, nature) and healing (rebalancing, bodily integration). The effect is much like that of a tuning fork.
Continue reading >> Pyramids As Tuning Forks for our Bodies