**The magical and mathematical connection between desert sand and the Great Pyramid of Giza**

**by Willem Witteveen**

**by Willem Witteveen**

**Sand dune**

**Sand dune**

**Sand dune**

**Sand dune**

**The angle of repose**

### The angle of repose or critical angle of repose of a granular material is the steepest angle of descent relative to the horizontal plane to which a certain material can be piled without slumping. At this particular angle, the material is on the verge of sliding and forms a stable angle with a horizontal plane. Rough angular sand has a larger angle of repose than smooth rounded sand grains. When bulk granular materials are poured onto a horizontal surface, a conical pile will form and this cone will form a stable angle with the horizontal surface which is known as the angle of repose. This angle of repose does not change when more granular materials are poured onto this cone. A slope remains stable when the slope angle is less than the angle of repose.

**Pdf-file 1. “The angle of repose of granular materials” – CC BY License**

**Pdf-file 1. “The angle of repose of granular materials” – CC BY License**

**Pdf-file 2. “Avalanche slope angles in low-gravity environments from active Martian sand dunes” – © Geophysical Research Letters**

**Pdf-file 2. “Avalanche slope angles in low-gravity environments from active Martian sand dunes” – © Geophysical Research Letters**

### There are different methods of measurement of the angle of repose as explained in the attached Pdf-file 1: “A review on the angle of repose of granular materials” by the 2018 research of Hamzah M. Beakawi Al-Hashemi and Omar S. Baghabra Al-Amoudithe of the King Fahd University of Petroleum and Minerals in Saudi Arabia. The angle of repose of granular materials is used in different fields, such as agriculture (design of silos), pharmacology (flowability in drug production), geology (sand dunes and formations), bulk cargoes on ships regarding stability, mining and civil engineering and the study of avalanches. This research is mainly about the reliable measurement of the angle of repose of different kind of materials under varying conditions. My research focuses mainly on the angle of repose of desert sand and the forming of sand dunes of the North African deserts to find a connection with the ancient building methods of pyramids. Is there a connection between the Great Pyramid of Giza and the angle of repose of local desert sand? For ordinary sand, the angle of repose ranges from 30^{0 }to 35^{0}.

**Sand dune on the Moon**

**Sand dune on the Moon**

“The angle of repose is the maximum angle at which a material can be stable and does not slide or fall. This angle is independent of gravitational acceleration (g), so whether it is on Earth, Mars, or the Moon this angle is about 35º“

**Sand dune on Mars**

**Sand dune on Mars**

**The universal angle of repose concerning gravity**

### The angle of repose can theoretically range from 0^{0 }to 90^{0} and is strongly dependent of density, surface area, size and shape of the particles and the static and rolling (dynamic) coefficient of friction of the material which is directly related to the mass of the individual particles. Mass is gravity-dependent and that means that the angle of repose is also gravity-dependent as a result of a scientific 2011 study into this matter. However, a 2013 geophysical research paper (Pdf-file 2) of Corwin Atwood-Stone and Alfred S. McEwen called: “Avalanche slope angles in low-gravity environments from Martian sand dunes.” These research results show that the dynamic angle of repose for the sands in several areas on Mars (and the Moon) fall within the 30^{0} to 35^{0}-window for the dynamic angles of repose for terrestrial dunes with similar flow depths and grain properties and thus show that this angle does not significantly vary with decreasing gravity. This scientific paper concludes that the angle of repose is independent of gravitational acceleration (g), so whether it is on Earth, Mars, or the Moon this angle is about 35^{0}. Gravity, mass, and mutual friction are of minor importance to the angle of repose of sands. This is inconsistent with our terrestrial physics! In other words: what unknown universal force causes this angle to be roughly equal throughout the universe and were the ancients aware of this extraordinary property of sand?

**The sand box experiment**

**The sand box experiment**

**Desert sand**

### Desert sand is a granular material composed of finely divided rock and mineral particles as a result of erosion and weathering (water and wind) over long periods. The rocks continuously break into smaller pieces until they become fine grains of sand with a diameter of between 0.074- and 4.75 mm. African desert sand is very fine sand with a reddish yellow colour. The most common rock to form sand is granite. Sand dunes are a consequence of an accumulation of sand grains shaped into a mound or ridge by the wind under the influence of gravity. A sand dune has an angle of repose of about 34^{0} and the same angle was measured by scientific researchers on sand dunes on the Moon and Mars (Pdf-file 2) at much less gravity than on Earth. My sand box experiment shows that the angle of repose of fine North African yellow desert sand is exactly 32^{0} and equals the angle of sand dunes in adjacent areas. But what is the importance of this angle of 32^{0} concerning the Great Pyramid?

“A large part of the Earth consists of sand and just like water, sand also has very special properties. Deserts on Earth are magical places that reveal a vast natural world of beauty, secrets, and healing powers“

**Sand dune**

**Sand dune**

**The homemade sand box**

**The homemade sand box**

**The Great Pyramid of Giza**

### Each Egyptian pyramid has a unique slope angle between 50^{0} and 56^{0} of which the bent pyramid at Dashur is an exception with the top section built at the shallower angle of 42^{0}. The shape of the Great Pyramid is an isosceles triangle of which each side rises at an angle of 51^{0}51′ (51.85^{0}) to the top. The cosine of this slope angle of 51.58^{0} is 0.618 which equals the Golden Ratio. The Golden Ratio is an irrational number with an infinite number of digits and is approximately 1.618, indicated by the Greek letter Phi (F) and with the unique property that it is 1 more than its reciprocal; 1/F = 0.618. The Golden Ratio is related to both 1.618 and 0.618. The mathematical constants F (Phi) and p (Pi) are both encoded in the design of the Great Pyramid. This can be read in various publications, including my English book on the Great Pyramid of Giza from 2016. The Golden Ratio is underlying the universal design principles of all organisms and is a very important number concerning the Great Pyramid. The Golden Ratio as a number and the Great Pyramid as a monument are both an expression of creation. The Golden Ratio is a unique divine relationship to describe our entire universe.

## Line segments ratio 1 : 2

## PT = 2PR = 2RT

## AR = 2RD and FR = 2RC

## FD = 2TD and AC = 2TC

## PQ = 2BQ and PS = 2SE

## 51.8º / 32º = 1.618 = Golden Ratio

## Six equal layers: 51.85º/6 = 8.64º

**The Connection**

### The slope angle of the Great Pyramid and the angle of repose of African desert sand are mathematically connected through the Golden Ratio. The angle of repose of 32^{0 }is 51.85^{0}/1.618 or 32^{0} x 1.618 equals the slope angle of the Great Pyramid. The height of the “sand pyramid” is exactly half the height of the Great Pyramid and this ensures a 1:2 ratio of all drawn line segments emanating from the 32^{0 }angle as shown in the combined drawing of the sand pyramid and the Great Pyramid. The 32^{0} angle divides the total height of the Great Pyramid into 6 equal layers of exactly 24.3 metres. The slope angle 51.85^{0} divided by 6 is 8.64^{0 }where the universal number 864 is related to the Sun by its diameter (864,000 miles) and by time (86,400 seconds in 24 hours) and thus related to creation. Of interest is the 1:2 ratio and therefore the numbers 864, 432, and 216 are closely related in decoding the universal principles of the Earth, the Sun, and the Moon concerning our existence. The explanation of the importance of these numbers are not the topic of this article, but is explained in more detail in the book on the Great Pyramid of Giza.

**“Monument of Creation”**

**“Monument of Creation”**

### The slope angle of the Great Pyramid is mathematically related to the angle of repose of North African desert sand. For me, this is yet another example that our earthly physics is unable to explain the design principles of these intricate ancient monuments of creation and so is the true function of the Great Pyramid and pyramids in general. The blueprint for the design of the Great Pyramid is determined by the coherence of universal laws and numbers and the divine confluence of the five elements.** **

“Every grain of sand reveals the ancient history of the Earth and its place in the universe“

### © Willem Witteveen – June 2020

**Ancient Egyptian Connections**