12- Angles in the pyramids – The 7 great Pyramids Unveiled (2024)

Everybody would have understood by now that a pyramid is a matter of angles.

However, the angles of the pyramid have ordinary values compared to what we are used to. For example, the angle of the inner slopes of the pyramid of Cheops is very close to 26°56’, and the faces’ angle is close to 51°84’ with the horizontal, and the angle of the edges is close to 52° with the horizontal in the median plane.

This is due to the way ancient Egyptians measured angles indirectly using the cotangent of the angles, the 12- Angles in the pyramids – The 7 great Pyramids Unveiled (1), or seked; they did not use degree. This information comes from the Middle Kingdom of Egypt, but the sine, the cosine or else the tangent could have been used from time to time.

More precisely, they used to express length in Palm and height in Cubits, so an SDK was 7 * cotangent of the same angle.

So the chosen angles had at least a value, whether it was the sine, the cosine or the tangent, as simply as possible using the measure scale based on the royal cubit for which the smallest subdivision is the finger, i.e. 1/28.

As for numerical writing, the Ancient Egyptians used fractional notation and not decimal notation.

We can then expect that one, or several, of these trigonometric values of an Egyptian angle will be expressed as a whole multiple of the fraction 1/28.

Many archaeologists have endeavored to record the pyramids’ angles in degrees, minutes and seconds. They better should have recorded the cotangent, the sine or cosine of these angles, which is a ration expressed by the Egyptian fraction for length based on the royal cubit; for example, a 45° angle would equal a seked of 7.

If they had proceeded that way, as they did for the lengths expressed by royal cubits, measurements would have been more meaningful.

The royal cubit (MH NSWT) 12- Angles in the pyramids – The 7 great Pyramids Unveiled (2)

12- Angles in the pyramids – The 7 great Pyramids Unveiled (3)

  • The royal cubit is divided into 28 segments of 1 digit.
  • The palm is 4/28 or 1/7; the double palm is the double.
  • The small span is 12/28 or 3/7, which equals 3 palms.
  • The djeser is 16/28 or 4/7, which equals 4 palms.
  • The remen is 20/28 or 5/7, which equals 5 palms.
  • The short cubit is 27/28 or 6/7, which equals 6 palms.

As a result, when an angle is found in a pyramid, its SKD should be checked to ensure that it can be expressed in fractions of the units of measurement.

Let’s take, for example, the angle of the face with the horizontal measured by Petrie which used different measurement methods that all gave a different result:

12- Angles in the pyramids – The 7 great Pyramids Unveiled (4)

In conclusion, he suggested retaining the value 51°52’ with an error of more or less 2’, i.e., an interval between 50’ and 54’.

He deduced the height from this value, after measuring the base.

Petrie measurements for the base give 9068.8 inches, or 230.34 meters, which, with the addition of a royal cubit of 0.5235 m (1,717 ft.), would give 440 cubits exactly, so the height is 220 * tangent 51°52’, i.e., 280 or 24 cubits.

It seems the constructors made sure the base measurement was a whole number, so we could venture that they did the same for the height, i.e., 280 cubits. Consequently, the tangent or seked would be 22 * 7/28, or 11/2, which probably could be expressed by the value 5 + a half-cubit or big span.

To conclude, in our notation, the angle is 51°50’35’’ as the nearest approximation, which falls within the interval given by Petrie.

However, this value is theoretical because the faces’ median is “hollowed” by 2 cubits from the base, giving the real SKD value at the median level to be 7 * (220-2)/280, or 109/20, or 5 + 9/20, or else 5+1/4+1/5 to use the old Egyptian notation system, or 52°5’48’’ in our current notation system.

We can guess that any angle of the pyramid is at least a trigonometric function (7 x cotangent) expressed by a whole multiple of the fraction 1/28, in other words, a whole number of “digits”.

The angle of the slopes is 26°56’ with the horizontal, i.e., a SKD of 14.

Throughout the construction time, there were two days per year when the shadows on the North, East and West faces, as well as the shadows on the north edges, were invisible, as if they “swallowed their shadows”. First, it permitted to position the pyramids in South North and East West with great accuracy using a model, and also to check the correct pyramid alignment thanks to the faces and edges’ shadows, so the edges would meet at the summit, invisible until the last day.

The sun was thus used as a giant instrument of measure to the pyramid’s scale!

Furthermore, the 51.8° angle gives a ratio of 22/7 between the base perimeter and the height, a value near π to 1 per thousand, and gives a ratio between the apothem of one face and the half-base close to the golden ratio with higher accuracy, which is no coincidence!

12- Angles in the pyramids – The 7 great Pyramids Unveiled (2024)

FAQs

What are the angles of the Great pyramids? ›

PYRAMIDANGLE OF FACEANGLE OF EDGE
RED PYRAMID43o22'00"33o44'20"
KHUFU51o50'40"41o59'15"
KHAFRE53o10'00"43o21'07"
MENKAURE51o49'38" 51o10'46"41o38'08"
1 more row

What is the hidden math in the pyramids? ›

More specifically, it is commonly asserted that the perimeter of the base of the Great Pyramid divided by twice its height gives a remarkably accurate estimate of pi. Indeed if one performs this computation a good estimate of the value of pi (3.150685) does emerge.

What do the pyramids have to do with the number 7? ›

When we talk about seven, we are talking about perfecting human nature, seeing as it joins the Holy Trinity (3) with the Earthly Elements (4), thereby reconciling the physical and spiritual realms, human and divine. It is also the number of the pyramid, which is formed by a triangle (3) on a square base (4).

What are the angles of a pyramid? ›

ANGLES: A square pyramid has 16 angles, four right angles on the square and 3 acute angle on each triangle. NETS: To make a square pyramid you need a square and have a triangle come from each edge.

Are the pyramids 60 degrees? ›

The Great Pyramid at Giza in Egypt holds a constant temperature of 68 degrees Fahrenheit.

What are the angles of a 6 sided pyramid? ›

At the base of the pyramid is a regular hexagon (all sides are equal, the angles between the sides are 120 degrees). The height of the pyramid is exactly at the center of the hexagonal base.

Why is 43200 important? ›

The number 43,200 has been suggested in various sources as the factor by which one may multiply the size of the Pyramid to arrive at the size of the Earth to within a reasonable approximation, however, it shall be seen that the use of this number was purposefully chosen to convey highly accurate knowledge of the Earth.

Do the pyramids equal pi? ›

Pi and the Great Pyramid. It was John Taylor who first proposed the idea that the number &pi might have been intentionally incorporated into the design of the Great Pyramid of Khufu at Giza. He discovered that if one divides the perimeter of the Pyramid by its height, one obtains a close approximation to 2&pi.

What is the Golden Ratio of the Great Pyramids? ›

pyramid By taking the slant height and half base length of the great pyramid of Giza, its significance to the golden ratio can be calculated (Fig. 4). Dividing slant height s by half base gives, 186.369 ÷ 115.182 = 1.61804.

What does 43,200 have to do with the pyramids? ›

The number 43,200 is vastly important within the Great pyramid as it is used to demonstrate knowledge of the circumference of the Earth, the distance between the Earth and the Sun, the distance between the Earth and the Moon, and allowed for the measurement of the great precession.

Why is number 7 special? ›

There are Seven Colors in the Rainbow, Seven Days in a Week, Seven Wonders of the World, Seven Major Seas, and even the total number of Continents Are Seven! No other number is having so many connotations and references in many different fields like the number Seven. So, it's a very important number indeed.

What is the most mysterious pyramid in the world? ›

The Great Pyramid of Giza is actually the last standing 'wonder' of the Seven Wonders of the Ancient World.

What math was used to build the pyramids? ›

The angle of the pyramid's slope was another mathematical marvel. Ancient Egyptians employed trigonometric principles to determine the ideal angle, balancing structural stability with aesthetic appeal. The primary pyramid angle was around 51 degrees, meticulously calculated and vital for the pyramid's stability.

Are pyramids 3 or 4 sided? ›

All but one of the known ancient Egyptian pyramids have four sides. The base of a pyramid is a square, so there are four triangles that make up the faces of the pyramid. The only ancient Egyptian pyramid that doesn't follow this rule is the Great Pyramid of Giza.

Are the pyramids 90 degrees? ›

Its compliment is 90º-38.16º=51.84º. This is precisely the angle the sides of the pyramid make with respect to the horizontal as indicated by the pre-carved angles present in the pyramid outer casing stones located along the bottom of the Cheops pyramid.

What is the angle of the Mayan pyramid? ›

The sides of the pyramid are approximately 55.3 meters (181 ft) at the base and rise at an angle of 53°, although that varies slightly for each side. The four faces of the pyramid have protruding stairways that rise at an angle of 45°. The talud walls of each terrace slant at an angle of between 72° and 74°.

What angle were Nubian pyramids built? ›

The physical proportions of Nubian pyramids differ markedly from the Egyptian pyramids: they are built of stepped courses of horizontally positioned stone blocks and range approximately 6–30 metres (20–98 ft) in height, but rise from fairly small foundation footprints, resulting in tall, narrow structures inclined at ...

What did the angled sides of a pyramid symbolize? ›

Did you know? The pyramid's smooth, angled sides symbolized the rays of the sun and were designed to help the king's soul ascend to heaven and join the gods, particularly the sun god Ra. Ancient Egyptians believed that when the king died, part of his spirit (known as “ka”) remained with his body.

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