Introduction
Giza plateau, Cairo is possibly best known for the location of the last remaining Seven Wonders of the Ancient World, The Great Pyramid. It is so big, it could be described as an artificial mountain, and nothing will prepare you for its grandness. No photos or videos will come close to the real experience. It is a wonder of precise engineering, but it does not stand separate from the rest of the edifices in the complex, equally captivating and showcasing unexpected ancient knowledge.
Solstice is an astronomical event whereby the Earth’s poles are most inclined towards or away from the Sun. These also mark the shortest day in winter, between the 21st and 22nd Dec and the longest day in summer, between the 21st and 22nd of June in the northern hemisphere. In the southern hemisphere, these events are the opposite.
Just as solstices, the equinox comes twice, when the Earth’s axis is in such a position where the Sun’s rays fall vertically onto the Earth’s surface; it comes around March 21st to 22nd and from September 22nd to 23rd. A true equinox indicates an equal length of day and night (12 hours), giving symbolic importance to this day. The sun rises exactly due east and sets exactly due west.
Culturally, equinoxes like solstices are historic markers of seasonal change. The spring equinox in March in the Northern Hemisphere is regarded as the start of the spring season and a time of rebirth and renewal. In ancient Egypt, the summer solstice signalled the beginning of the New Year. Soon after, the appearance of the star Sothis (Sirius) above the horizon, around mid-July, coincided with cyclical flooding of the Nile, which brought annual flooding and fresh silt for crops and therefore life for the region. Ancient Egyptians only recognised three seasons: Akhet (inundation; which also means horizon), Peret (growth) and Shemu (harvest).
The start of the seasons, the New Year or Wep Renpet on summer solstice held significance in the cyclical understanding of time, life, and death in ancient Egypt. Ancient Egyptians lived by the laws of Maat, Cosmic Order which would lead to the afterlife where they would become an effective spirit or Akh. Cosmic Order was their sacred science and religion that had to be honoured and maintained. It was evident in the repetition of seasons, in timely floods of the Nile, in the daily travel of the Sun disc over the horizon and in other natural phenomena. They were obsessed with observing and maintaining it as they were convinced that Cosmic Order maintained their world.
The importance of following and maintaining constant cosmic cycles in ancient times is reflected in the positioning of the Giza Plateau edifices positioned, oriented and built such that they show either equinoxes or solstices. This proves that these ancient structures still standing are embedded with the sophisticated knowledge of the ancients and their understanding of the calendar and timekeeping, astronomy, geodesy, geometry, mathematics, engineering, architecture and masonry.
Spring Equinox at the Giza Plateau
The Great Sphinx, the largest sculpture on the African Continent, is positioned in such a way as to show the time of the setting sun on the spring equinox. ‘Sphinx is aligned towards the spring equinox’ the Egyptian Ministry of Antiquities has recently declared. As the sun sets on this day, it touches the right shoulder of the Sphinx, showing the intended alignment (Figure 1). The alignment by the ancient builders is intentional and requires astronomical calculations and therefore scientific superiority of the Ancient Egyptians, according to the Ministry. There was no information on the viewpoint spot that is required to see this intended alignment and we are left to do our best educated guess.
It has been noted by different authors that Sphinx’s body is not done in proportion with its head. This is easily seen in the aerial photographs: the head is too small for its large body. The body itself looks more like a dog than a lion since the sitting position is reminiscent of how dogs sit. It also misses the tuft, found in a lion’s tail, so it seems it has a dog tail. While the body of the Sphinx was shaped out of the surrounding bedrock, the head was carved out of the stone outcrop. The head of the Sphinx shows deep antiquity and was obviously re-shaped. The original shape of the head was probably of the God Anubis, a jackal or wild dog, the guardian of the dead. After all, the statue was erected near the cemetery, and who else is better to position there to guard the dead, but God Anubis? It could also be that the statue came first and the cemetery later. So, the statue of God Anubis is positioned to look due east on the day of the equinox, the day of renewal and rebirth. Here, we see the interwoven elements of ancient Egyptian religion and belief in the afterlife, with the visible timely manifestation of celestial cycles as part of the Cosmic Order overseen by many ancient Egyptian Gods and Goddesses.
Figure 1: The Sun setting on the right shoulder of the Great Sphinx on the 21st of March, the spring equinox in the northern hemisphere. The viewpoint is in front of the Sphinx Temple (photo by Whelan, 2020).
All pyramids of the Fourth Dynasty age are so accurately surveyed that this could have been achieved only with theodolites. i.e. optical surveying instruments. According to Dr Robert Temple, short of magic, the building of the pyramids is a physical impossibility without such instruments.
The Great Pyramid of Giza is almost perfectly aligned with the true north, meaning that it aligns with the planet’s axis poles, not the magnetic north that constantly varies. It is offset -3’ off true north, according to a recent survey, an accuracy impossible to achieve using the human eye only, at such a huge scale. Due to its precise alignment with cardinal points, its peculiar angle and the white casing it had in the past it shows the timing of the sun’s meridian passing on the spring equinox day. That is to say, at noon at the spring equinox, its northern side slope which is in the shadow between the autumn equinox and the spring equinox, becomes gradually lit, marking the equinox day (Figure 2). Only the stone edges of all the courses become lit as the structure has lost its casing stone surface. But, in ancient times when still intact, highly polished white Tura limestone would act as a mirror that would suddenly cast the triangle of light, not a shadow, onto the northern pavement, marking noon on the equinox day. Today, the structure casts a shadow every day onto the northern pavement apart from the day of the equinox when it disappears. The length of the shadow each day differs, shortening as it is approaching the equinox and lengthening as it is moving away from it. Between the spring equinox and the autumn equinox, the sun illuminates the north face but not the south face. Between autumn equinox and spring equinox, the sun illuminates its south face. So, we see here, that one of the purposes of the Great Pyramid was to inform about the seasonal cycles and time.
Figure 2: The northern slope of the Great Pyramid showing its courses just slightly lit by sun rays at 12.00 on the spring equinox day, the entrance is to the left (photo by author, 21.03.2023).
Solstices: Summer
During the summer solstice that marks the beginning of the ancient Egyptian New Year, the sun sets almost exactly midway between the Great Pyramid (Khufu) and the Middle Pyramid (Khafra), forming an image of a huge hieroglyph of akhet (horizon).
Figure 3: The sun setting midway between the two pyramids, as large as mountains, forming an enormous hieroglyph for the horizon (akhet) (photo by Magli, 2014).
The hieroglyphic sign shows the sun (𓇳)setting between two mountains (𓈋). Interestingly, the akhet sign first appeared during the 5th dynasty and we actually do not know the sign for Khufu’s complex used during Khufu’s time. The name of the Great Pyramid itself comes from the 6th dynasty tomb of the funerary priest Qar, and it is called Akhet Khufu or Horizon of Khufu where the hieroglyphic sign shows ibis and a bread loaf, not the sign. Therefore, the Giza landscape triggered the creation of the new akhet sign; the landscape came first and the sign came later.
At the Giza Plateau, the two sides of the mountains are represented by two sides of the pyramids (Figure 3). The effect is best seen standing in front of the Sphinx Temple. During the New Kingdom, Sphinx was also known as Hor-em-Akhet, or Horus of the Horizon, and it is easy to see why. On summer solstice, the huge monument becomes Hor-em-Akhet with the image at the rear of the Sphinx forming the sign for akhet. This dramatic observable event is a hierophany, a manifestation of divinity dependent on a celestial cycle and architecture on the ground that frames it. Here too, the landscape came first and then the new name for the Sphinx. Akhet also means a region where the blessed dead are transformed for the afterworld, where they become Akh or an effective spirit. All living aspired to live by the laws of Cosmic Order and become Akh in their afterlife. The huge akhet sign therefore underpins the ancient Egyptian religious belief that this is the place where the dead pass on to become the Akh.
Solstices: Winter
Giza Plateau topography is riddled with the Golden Triangles and rectangles connecting the monuments seen from above but also found in the dimensions and internal features of the Great Pyramid. There are multiple interlocking Golden Angles and rectangles that connect Giza monuments geodetically. The Great Pyramid itself is resplendent with the internal occurrences of the Golden Angle.
The Golden Triangle is a right-angle triangle with an acute angle of 26° 33’, a height of 1, a base of 2 and a hypotenuse of √5. The 26° 33’ angle is thus called the Golden Angle. The hypotenuse (x) is worked out using Pythagoras’s theorem 1²+2²=x²; x=√(1²+2²) =√5.
This 1:2:√5 triangle is observed to be the quintessential form of the number φ (phi), also known in the Renaissance as ‘the divine proportion’ or Golden Ratio, 1.618 (Figure 4). It is an irrational number and cannot be obtained arithmetically but only geometrically. It is found ubiquitous in nature, from sunflower florets and mollusc shells to the shape of the galaxies and distances between internal planets of the Solar System.
Figure 4: Golden Right Triangle with an acute angle of 26.56 (26°33’) (Drawing by Rajput, 2021).
Golden Ratio φ is found embedded in the dimensions of the Great Pyramid. It is found in the triangle formed by its height, the half base and the slant height. Using that triangle, which is the basic cross-section of the structure (Figure 5), if 356 cubits of the pyramid’s slant height are divided by half the base length (220 cubits), the result is 1.618 or φ.
Figure 5: Internal cross-section triangle in cubits of the Great Pyramid and 1:√φ: φ triangle when all sides are divided by 220 (Posamentier, 2013).
Also, if the height (280 cubits) is divided by the half base (220 cubits), we get 1.27272, which is very close to the real value of √φ. Therefore, by dividing the dimensions of this triangle by 220, we would get a 1:√φ:φ triangle, also known as a Kepler triangle!
Cubit is an ancient Egyptian measure used in the construction of pyramids and is equal to π/6 or 0.5236 m. Also, π (Pi) and φ are related through the equation π/ φ²=6/5, so if you have one of these values, you also have the other one. Besides, if you divide the perimeter (p) of the Great Pyramid base (880cubits), by twice its height (h) (2X280cubits), we get 3.1428, very close to the value of π, computed as 3.1416. So, the height of the pyramid is in relation to the parameter of its base as the radius of a circle is to its circumference (c=2rπ; c/2r =π; p/2h= π). Therefore, the pyramid builders have found a way to incorporate a circle into this pyramidal shape.
The Golden Ratio is also found in the Giza Plateau layout of the main three pyramids. If two golden rectangles, which contain the Golden Ratio in them, are superimposed over the Giza layout, (one in landscape orientation, one in portrait orientation) we see their corners align with the apex of each of the pyramids (Figure 6).
Figure 6: Giza layout reveals the positions and relative sizes of the pyramids may be based on the golden ratio. Golden Rectangles are connecting all three main pyramids via their apexes (Drawing by Meisner, 2018).
When all four key monuments of the Giza are connected, using geometrical relations they reveal the maze of Golden Angles interconnecting them, with Sphinx included. Dr Temple calls this alignment the Golden Giza Plan (Figure 7). Golden Angles are marked as G.
Structurally, we find the Golden Angle inside the Great Pyramid: the angle of the internal Ascending and Descending passages of the Great Pyramid; it is the same angle found in the triangle 1:2:√5 formed by the Grand Gallery and Ascending Passage (the hypotenuse of value √5) with the horizontal line leading from the spot where Descending and Ascending Passages meet to the vertical line dropped from the pyramid apex (base of value 2) and part of the same vertical line dropped down from the pyramid apex that starts at the Great Gallery end (height of value 1); it is the same angle of the ancient passage that leads from the Valley Temple onto the Causeway of Khafra where tourists walk daily.
Figure 7: Golden Giza Plan, showing multiple Golden Angles (G), (Temple, 2009).
Visually, the Golden Angle is best observed on the winter solstice day, 21st December in the afternoon hours, when the shadow cast by the Middle Pyramid onto the south side of the Great Pyramid reaches its height and cuts through the pyramid slant height (Figure 8). The triangle formed by the shadow has a half base length, about 1/3 of the pyramid slant height and a hypotenuse that runs from the SW corner to the 1/3rd of the slant height of its side, forming the Golden Angle of 26° in its SW corner. This huge display of the Golden Triangle with its natural φ constant along the edge of the pyramid exactly on the winter solstice day also constitutes the hierophany, a display of divinity dependent on the cosmic cycle.
The ancient builders were aware of ‘the divine proportion’ found in nature and they understood it as a sacred science and divine order of the reality. They were obsessed with it and embodied it superstitiously into the pyramids and their positions now manifesting in the silent language of the Sacred Architecture. The purpose was to honour the Cosmic Order by imitating the underlying sacred design of the cosmos so that what was below would be the same as what was above. This old hermetic axiom is known as ‘As above, so below; as below, so above’ and came to us from the depths of time when the great teacher and master of occult knowledge, Hermes Trismegistus lived and taught in Egypt many centuries ago. Do we have to thank him for the secret knowledge of mathematical constants Phi and Pi now embedded into the silent language of the Giza monuments?
Figure 8: The Middle Pyramid (G2) casts a shadow onto the southern side of the Great Pyramid (G1) at the Golden Angle of 26° on the winter solstice (photo by author 21st Dec 2023).
Unifying Giza Sacred Landscape Sun Alignments
The only way to anchor astronomical cycles into the landscape was to build the whole complex at the same time according to the unifying plan. The plan is obvious if we include the still unearthed Valley Temple of Khufu, which lies beneath the houses of the village of Nazlet el Samman, east of the presently unearthed complex. The archaeological excavations have already started here in 2022, as the ground penetrating radar (GPR) anomalies have pointed to the existence of tunnels and chambers containing metals and other artefacts.
Figure 9: The Giza sun alignment unifying plan (original drawing by Magli, 2014, augmented by author).
Here, near the still unearthed valley temple of Khufu, presumably at one of its corners (Figure 9) the ideal prolongation of the northern side of the Great pyramid (G1) and its causeway (BO) intersect each other and marked O; the point O’ is the Khafra valley temple spot where Middle or Khafra’s Pyramid (G2) ideal prolongation of its southern side and its causeway (B’O’) intersect each other. A line drawn from O directed due west passes along the north side of the pyramid G1, and the sun at both equinoxes is seen setting in alignment with the northern corner; the same can be seen from the O’ point, where a line from O’ directed due west passes along the south side of the pyramid G2.
The alignment defined by the causeway of G2 and its southern side is 14°north of west (or it's azimuth is 284°) and coincides with the midpoint of the path of the setting sun at the horizon between the equinoxes and summer solstice (summer solstice line O’C’ points 28° north of west, or it’s azimuth is 298°). The summer solstice azimuth line points to the setting sun in the middle of the horizon which produces the huge akhet sign (Figure 3).
The alignment defined by the G1 causeway (BO) is oriented 14° south of west (azimuth 256°) which coincides with the midpoint of the path of the setting sun at the horizon between equinoxes and winter solstice (28° south of west, or azimuth 242°). Here, the sun is seen setting beyond the second pyramid at winter solstice, just passed its SE corner. Together, G1 and G2 complexes, with their causeways and valley temples form the opposite symmetric solar alignments. The two causeways have azimuths that show a 28° difference, which is also an angle between the equinox and winter solstice (G1 complex) and equinox and summer solstice (G2). Double that angle and we get the angle between the winter solstice setting sun and the summer solstice setting sun (∡56°), as seen in Figure 9.
Both G1 and G2 complexes embody a hierophany (a manifestation of the sacred) at different solstices:
On the summer solstice, standing at O’ we observe the setting sun between the pyramids making a huge akhet sign.
On the winter solstice, standing at O, we observe the setting sun just beyond the G2 pyramid’s SE corner. At the same time, the Middle pyramid (G2) casts a shadow that forms a 26° Golden Angle visible on the Great Pyramid (G1) south side, with its 26° angle in G1 SW corner, cutting the pyramid face slant height and forming a Golden Triangle. To see this shadow, we need to stand south of G1, looking into its south face (Figure 8).
Conclusions
At the Giza Plateau, we find topographical order, orientation, mathematical constants, and connection with the celestial cycles on a huge scale. The ancient builders incorporated mathematical values of φ and π architecturally, into the Giza Plateau plan and The Great Pyramid itself. The Giza Plateau and its main monuments are all geodetically interrelated via the many golden angles, rectangles, and particular azimuths.
At the ground level, we see solar alignments that produce such effects as telling the time exactly on equinoxes and solstices; we see hierophany of ancient Egyptian signs, occurring on conspicuous days of a celestial cycle. The Great Pyramid, in particular, has been located, oriented and sloped in order to mark equinoxes and solstices. It marks the noon of the spring equinox when the shadow on its northern slope disappears as the sun illuminates it. It marks the winter solstice as the triangular shadow cast by the middle Pyramid appears on its southern side with its Golden Angle characteristic of the Golden Triangle that holds mathematical relations producing the Golden Ratio Phi. All this could only be done if the Giza was a planned, unified project, and as such it demonstrates the advanced scientific knowledge of the builders.. whoever they were.
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