Pyramid Quest (44 page)

On the basis of his novel assumptions and analysis, Stecchini (1971, p. 367) concludes that the western face of the Great Pyramid was designed using the factor pi (π, approximately 3.14) while the northern face was designed using the factor phi (Φ, or the irrational Golden Number, approximately 1.618; see earlier). Furthermore, Stecchini (1971, p. 367) “concluded that the height of the [Great] Pyramid was either 279.53 cubits = 146,515.174 millimeters or a figure very close to 279.53 cubits.”

Let
Z
be the horizontal length from the middle of the western side at the base to a point directly under the apex of the Great Pyramid, which equals 115.090 meters, according to the Cole Survey (1925), as interpreted by Stecchini. To say that the western face was designed with pi in mind means that 2 times value
Z
times 4 divided by 2 times pi equals the height of the Great Pyramid, or (2 × 115.090 meters × 4) / (2 × 3.14) = 146.6 meters. If a more accurate value of pi is used in this equation, such as 3.14159, then the calculated height is 146.537 meters. Using the approximation of 3.1420 for pi, the calculated height is 146.518 meters.

Note that these concepts of the Kepler triangle theory and the equal area theory discussed earlier, the former of which Stecchini uses to relate the length of the northern face to the height using phi, are very different from the “side : height = Golden Number” concept discussed by Herz-Fischler (2000, pp. 92-95). According to the Cole Survey (1925), the northern side has a length of 230.251 meters, and 230.251 meters divided by a height of 146.515 meters, as used by Stecchini, equals 1.5715182, a far cry from the value of phi. The side : height = phi theory yields a theoretical slope of 51.027° for the sides of the Great Pyramid. Let
s
be the length of a side. To calculate the theoretical angle for this relationship, we can use the tangent of the height over one-half the side length: Φ = s / h, so h = s / Φ, s = hΦ, and s / 2 = hΦ / 2, so h / (s / 2) = h / (hΦ / 2) = 2 / Φ; 2 / Φ = 1.2360679, and the cotangent of 1.2360679 is 51.02655°, a value that is not particularly close to the actual value calculated for the Great Pyramid.

After much astute analysis, Stecchini (1971, p. 378) summarizes his conclusions as follows:

According to Stecchini’s (1971, p. 365, 373) interpretations of ancient Egyptian geodesy, his analysis of the Great Pyramid directly, and his research on ancient authors, drawing from the comments of Agatharchides on the Great Pyramid, the perimeter of the base of the Great Pyramid was specifically designed to be one-half minute of latitude at the equator, which the Egyptians calculated as 3,516 cubits. Thus the perimeter of the Great Pyramid is 1,758 cubits (average of 439.5 cubits per side times four sides). The ancient Egyptians were interested in latitude, not longitude, in this case because they were concerned with the length and shape of the north-south meridian, from the equator to the North Pole, or more generally the nature of a great circle through the poles that describes the shape of Earth and also determines the polar diameter of Earth. If the perimeter of the Great Pyramid describes, or contains a unit of measure of, a great circle through the poles of Earth, and the pi relationship holds for the Great Pyramid, then the height of the Great Pyramid is indeed a measure of the polar radius, and therefore also the diameter (2 times radius = diameter), of Earth. The Egyptian value of 3,516 cubits = 1,842.905 meters for a minute of degree of latitude at the equator is incredibly close to the modern 1,842.925 meters cited by Stecchini (1971, p. 365).

A great circle through the poles is not a perfect circle, however. There is a minor flattening at the poles. According to Stecchini’s analysis of the Great Pyramid, which he calculates rose to a final height at the apex of 279.53 cubits or thereabouts (Stecchini, 1971, p. 367), the ancient Egyptians were not only aware of the polar flattening and its magnitude to a very fine degree but they incorporated this information into the design of the Great Pyramid. He believes that the original design for the Great Pyramid called for a height of 280 cubits to the apex, but this was reduced to about 279.5 cubits as an indication of the polar flattening and its order of magnitude (which is very slight and was not demonstrated in modern times until the eighteenth century, although Newton had predicted the polar flattening in the late seventeenth century).

Hawass (
Update to Petrie,
1990, p. 98) says that the original name for the Great Pyramid was “Horizon of Khufu,” and this may indicate, according to Hawass (1990, p. 99), that Khufu was associated with Ra, the sun god, who of course rose from and set into the horizon. According to Pochan (1978, p. xiii), the name of the Great Pyramid was “Akhet Khufu” (Khufu’s Luminous Horizon). Pochan (1978, p. xiii) argues that “the Great Pyramid was both the tomb of Cheops and the temple of the sun god Khnum.” Adams (1895, p. vii; 1933, p. 23) says that the Great Pyramid was “called by the Egyptians of old” “Khut” (Lights). D. H. Lewis (1980, p. 9) says that the ancient Egyptian name for the Great Pyramid was “Khuti,” meaning “the Lights.” Adams (1895, 1898, 1933; see also Hall, 1945, 2003, p. 117) also refers to the Great Pyramid as “the House of the Hidden Places.” Baines and Málek (1980, p. 140) give the ancient name of the Great Pyramid as “The Pyramid which is the Place of Sunrise and Sunset” (this corresponds to the same hieroglyphic inscription that Pochan translated as “luminous horizon”). According to Baines and Málek (1980, p. 140), the second (Khephren or Khafre) pyramid of Giza was known as the “Great Pyramid” by the ancient Egyptians, and the third (Menkaure) pyramid was known as the “Divine Pyramid.” According to Pochan (1978, p. xv) the second and third pyramids were known as “Khefra the Great” and “Menkaura the Divine,” respectively. Wake (1882, p. 38) says: “From the inscriptions, it would seem to have been called ‘the Great Temple of Shofo [Khufu or Cheops],’ and within its precinct to have been dedicated at one time to the worship of that king.”

The ancient writers Herodotus (fifth century B.C.) and Diodorus (first century B.C.) both clearly attribute the Great Pyramid to the pharaoh now commonly known as Khufu. Sandys (1621, p. 129) accepted the attribution to Khufu (Cheops). Greaves (1704, p. 704) assigned the Great Pyramid to “Cheops or Chemmis,” the second Giza pyramid to “Cephren or Chabryis,” and the third to “Mycerinus.” Greaves thought that these three kings should be assigned to the Twentieth Dynasty, and he calculated that the beginning of the reign of Cheops could be dated to 1,266 years “before the beginning of the Years of our Lord” [i.e., 1266 B.C.]. Since the time of Greaves, the vast majority of Egyptologists have attributed the Great Pyramid to Khufu.

It is often said (for instance, by DeSalvo, 2003, p. 3; also Fix, 1978, p. 82) that the only known representation of Khufu is a small (approximately 3 inches tall, according to Lepre, 1990, p. 61, but “barely two inches tall,” according to El Mahdy, 2003, p. 82; I have seen it behind glass, and my guess would be about 2½ inches) ivory seated figure found by Petrie in a temple at Abydos in 1909 (Lepre, 1990, p. 62; see Petrie, 1923,
Arts,
p. 134, fig. 123; Petrie, 1923,
History,
p. 57), and now housed in the Egyptian Museum in Cairo. However, this is not precisely true, as a stylized image of Khufu was found carved into a rock cliff face in Wady Maghara [Magháreh], in the Sinai (Lepre, 1990, p. 61; see also Petrie, 1906, p. 46, where he says that not long before he studied the area the “Khufu sculptures were smashed up” by recent miners, and p. 259, where Petrie notes: “we secured a piece [among the fragments of stone collected in the wake of the modern mining] that showed the face of the king [Khufu]”). It has also been suggested that the face of the Great Sphinx represents Khufu (see, for instance, Stadelmann, 2000), in part on the basis of the reputed similiarity between the Great Sphinx’s face and the ivory statuette. Returning to the ivory statuette from Abydos, El Mahdy (2003, p. 82) writes: “As for Cheops [Khufu] himself, only one image of him survives as King. This tiny ivory figurine . . . bears his name, although recently even this has been questioned.” She includes a photograph of the figurine, and her caption reads: “This tiny ivory figurine is the only surviving image of Cheops, although some authorities are now questioning its authenticity.” So what did Khufu look like? We really don’t know precisely. El Mahdy (2003, p. 31) says: “In images of Snofru and his son, Cheops, their faces are African.” The same appears to apply to known images of other relatives of Khufu, such as his brother Rahotep.

Ivory statuette portrait of Khufu. (
From Petrie, 1923,
Arts and Crafts of Ancient Egypt
, facing page 136.
)

Lepre (1990, p. 61) lists the following as names of the pharaoh commonly known as Cheops or Khufu: Metheru (“The Energetic”—so called “Hawk name” and “Vulture-and-Cobra name”), Khufu (“He Protects”—so called “Set or Hawk-of-Nubi name” and “Reed-and-Hornet name”), Chembres, Chemististes, Chemmis, Cheop, Cheops, Comastes, Khembes, Khemmes, Kheop, Kheops, Kheuf, Khnem-Kheuf, Khnum-Kheuf, Khnum-Khuf, Khuf, Khufu, Khufui, Khufwey, Kouf, Koufou, Nem-Shufu, Noh-Suphis, Saoph, Saophis, Sen-Suphis, Shofo, Shufu, Shure, Soris, Suph, Suphis, Surid, Xufu. Pochan adds Saurid and Khoufou to this list (1978, p. xiv and title page, respectively). Bonwick (1877, pp. 75-76) adds Xeopos, Khoofoo, Soyoof, Souphis, and Shoopho. D. H. Lewis (1980, p. 14) lists the names Khupfu and Saophia. Other variants on the foregoing forms are found in the literature. Bonwick (1877, p. 76, italics in the original) says: “Eratoshtenes speaks of King Saophis, the many-haired; and, in Coptic,
shoo
is
many,
and
pho
is
hair.
Bonwick (1877, p. 75, quoting Mr. Gliddon) also cites the tomb of a certain “Eimei, chief priest of the habitations of King Shoopho” as having been discovered near the Great Pyramid, and suggests that this Eimei may have been the architect of the Great Pyramid.

According to Herodotus and Diodorus Siculus, Khufu reigned for 50 years; however, Mantheo wrote that “Suphis reigned 68 years. He built the largest Pyramid. He was also called Peroptes” (Kingsland, 1935, p. 2).

According to Pochan (1978, p. xiii), the full name of Khufu, with the title “Hrw” before it, based on inscriptions in the so-called Relieving Chambers and also an inscription found at Wadi Magharah on the Sinai (illustrated by a drawing in Fix, 1978, p. 86) is “Hrw-Khnum-Khufu” (“the most high”—“Khnum protects me”). The simplified cartouche by which he is more commonly known reads, according to Pochan (1978, p. xii), simply “Khufui” (“He protects me”). Pochan (1978, pp. xiii-xiv) contends that the Fourth Dynasty originated in Upper Egypt and was associated with the ram-headed sun god of Elephantine known as Khnum (and associated with Ra and Amon in New Kingdom times). Further north in Egypt, around the Memphis and Heliopolis area (in the region of the Giza Plateau), the god Khnum was considered an intruder relative to the native gods, so the pharaoh’s name was often shortened to be less offensive, reading simply “He protects me,” and the “He” could be considered to refer to any of the gods. Pochan (1978, p. xiv) further suggests that the names Saurid, Surid, and Soris, sometimes applied to Khufu, derived from the Egyptian “Sri” (“ram”), as Khnum was a ram-headed god.

During the nineteenth and early twentieth centuries, many Egyptologists suggested that the names “Khufu” and “Khnum-Khufu” might refer to two different persons, especially since they occur together in the same inscription on the Sinai (see discussion and quotations from Petrie and Gaston Maspero in Fix, 1978, pp. 85-87; see Petrie, 1923,
History,
p. 62), and it was only in the later twentieth century that opinion solidified around the notion that both refer to the same man, the pharaoh Khufu of the Fourth Dynasty. Fix (1978, p. 89) suggests that these are not even the names of a person or persons but rather either two different names for a single god or the names for two different gods. He further hypothesizes (p. 89) that “if there ever was a King Khufu he lived long after the Pyramid was built and
was named after the Pyramid
” (italics in the original). Fix (1978, p. 93) further suggests, based both on the attributes of various gods, their symbolism, and etymological similarities, that “Khnum, Khnoum, Khufu, Souphis, Khnoubis, Chnouphis, Tehuti, Thoth, Mercury, Enoch, Hermes, and possibly ‘Christos’ are simply different representations of the same figure and power that finds remarkably similar expression in cosmologies extending over many thousands of years.”