architecture and mathematics in ancient egypt

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Documents on the planning and building process

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distance between the axes of free-standing columns, as we have seen, corresponds to 1 palm (7.5 cm); and the distance between free-standing and engaged columns (8 cm) can be expressed as 1 palm + 14 finger. The artist might have chosen to represent the plan of the temple (or a part of it) in an approximate but realistic way, choosing ‘simple’ dimensions such as 1 palm and 2 fingers for the main elements. In this case, it is likely that this model was part of a votive object, rather than an architectural plan. Finally, it is worth mentioning the model of a step pyramid found at Memphis by Petrie, which he thought might be the a model of the ‘step pyramid of Saqqareh’59 (fig. 66). This model cannot be identified with a precise monument for several reasons. First of all, nothing is known about the circumstances of its discovery, apart from the fact that it was found at Memphis,60 and its date is impossible to establish. The model consists of a large limestone block cut in at least seven steps, of which six still remain, while only a fragment of the seventh survives. It is the representation of a step pyramid, but it does not seem to have been a working model, since it lacks the precision that this would have required. The overall appearance of a step pyramid is well rendered, but the steps are very roughly outlined, their corners are blunted and irregular, and there is a consistent discrepancy in the depth of the steps of two adjacent sides.61 If it represented the pyramid of Djoser, as Petrie suggested, it must be noted that the model does not show the specific feature of that pyramid, that is, its rectangular plan. The model cannot be identified with certainty as any existing step pyramid. Its outline, that is, the imaginary line connecting the steps from the ground to the top, is about 63◦ , much steeper than the funerary monuments of Djoser (about 52◦ ), Sekhemkhet (about 50◦ ), the so-called Layer Pyramid at Zawiyet el-Aryan 59

60 61

W. M. Flinders Petrie, The Labyrinth, Gerzeh and Mazghuneh, BSAE ERA 21, London, 1912, p. 35. Photographs of both models were published by Iorweth E. S. Edwards, The Pyramids of Egypt, London: Penguin Books, 1993 (revised edition), pl. 61. Petrie, Labyrinth, 35. According to Edwards (Pyramids, p. 260) the model was purchased and not directly found by Petrie. This model, therefore, does not provide any answer to the discussion about the exact shape of the steps, that is, whether they had all the same ‘riser’ (as they are generally represented) or whether it diminished towards the top (as suggested by Vyse and Perring in Operations Carried On at the Pyramids of Gizeh, London: Fraser, 1840–2, pl. A, according to whom the steps were 22, 21, 20 19, 18 and 17 cubits high, and Legon in ‘The 14:11 Proportion at Meydum’, DE 17 (1990), 15–22), and whether the ‘tread’ was flat or sloping. The major step ¨ pyramids are generally reconstructed with sloping steps (as in Rainer Stadelmann, Die Agyptischen Pyramiden, Mainz: Von Zabern, 1985, figs. 18 and 19 and Edwards, Pyramids, figs. 6 and 13). The pyramid of Meidum is usually represented with flat steps (Vito Maragioglio and Celeste Rinaldi, L’architettura delle Piramidi Memfite, ¨ vol. IV, p. 1220 Torino: Artale, 1963–77, vol. iii, pl. 2, fig. 2; Stadelmann, Pyramiden, fig. 21, although in LA, he adopted sloping steps; see also Jean-Philippe Lauer, Le myst`ere des pyramides, Paris: Presses de la Cit´e, 1988, p. 235 and Gay Robins and Charles Shute, ‘The 14 to 11 Proportion in Egyptian Architecture’, DE 16, 1990, 75–80 for calculations of their proportions) and its satellite might have had the same shape (Maragioglio and Rinaldi, Piramidi MDAIK 38 (1980), 83–95, fig. 3) suggested flat steps for their reconstructions of the step pyramid at Sinki. J´anosi suggested two possible reconstructions of the casing of GIIIb and c, of two queens of Menkaura: one with flat and one with sloping steps (Peter J´anosi, Die Pyramidenanlagen der K¨oniginnen, ¨ Vienna: Osterreichischen Akademie der Wissenschaften, 1996, pp. 86–7 and fig. 33).


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