User:Dave Light/Pi
At the end of the lengthy series of entrance ways leading into the interior is the structure's main chamber, the King's Chamber. This granite room was originally 10 × 20 × 11.4 cubits, or about 5.235 m × 10.47 m × 5.974 m[1][2], comprising a double 10 × 10 cubit square floor, and a height equal to half the double square's diagonal. Some believed that the height was consistent with the geometric methods for determining the Golden Ratio φ (phi) as the height is approximately phi times the width minus ½, while phi can be derived from other dimensions of the pyramid[3], but evidence from Petrie’s surveys and later conclusions shows that it was in fact the circular proportions that were deliberately incorporated into the internal and external designs of the Great Pyramid by its architects and builders, for symbolic reasons[4]. The so called golden ratio phi simply existed in the proportions of the architecture as an inadvertent by-product of the inclusion of the circular proportions. The reason for the inadvertent inclusion is that phi, the golden ratio, has a naturally occurring mathematical relation to the circular ratio pi that is unrelated to the architecture or geometry, and which was unknown to the pyramids builders. Petrie confirmed that the King’s Chamber was a triumph of Egyptian geometry, the ratio of its length to the circuit of the side wall being the same as the ratio of 1 to pi, and that the exterior of the pyramid had been built to the same proportions[5][6][7]
Jackson, K and J Stamp. 2002. Pyramid: Beyond Imagination. Inside the Great Pyramid of Giza. BBC Worldwide Ltd. London.
The earliest evidenced conscious use of an accurate approximation for the length of a circumference with respect to its radius is of 3+1/7th in the designs of the Old Kingdom pyramids in Egypt. The Great Pyramid at Giza, built c.2550-2500 B.C, was precisely 1760 cubits around with a height of 280 cubits (1760/280=2xPi). Egyptologists such as Professors Flinders Petrie [8]and I.E.S Edwards[9] have shown that these circular proportions were deliberately chosen for symbolic reasons by the Old Kingdom scribes and architects[10][11]. The same apotropaic proportions were used earlier at the Pyramid of Meidum c.2600 B.C. This application is archaeologically evidenced, whereas textual evidence does not survive from this early period.
The early history of π from textual sources roughly parallels the development of mathematics as a whole.[12] Some authors divide progress into three periods: the ancient period during which π was studied geometrically, the classical era following the development of calculus in Europe around the 17th century, and the age of digital computers.[13]
- ^ Petrie (1883) The Pyramids and Temples of Gizeh pp 83 and Xiii
- ^ Maragioglio and Rinaldi (1964)L’architectura delle Pyramidi Menfite IV
- ^ Calter (2008) pp. 156-171, 548-551.
- ^ Jackson and Stamp (2002) Pyramid: Beyond Imagination. pp153
- ^ Petrie (1940) Wisdom of the Egyptians pp. 29
- ^ Lightbody (2008) Egyptian Tomb Architecture. The Archaeological Facts of Pharaonic Circular Symbolism. pp 29
- ^ Jackson and Stamp (2002) Pyramid: Beyond Imagination. pp153
- ^ Petrie, W.M.F. 1940 Wisdom of the Egyptians: pp 27
- ^ Edwards. I.E.S. 1979: The Pyramids of Egypt: pp269
- ^ Jackson and Stamp (2002) Pyramid: Beyond Imagination. pp153
- ^ Lightbody, D.I. 2008. Egyptian Tomb Architecture: The Archaeological Facts of Pharaonic Circular Symbolism. British Archaeological Reports. pp36
- ^ Beckmann, Petr (1976). A History of π. St. Martin's Griffin. ISBN 0-312-38185-9.
- ^ "Archimedes' constant π". Retrieved 2007-11-04.