Company LOGO Great Pyramid Mystery, History, Science & Engineering By DPN Samarasiri & Nirmala De Silva Introduction Pyramids is the series of Cemeteries which lie along the western bank of the Nile. The word Pyramid literally means fire in the middle. Stretching from ancient city of Leopolis to Heracleopolis, over 50 Kilometers, over 80 Pyramids. Many of the Phyramids are smooth faced while a few are stepped. Their head stand the monumental Pyramids of Giza. 1
Introduction Introduction Heroditus ; called the Father of History; was the first to write about the Pyramids around 440 B.C. In his History Heroditus says that the Pyramids, already ancient, were covered with a mantle of highly polished stones joined with the greatest exactness. 2
Great Pyramid Great Pyramids of Giza is considered to be one of the Seven Wonders of the world. The world s tallest building from 2570 BC to 1300 AD. Self-supported from main entrance to roof top. The Pyramid was constructed over 20 years period from 2589 2566 B.C. The Great Pyramid was built as the tomb of Forth dynasty Egyptian pharaoh khufu (Cheops) during his perid. Lies on the best ground on the Giza; on top of a rock core which reaches at least 7.9 m height under the Pyramid. Great Pyramid 3
Layout Layout Mortuary Temple at base. Causeway gallery - joint Valley temple on the bank 4
Great Pyramid Interior View 8 (h) x 12 (w) 175 (l) - 41 0 8 (h) x 12 (h) 235 (l) - 35 1. Entrance 2. Entrance cut by grave robbers 3. Subterranean chamber 4. Grand Gallery 5. King's chamber, relieving chambers, granite portcullis slabs 6. Queen's chamber 7. Shaft 8. Limestone plugging the air shaft A= "Air shafts" 5
Plan of the Great Pyramid Length (a) - The average length of the edge is ~ 230.360m. (largest difference is only 4.4 cm) Height (h) - Originally 146.59m high (480 ft), now only 138.75m high (455.2 ft) Pyramid angle - 51 50' 40'' Base area - 53,065.73m² Dimension of the Great Pyramid Pyramid volume - 2,592,968.43m³ Alignment - Exactly to the north (deviation only 2' 28'') 6
Building Materials Stone Blocks 2,300,000 stones Total blocks 2,500,000 stones Stone layers Originally 210 stone layers, now only 201 layers Weight of the stone blocks With an average density of 2,6-2,9 t/m³ the large limestone blocks weighted 6.5-10 tons and the smaller ones about 1.3 tons. Special blocks For the King's chamber granite blocks from 40 to 50 tons were used Total weight 6'500'000 tons (average weight of a block was about 2.5 tons) Building materials Pyramid: Nummulite limestone from quarries about 200-400m south of the pyramid were used for the core stones. Casing: light white limestone, so called Tura-limestone from quarries from the eastern shores of the Nile (Tura about 13 kms) King's chamber: Rose granite from Aswan 900km away from Giza 7
Material & Workforce Many estimates have been made regarding the workforce needed to construct the Great Pyramid. 20,000 workers for 20 years. Average workforce of 14,567 & peak workforce of 40,000. Number of blocks used in construction was about 2.4 million If 2,400,000 stones used 20 years constructed 365 days per year worked 10 working hours per day 1.01 stones has to be laid per every two minutes. 8
Egyptian units of Measurement The ancient Egyptians used cubits, palms and fingers as units for measuring. The cubit was divided into 7 palms and a palm into 4 fingers which resulted in 28 fingers for one cubit. 1 cubit = 52.4cm 1 palm = 7.48cm 1 finger = 1.87 cm The Egyptians didn't know the theory explaining the Pythagorean theorem but they knew from experience, that they could form right angles by using a so called primitive Pythagorean triple. It was very important to control the angle of inclination of the pyramid sides and the pyramid ridge. Any mistakes had a major effect on the shape of the pyramid. So it was important, that the outer stones were already bevelled to the right angle, where the so important exactness could be guaranteed and not on the pyramid plateau, where there was not enough time and room to accomplish this important task. For the angle of inclination of the sides of great pyramid the offset is 5½ palms (22 fingers) for 1 cubit hight, which gives an angle of inclination of 51.84 or 51 50'24''. This is - with a tiny difference - just the official angle of inclination of the pyramid of Khufu which is given as 51 50'40'. 9
Precise North-South Alignment The Great Pyramid's north-south axis is nearly aligned to true north, the deviation is only 2' 28''. It is easier to make measurement during the winter months. Possible Methods of Constructions 10
Possible Methods of Constructions Possible Methods of Constructions 11
Possible Methods of Constructions Possible Methods of Constructions 12
Possible Methods of Constructions Possible Methods of Constructions 13
Possible Methods of Constructions Possible Methods of Constructions 14
Possible Methods of Constructions Mathematics behind Pyramids 15
Actual length of the base of the pyramid = 755.73 2 x Perimeter = 8 x 755.73 = length of one minute of latitude as measured at the equator Side of the pyramid = 1/8 x minute of latitude Height of the pyramid = 1/8 x 2 π History Builders of the Great Pyramid had insufficient knowledge of the number Pi (π ) Pi is used to justify the statement of the Greek historian Herodotus, who recorded that the surface area of each face of the pyramid is equal to the square of its height. Apparently, Egyptian priests revealed this crucial piece of information to Herodotus. With Pi the accuracy of the above is 99.9%. But it can also be assumed that the designers of the pyramid were not content with "approximately" 99.9% and that the mathematical term "equal" meant for them 100%. From R. A. Schwaller de Lubicz, the brilliant Egyptologist, that in ancient Egypt temples and other buildings were designed and constructed according to the proportions of the golden mean. 16
Golden mean The Golden Mean is a ratio which has fascinated generation after generation, and culture after culture. It can be expressed succinctly in the ratio of the number "1" to the irrational "l.618034... ", but it has meant so many things to so many people, that a basic investigation of what might is the "Golden Mean Phenomenon" seems in order. In modern times there has been much interest in the Golden Proportion, Section or Mean. Since the Renaissance it has been used extensively in art and architecture. Golden Mean 1 x 1-x The Golden Mean is the division of a given unit of length into two parts such that the ratio of the shorter to the longer equals the ratio of the longer part to the whole. Calling the longer part x and accordingly the shorter part 1-x, this condition reads 1/x=x/(1-x) x 2 +x-1=0 Positive root; x=(-1+ 5)/2=0.61803398875 1/x=1.61803398875 Φ is used to represent the golden ratio 1.618 17
Angle of inclination The highly disputed angle of inclination or slope of the Great Pyramid ranging anywhere from 51 51' to 52, as well as the no longer measurable height (estimated to be 146 to 147 m), contributed to further speculations. Unfortunately, for whatever reason, science never acknowledged the fact that the ancient Egyptians were well aware of the hermetic rule of the golden mean. As a matter of fact, the assertion that the surface area of each face of the pyramid is equal to the square of its height can be mathematically verified. Phi Phi is an irrational number that is usually derived from the socalled Fibonacci* series. We get the value of Phi of 1.61803398... * Fibonacci, who lived in the 12th century, was a mathematician. During his journeys to Egypt he also discovered the mathematical relationship of the golden mean. 18
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COB OC = 1 OB = 0.618034 Angle OCB = 31 o 43 Angle OBC = 58 o 17 20
ED = 0.618034 OE = 1 Angle EOD = 38 o 10 Angle OED = 51 o 50 OD = 0.78615 Interesting things ED/OD = 0.78615 Tan 38 o 10 = Cos 38 o 10 Cos 51 o 50 = Sin 51 o 50 OD x 4 = 3.1446 π Unique point of intersection between π and Φ 21
BC = 0.618034 AB = 0.78615 AC = 1 Pyramid dimentions AB = 481 BC = 377.9 AC = 611.5 Perimeter of the pyramid = BC x 8 = 0.618034 x 8 = 4.9443 Perimeter of a circle with 0.78615 radius = 0.78615 x 2 x π = 4.9443 This shows that the perimeter of the base as a square (horizontal plane) is equal to the perimeter of a circle (vertical) which is having a radius is equal to the height of the pyramid. 22
Investigation of the Pyramids Professor from Britain s Oxford University under took the first organized Scientific expedition in 1638. Since then peoples from France, Britain, Denmark, Italy came to investigate about Pyramids. Explorations continues upto now by the use of robots and computers to map and analyze the structure of the pyramids. Many aspects of the Pyramids remain a mystery, but scholars continue to excavate, explore and learn more about them. End 23