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Great PyramidGreat PyramidMystery, History, Science & Engineering

By DPN Samarasiri & Nirmala De Silva

“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.

Introduction

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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.

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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

Great Pyramid

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Layout

Layout

Mortuary Temple at base.

Causeway gallery - joint

Valley temple – on the bank

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Great Pyramid

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"

Interior View

8”(h) x 12”(h) 235’(l) - 35’

8”(h) x 12”(w) 175’ (l) - 410

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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

Pyramid volume - 2,592,968.43m³

Alignment - Exactly to the north (deviation only 2' 28'')

Dimension of the Great Pyramid

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Stone Blocks 2,300,000 stonesTotal blocks 2,500,000 stonesStone 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 usedTotal 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

Building Materials

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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

Material & Workforce

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.

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• 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

Egyptian units of Measurement

• 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 thepyramid 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'‘.

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• The Great Pyramid's north-south axis is nearly aligned to true north, the deviation is only 2' 28''.

Precise North-South Alignment

It is easier to make measurement during the winter months.

Possible Methods of Constructions

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Mathematics behind Pyramids

Mathematics behind Pyramids

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• 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.

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Golden mean

• The Golden Mean is a ratio which has fascinated generation aftergeneration, 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…

• 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 reads1/x=x/(1-x)x2+x-1=0Positive root; x=(-1+√5)/2=0.618033988751/x=1.61803398875Φ is used to represent the golden ratio 1.618…

x 1-x1

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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 so-called 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.

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COB ∆ OC = 1OB = 0.618034Angle OCB = 31o 43’Angle OBC = 58o 17’

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ED = 0.618034OE = 1Angle EOD = 38o 10’Angle OED = 51o 50’OD = 0.78615

• Interesting things– ED/OD = 0.78615– Tan 38o 10’ = Cos 38o 10’– Cos 51o 50’ = Sin 51o 50’– OD x 4 = 3.1446 ≈ π– Unique point of intersection between π and Φ

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BC = 0.618034AB = 0.78615AC = 1Pyramid 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.

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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.

Investigation of the Pyramids

EndEnd

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