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Ancient Egypt : Its Salient FeaturesA picture story

BYAVANEESH NAMAN YADAV 9A 127


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Acknowledgements

Without the support of the internet, this project would not exist.The internet offered me the richest library to delve into, and all my researchis internet-based. I have listed all the names of websites I referred to in the

bibliography section.


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INDEX

Ancient Egypt : Post 3000 BC 4

Geographic History 5

Agriculture 6

Social Structure 7

Hieroglyphics 8

Mummification 9

Sports /Entertainment 10

Architecture 11

a. Mathematical connections 13-24

TITLE S PAGE NUMBERS


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Ancient Egypt : Post 3000 BCThe Egyptian Civilization is one of the earliest onearth. It marked the transition of the human from ahunter-gatherer to a settled farmer, and theestablishment of kingship-governments headed byPharaohs (above: the Pharaoh Tutankhamun)


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Geographic HistoryAncient Egypt was prey to anarid climate. Naturally, settlements arose beside theNile. In fact, Ancient Egypt was divided as red and

black, the former referring to deserts and the latterreferring to a fertile river-plain. Furthermore, it wasdivided into Upper Egypt and Lower Egypt. Inaround 3200 BC, King Menes of the north conqueredthe south, uniting Egypt. The capital was christenedMemphis, the greek for balance between two lands.

Desert BufferA vast

region extending after theriver plain was desert.This provided a veryeffective buffer zoneagainst invading armies


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Agriculture Egypt is called the gift of Nile. Since 3000 BC, its civilization hasgrown from the Nile. The Nile river flooded every year, washing as well as

fertilizing its banks. Agriculture of all types thrived here. Wheat was ground tomake bread and barley was fermented for wine. The Papyrus plant, whose stemwas valued for paper, grew on the banks of the Nile river. Other vegetables likemelons, garlic, pulses and lettuce were also grown. Egyptian agriculture wasdivided into Akhet(flooding), Peret(planting) and Shemu(Harvesting).Egyptian farmers also herded cattle. Food surplus was exported. Fishing was

also a popular activity among the lower and middle classes as fish was asubstitute for meat.


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The Egyptian Pyramid Social Pyramid of Egypt


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Hieroglyphics The Egyptians had a unique script. They wrote withwith the help of pictures, and this form of writing was done byskilled scribes. They had an edge over other artisans, as dignifiedwriters. Today, they can be still found inside pyramids, scribbled

over its walls.(Above) A hieroglyph tablet ; numeral translations


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Egyptian Culture : The Beliefin Afterlife andMummificationThe belief in afterlife wasperhaps one of the strongest

elements of Ancient Egyptianculture. They believed in aheavenly notion ofAfterlife.The AfterlifeThe Afterlife was a heavenlyplace, complete with a holy Nile

river. Earlier, only pharaohscould enter it after they died.Later, the god Osiris opened itfor everyone.But to attain Afterlife, one hadto do good deeds in his/her life

and had his heart weighed.Only then could one get toboard Ras boat in the Afterlife.This belief also kept crime lowin Egypt, since everybodywanted to attain Afterlfe.

For this reason, the E tians

Mummification

To be mummified, ones dead bodywould be emptied of all organs exceptthe heart, which was considered thecentre of intelligence. Then it would bedisinfected with Natron and wrappedwith strips of linen. Mummification was

an intricate process as long as 70 days!


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Sports /Entertainment Ancient Egyptians were masters of sport.Many hieroglyphs depict people boxing, horse-riding, and swimming.They entertained themselves hunting, playing and also by gettinginvolved in boat games. The wealthy would organize extravagant partiesof food, wine and music. They would hire dancers, musicians andacrobats to entertatain the crowds.


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ArchitectureThe Ancient Egyptians werevery particular about their

architecture. If you see, everystructure built in Egypt wasmade out of stone. Limestonewas a popular throughoutEgypt, as it was used to createthe interiors of Pyramids.

Egyptian Architectureconsisted of temples,

monuments andsignificantly the

Pyramids(which I willelaborate on).

Front: The Sphinx; Backdrop: TheGreat Pyramid of Giza


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Pyramids If there is one thing Egypt isstill remembered for, it is its pyramids.Built thousands of years ago by thousandsof labourers and farmers to suit the

funerary needs of the Pharaoh, thePyramids serve tombs as well asmasterpieces of architecture. Amongthem, the most famous pyramid issupposed to be the Great Pyramid of Giza,or Khufus Pyramid which has dazzled

travelers, mathematicians and architectsalike.

The Pyramids Of Giza, Egypt

What Astonishes Architects

What astonishes architects is howthe pyramids were constructed.

The idea of placing millions of

blocks of limestone weighing more

than a ton each puzzles architects

as to the engineering used to build

them. Many theories have beenmade to tackle this mystery. One

such theory is the Ramp Theory.

The Ramp Theory

The ramp theory suggests that

ramps were stationed alongsidethe construction areas. They were

then lubricated with water, and

with the help of ropes and levers,

the stones were dragged by groups

of ten men to where they would be

positioned.


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The Cheops Pyramid covers

a total area of 13 acres. The Pyramids construction

was started 4617 years ago,

and took 20 years tocomplete! It is the oldest of

the Seven Wonders of the

World.The Pyramid is 30 times

larger than the Empire State

Building! It can be seen from

the moon.

The Cheops Pyramid faces

true north.

The Cheops Pyramid is at

the exact centre of the Earthslandmass, though the odds of

building it over there would

be 1:3 billion!

The average altitude of earthis 5449 inches (considering

Mount Everest and Miami).

That is the exact height of the

Cheops Pyramid

The Great Pyramid Of Giza: Mathematical Connections

Fast facts


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The Great Pyramid of Giza is a remarkable feat of architecture. Considering the time it was built in

(2560 BC), and the weight of its 26, 00,000 stone blocks (2.5t each), we cannot help but admire it in

awe.

Many architects have had different interpretations to its design. Many infer it as a representation of

our galaxy, which I will explain to you now with a theory which was proposed by Tom Valentine in his

book, The Great Pyramid : Mans Monument to Man.

Above, a cross section of the Cheops Pyramid


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The Year Circle

The diameter of the largest circle that can fit in the pyramid is 4,382.9 inches. Divide it by 12, and you will get

365.242 feet. This is the number of days we have in a year!

So, what else does this mean? Valentine, in his book says that the word Pyramid originates from the Greek

word Pyramidos, pyro meaning fire and midis meaning middle. This further concludes to fire in the

middle. Thus, Tom suggests that the Pyramid is a representation of our local cosmos, where the Year Circle is

our orbit and the sun is supposed to be in the middle!

The Earth Circle

Above diagram: A circle fit into the truncated upper part of the pyramid

Further research brought me some more queer discoveries. If you fit in a circle in the truncated cross section of thepyramid, you find that the diameter is around 948 inches. Divide that by 12, and you get 78.99 feet. So, you might

ask, Is that of any significance? Well, the number exactly corresponds to the diameter of the earth at the poles,

which is 7899 miles!


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The Obliquity Circle

Rested between the side and the base will be the obliquity circle. So, now what? Well, the diameter of this

circle is 1747.8 inches. Now, divide it by 12 and you get 145.64 feet. Insignificant, isnt it? Divide this number bythe year circle and you get .3987. This is the sine(well, Im not sure what sine means) of 23.5 degrees, the

Earths angle of obliquity to the plane of the ecliptic!


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In the next section, I will talk about more particular mathematical connections in KhufusPyramid:

Its relationship with

The Golden Ratio

The Pi

The Squaring Of The Circle


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In Brief

According to Euclid,

A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the

greater segment, so is the greater to the less.

The Golden Ratio is denoted by phi =1.61803

Objects containing the Golden Ratio are supposed to be the most pleasing to look at.

Back to the Pyramid

CROSS SECTION OF KHUFUS PYRAMID; ALIGNMENT OF

ITS SHAFTS WITH STARS


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In the cross section of the pyramid, we get a triangle which is popularly called the

Egyptian Triangle or the Kepler Triangle. The ratio of the slant height s to half thebase b is said to be the Golden Ratio.

Slant height(s) = 186.369 m

Base (b) = 230.363 m

b = 115.182 m

s/ b =1.61804 m (which is only different from in the fifth decimal place)

Computation

Take base of the triangle as I and hypotenuse

, then height h will be h2 =2 - 12

We get h =

Thus, the sides of the cross-sectioned triangle (Kepler triangle or Egyptian Triangle)

are in a ratio of


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2. The Pi and the Cheops Pyramid


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There are a couple of theories regarding the Cheops Pyramid somehow relating to the pi. Through some doubtful

research, I have gathered this:

The Great Pyramids height = 146.6 m

The Great Pyramids base = 230.38 m

So whats significant?

2b /h = 3.14297408!

I mean to say, the value above is accurate to the pi, which is the ratio between a circles circumference and itsdiameter, up to two decimal places!

Well, this shows that the Ancient tomb raiders knew something about the math of circles. Now, my question is,

does the Great Pyramid actually relate to a circle, or is this recent discovery a mere coincidence?


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3. The Squaring Of the Circle

The Squaring of the Circle is an age-old geometrical puzzle

The problem of squaring the circle is not new. It refers to constructing a square with the same area or perimeter of a circle.

One of its earliest mentions is in the Rhind papyrus, a mathematical document which was purchased by Scottish sociologist AHenry Rhind in Luxor in 1858.

Back To the Pyramids

The idea is: The perimeter of the base of the Great Pyramid equals the circumference of a circle whoseradius equal to the height of the pyramid.


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Let me calculate;

Pyramid height =

So:

Perimeter of base = 4 x 2 = 8 units

Then for a circle with radius equal to pyramid height

.

Circumference of circle = 2 7.992

So the perimeter of the square and the circumference of the circle agree to less than 0.1%.


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Conclusion

Egyptian architecture is purely stunning. Tombs, monuments, temples and exclusively, the

Pyramids paint this marvelous cult. But the most amazing of them is The Great Pyramid of

Giza. The sheer beauty of its magnitude makes me question myself, How did they buildit?How could they have such a deep understanding ofMathematics? It is connected to

the Golden Ratio, the Pi, the squaring of the circle as well as our galaxy.

My curiosity has funded my effort. The Great Pyramid of Giza continues to stun me, and

dissecting its mysteries is not easy.

Avaneesh N Yadav 9 A


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