The Ancient Egyptians very early evolved a Calendar
based on a year of 365 days. When this happened, and the precise
way in which it was arrived at is not known, but observation of several
phenomena or the rising of the Nile over a period of time would
have been sufficient for its calculation. Intense observation of
the heavens was already carried on in predynastic times, and by the founding
of the First Dynasty the Egyptians had already constructed a practicable
calendar. The invention of the calendar has been hailed as the greatest
scientific achievement of the Egyptians and the precursor of the science
reasons which may have been closely connected with the provisioning of
officials and the rudimentary system of collecting taxes, the new
state bureaucracy soon felt the need for a dating system which distinguished
between different years so that they could be recorded. The numbering of
years starting from a fixed point was not known, and so each year was described,
or named, by one or more of its outstanding events. All of these requirements
gave rise to the development of "Hsb"
exact science of mathemathics.
As a result of
advancements in the science of Hisb;
the burial chamber structure along some of the magazines for tomb provisions
were soon dug in the gravel and rock substratum with astonishing precision,
which during the Second Dynasty became a veritable maze of underground
corridors and rooms.
(Ancient Egyptian Mathemathics) advances
made at this time had a direct bearing on the lives of ordinary Egyptians
as they helped the creation of the unified Egyptian state
which soon introduced a new ideological framework and a new political organization
of the country. Centralized government based on a powerful bureaucracy
(known as per
the house of counting) skilled in the science of mathemathics
a degree of safety and political stability, and the greater resources of
the country under control provided better security against the consequences
of natural disasters such as famine, but the greatest effect of the change
was in the sphere of Art and Architecture all of which required
the intimate knowledge of mathemathics.
Art and Architecture, inasmuch as the distinction between
them was in Egypt always rather tenuous, now came to the fore. Architecture
which benefited from the use of "Hsb";
The largest customer was the state itself, personified by the king
and his immediate family, and many items of everyday life were now also
made for the growing numbers of officials. Craftsmen and artists had easier
access to raw materials, and were able to specialize as a result of the
larger market for their products. When need arose, the state could mobilize
a manpower which, in both number and quality, had been undreamt of by local
chiefs of the Predynastic Period.
At the beginning of the First Dynasty, a new administrative
capital was founded and became known as Ineb-hedj,
' White Wall', presumably because of its appearance. A series of
large tombs of high officials and some other members of the royal family
were built in the cemeteries in this area, particularly at Saqqarah.
The ruins of the first
Dynasty administrative capital "Inb-hdj" or
' White Wall'
Egyptian monumental relief could only develop significantly when
the changes in state ideology and religion, and the growing familiarity
with mathemathics "Hsb"
along the use of stone, found their expression in monumental building.
As yet the opportunities offered were few, and until the situation changed
in the Third and Fourth Dynasties, the ability displayed
at the end of the Predynastic Period could not manifest itself more
Our knowledge of official civil architecture, such as palaces,
is almost entirely second-hand, based on their representations or presumed
similarities in tomb architecture. The same is true of early temples,
but we are well informed about tombs. Graves of ordinary people of the
earliest period of Egyptian history were not richer or larger than their
Predynastic counterparts, but tombs built during the First Dynasty
for kings, close members of the royal family, and the highest officials
of the state, now increased enormously in size. The area of their superstructure
was regularly in excess of a thousand square metres (10,000 square feet),
and although working with unbaked mud-brick, Egyptian architects and
work supervisors were steadly acquiring their knowledge along the managerial
skills needed in large-scale monumental building of the Old Kingdom.
As a result the burial chamber and some of the magazines for tomb provisions
were soon dug in the gravel and rock substratum with astonishing precision,
and during the Second Dynasty became a veritable maze of
underground corridors and rooms.
Between 2700 and 2200 Bc royal tombs were surrounded
by a complex of temples and smaller tombs called mastabahs.
The burial chamber of the king was protected by a manmade mountain of stone
called a pyramid. Its four triangular sides spreading below a single
peak represented the rays of the sun shining down over the pharaoh, linking
him directly and for all time to Ra. A temple containing a
false door through which the ka traveled was built against the east
side of the pyramid. All burial grounds were located on the west bank of
the Nile since it was in the west that the sun set, beginning its
nightly journey into the other world - the same journey that the ka
had to make.
Plans were drawn up, several thousand men, including stonecutters,
masons, surveyors, mortar makers, carpenters, and general laborers were
brought to the area. They would work all year long either in the quarries
or on the site. Barracks and workshops were built at both locations. A
larger work force of over fifty thousand men, most of them farmers,
was also drafted every year between July and November when
the fields were flooded and farming was impossible. They were organized
into gangs to transport stone from the quarries to the site. Each gang
consisted of twenty-five men, including a soldier who was the foreman.
All the men were paid in food and clothing.
Before the building process could begin, the location of true
north had to be determined, so that the pyramid could be accurately
oriented. A circular wall was built approximately in the center of the
site. It was built high enough to block a view of the surrounding hills
and the top was made level. This created a perfect horizon line.
In the evening a priest stood in the center of the circle and watched
for the appearance of a star in the east. Its position was marked as it
rose above the wall and a line was drawn from that point on the wall to
the center of the circle. He watched the star as it moved in an arc through
the sky and finally set in the west. As it dropped behind the wall its
position was marked again and another line was drawn to the center of the
circle. Because stars appear to rotate around the north pole, the priests
knew that a third line drawn from the center of the circle through
the center of the space between the first two lines would point directly
was also used in surveying as a term for a measure of land equaling 2500
The pyramids serve as a tribute to those who so skillfully organized
the efforts of thousands of people using the science of hsb
in an attempt to deny the finality of death and the limitations of time
by leaving behind something that would last forever.
Egyptian Mathematics, like the writing of
given over more to practical than theoretical considerations. However,
our knowledge of all Egyptian sciences is restricted by the fact that the
basic formulae were closely guarded by their priestly practitioners and
never committed to papyrus.
Teaching in Egyptian schools for scribes was for the most part oral,
and it is certain that Egyptian mathematics were more extensive
than surviving documents suggest. Like so much else in Egyptian intellectual
life, mathematics were probably perfected by the Pyramid Age.
The decimal system of numeration, employing separate digits and multiples
of a hundred up to a million, was in existence as early as the First
Dynasty. The device of zero was not discovered, and even the
Greeks themselves did not hit upon it. Complex fractions were easily manipulated,
with the disadvantage that the only fractional numerator was I. Thus 3/8
was expressed as 1/8 1/8 1/8. Two-thirds, however, appears to have been
a fundamental concept. Arithmetical progression by fractions and elementary
geometrical progression were fully comprehended and digested. Surface calculation
was made on the properties of the triangle, the rectangle and the trapezium.
The great Rhind papyrus
papyrus below) in the British Museum contains many problems
devoted to the properties of the rectangle, the triangle and the circle.
One can see an example of Egyptian mathematical theories "Hsb"
recorded on it .
The papyrus, a scroll about 6 meters long and 1/3 of a meter
wide, was written around
1650 BC by Ahmas,
the scribe, who had copied a document which was 200 years older.
This makes the original papyrus date from about 1850 BC. The
Egyptians applied their mathematical knowledge to practical affairs with
extraordinary ingenuity. The papyrus Anastasi I, for example, contains
a series of the building problems concerning the transport and erection
of colossi, obelisks and enormous blocks of stone which the Egyptians solved
with conspicuous success in practice.