tians were the fi rst to develop a base-10 numbering system,
which allowed the use of unit fractions and binary fractions.
Square roots were in use by about 2000 b.c.e., at which time
the Egyptians were also calculating and using the value of
pi, the ratio of the diameter of a circle to its circumference.
Egyptian mathematicians created tables of addition and sub-
traction, solved algebraic problems, and developed a precise
system of weights and measures.
Th e Egyptians also studied the aerodynamics of sails and
the phenomenon of draft employed by a curving sail. Some
historians speculate that the Egyptians used kites and sails to
raise obelisks and other monuments.astronomy
Th e gods of ancient Egypt were present in all creation and in
visible form. Th ey were present in the stars and the promi-
nent constellations, a fact that bound astronomical knowl-
edge with the practices and rituals of religion. Osiris was
visible in the constellation Orion, for example, and the god-
dess Nut could be seen in the Milky Way. To the Egyptians,
the sky was a great roof, supported by immense pillars at the
four corners of the world, which corresponded to the four
cardinal points of the compass. Th e sun made a daily course
around the earth in a celestial boat, doing constant battle
with Set, the god of darkness and night. Th is striving forced
the sun to move from north to south in the course of the
year; at the time of the summer solstice, the sun reached its
furthest point north. Th e earth itself was a fl at rectangle, ex-
tending north to south and having its center in the valley of
the Nile, which arose in a great river that lay at the southern
boundary of the world.
Egyptian astronomers were priests as well as scholars,
for whom a close knowledge of the heavens was most useful
in its application to agriculture. Th e annual rising of Sirius
before the sun at the summer solstice, for example, presaged
the fl ooding of the Nile, the event that renewed the fertility
of the Nile Valley. Th e prediction of this event every year lent
the priestly caste its aura of mysterious power and esoteric
knowledge. It also provided a natural starting point for the
annual calendar of days, weeks, and months.
Th e Egyptian methods of mapping and measuring the
heavens gave the world one important basis for its advanced
time measurement systems. Egyptian astronomers divided
the heavens into 36 decans, with each group of stars covering
10 degrees of the sky. Each of these groups rose at dawn for
a period of 10 days, which formed a basis for the Egyptian
calendar of 12 months of 30 days, each composed of three
10-day weeks. Egyptian astronomers further divided the year
into three seasons—the season of the fl ood, the season of
planting, and the season of harvest—with each season four
months in length. Th e system of months left an extra fi ve days
each year that were set aside for feasting and a rest from labor.
Th ese intercalary days (inserted between others) were associ-
ated with a legend of the god Th oth, who allowed the goddess
Nut an extra fi ve days to give birth to her children.Th e actual solar year, being slightly longer than 365 days,
caused the months and seasons to gradually go out of phase.
Th e result was a long period known as the sothic cycle, in
which the seasons returned to their original positions in the
calendar every 1,460 years. Later astronomers of Alexandria
created a new calendar in which an extra day was added ev-
ery fourth year, a system adopted by the Romans and which
gave rise to the modern leap year. Th e system of decans and
constellations also led to the division of night and day into 12
equal parts, which in turn led to the 24-hour day now used
throughout the world. Th e Egyptians also considered the po-
sition of the stars and constellations in raising the pyramids.
Th e faces of these monuments are very carefully aligned. Most
face the rising sun at the summer solstice; others are aligned
with important stars or the points of the compass. Th e north
face of the Great Pyramid at Giza, for example, lies almost
precisely at a right angle to true north. Some have seen in the
arrangement of the three pyramids at Giza an imitation of
the stars in the belt of the constellation of Orion. Th e align-
ment of foundations and walls with the cardinal points of the
compass was done with the help of an instrument known as a
merkhet, a sighting tool made from the central rib of a palm
leaf, a string, and a weight, which gives a precise vertical line
and allows the user to make a determination of true north
and set the north–south axis.TECHNOLOGY
Th e Egyptians invented several devices to aid construction of
their palaces, monuments, and pyramids. Th e ramp, an in-
clined plane that allows large blocks to be raised using less
force, and the lever, which uses a fulcrum point to multiply
lift ing force, were both applied to moving and positioning
heavy objects, such as the immense blocks of stone laid for the
pyramids. Th e Egyptians invented papyrus as a writing me-
dium, developed long-distance ships, and adopted the wheel
and chariot—originally inventions of the Mesopotamians.
Egyptian farmers developed sophisticated irrigation systems,
including canals, dikes, and reservoirs to bring water to their
fi elds in times of drought or low rainfall.
Weaving and dyeing technology also made important
advances in ancient Egypt. Th e Egyptians developed new
methods of weaving and dyeing cotton and invented the
royal purple dye adopted by ancient Greece and Rome. Th ey
learned to manufacture pigments and dyes from minerals
like cobalt (for blue), iron oxide (for red), azurite or copper
carbonate (light blue), malachite (green), and charcoal or
charred bone (black).
Th e perception is widespread that Egyptian science was
less sophisticated than its Babylonian and Greek equivalents.
Hieroglyphic mathematics and astronomy never reached the
level of sophistication of Babylonian or Greek astronomy. But
this fact needs to be put in a proper historical perspective. It
would be false to conclude that Egypt somehow disappointed
or did not perform to expectation. Historically, thinking pro-
gressed more or less along parallel lines in Egypt and other928 science: Egypt0895-1194_Soc&Culturev4(s-z).i928 928 10/10/07 2:30:28 PM