Ancient Egyptian

Mathematics

The use of organized mathematics in Egypt

has been dated back to the third millennium BC. Egyptian mathematics

was dominated by arithmetic, with an emphasis on measurement and calculation

in geometry. With their vast knowledge of geometry, they were able

to correctly calculate the areas of triangles, rectangles, and trapezoids

and the volumes of figures such as bricks, cylinders, and pyramids.

They were also able to build the Great Pyramid with extreme accuracy.

Early surveyors found that the maximum error in fixing the length of the

sides was only 0.63 of an inch, or less than 1/14000 of the total length.

They also found that the error of the angles at the corners to be only

12″, or about 1/27000 of a right angle (Smith 43). Three theories

from mathematics were found to have been used in building the Great Pyramid.

The first theory states that four equilateral triangles were placed together

to build the pyramidal surface. The second theory states that the

ratio of one of the sides to half of the height is the approximate value

of P, or that the ratio of the perimeter to the height is 2P. It

has been discovered that early pyramid builders may have conceived the

idea that P equaled about 3.14. The third theory states that

the angle of elevation of the passage leading to the principal chamber

determines the latitude of the pyramid, about 30o N, or that the passage

itself points to what was then known as the pole star (Smith 44).

Ancient Egyptian mathematics was based

on two very elementary concepts. The first concept was that the Egyptians

had a thorough knowledge of the twice-times table. The second concept

was that they had the ability to find two-thirds of any number (Gillings

3). This number could be either integral or fractional. The Egyptians

used the fraction 2/3 used with sums of unit fractions (1/n) to express

all other fractions. Using this system, they were able to solve all

problems of arithmetic that involved fractions, as well as some elementary

problems in algebra (Berggren).

The science of mathematics was further

advanced in Egypt in the fourth millennium BC than it was anywhere else

in the world at this time. The Egyptian calendar was introduced about

4241 BC. Their year consisted of 12 months of 30 days each with 5

festival days at the end of the year. These festival days were dedicated

to the gods Osiris, Horus, Seth, Isis, and Nephthys (Gillings 235).

Osiris was the god of nature and vegetation and was instrumental in civilizing

the world. Isis was Osiris’s wife and their son was Horus.

Seth was Osiris’s evil brother and Nephthys was Seth’s sister (Weigel 19).

The Egyptians divided their year into 3 seasons that were 4 months each.

These seasons included inundation, coming-forth, and summer. Inundation

was the sowing period, coming-forth was the growing period, and summer

was the harvest period. They also determined a year to be 365 days

so they were very close to the actual year of 365 ? days (Gillings

235).

When studying the history of algebra, you

find that it started back in Egypt and Babylon. The Egyptians knew

how to solve linear (ax=b) and quadratic (ax2+bx=c) equations, as well

as indeterminate equations such as x2+y2=z2 where several unknowns are

involved (Dauben).

The earliest Egyptian texts were written

around 1800 BC. They consisted of a decimal numeration system with

separate symbols for the successive powers of 10 (1, 10, 100, and so forth),

just like the Romans (Berggren). These symbols were known as hieroglyphics.

Numbers were represented by writing down the symbol for 1, 10, 100, and

so on as many times as the unit was in the given number. For example,

the number 365 would be represented by the symbol for 1 written five times,

the symbol for 10 written six times, and the symbol for 100 written three

times. Addition was done by totaling separately the units-1s, 10s,

100s, and so forth-in the numbers to be added. Multiplication was

based on successive doublings, and division was based on the inverse of

this process (Berggren).

The original of the oldest elaborate manuscript

on mathematics was written in Egypt about 1825 BC. It was called

the Ahmes treatise. The Ahmes manuscript was not written to be a

textbook, but for use as a practical handbook. It contained material

on linear equations of such types as x+1/7x=19 and dealt extensively on

unit fractions. It also had a considerable amount of work on mensuration,

the act, process, or art of measuring, and includes problems in elementary

series (Smith 45-48).

The Egyptians discovered hundreds of rules

for the determination of areas and volumes, but they never showed how they

established these rules or formulas. They also never showed how they

arrived at their methods in dealing with specific values of the variable,

but they nearly always proved that the numerical solution to the problem

at hand was indeed correct for the particular value or values they had

chosen. This constituted both method and proof. The Egyptians

never stated formulas, but used examples to explain what they were talking

about. If they found some exact method on how to do something, they

never asked why it worked. They never sought to establish its universal

truth by an argument that would show clearly and logically their thought

processes. Instead, what they did was explain and define in an ordered

sequence the steps necessary to do it again, and at the conclusion they

added a verification or proof that the steps outlined did lead to a correct

solution of the problem (Gillings 232-234). Maybe this is why the

Egyptians were able to discover so many mathematical formulas.

They never argued why something worked, they just believed it did.

BIBLIOGRAPHY

Berggren, J. Lennart. “Mathematics.”

Computer Software. Microsoft, Encarta 97 Encyclopedia.

1993-1996. CD- ROM.

Dauben, Joseph Warren and Berggren,

J. Lennart. “Algebra.” Computer Software.

Microsoft, Encarta 97 Encyclopedia. 1993-1996. CD- ROM.

Gillings, Richard J. Mathematics

in the Time of the Pharaohs. New York: Dover Publications,

Inc., 1972.

Smith, D. E. History of Mathematics.

Vol. 1. New York: Dover Publications, Inc., 1951.

Weigel Jr., James. Cliff Notes

on Mythology. Lincoln, Nebraska: Cliffs Notes, Inc., 1991.