Egyptian Math Essay, Research Paper

Kevin Mann

4-20-00

Dr Johnston

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.