Ancient EgyptianMathematicsThe use of organized mathematics in Egypthas been dated back to the third millennium BC. Egyptian mathematicswas dominated by arithmetic, with an emphasis on measurement and calculationin geometry.
With their vast knowledge of geometry, they were ableto correctly calculate the areas of triangles, rectangles, and trapezoidsand 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 thesides 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 only12″, or about 1/27000 of a right angle (Smith 43).
Three theoriesfrom mathematics were found to have been used in building the Great Pyramid. The first theory states that four equilateral triangles were placed togetherto build the pyramidal surface. The second theory states that theratio of one of the sides to half of the height is the approximate valueof P, or that the ratio of the perimeter to the height is 2P. Ithas been discovered that early pyramid builders may have conceived theidea that P equaled about 3.
14. The third theory states thatthe angle of elevation of the passage leading to the principal chamberdetermines the latitude of the pyramid, about 30o N, or that the passageitself points to what was then known as the pole star (Smith 44). Ancient Egyptian mathematics was basedon two very elementary concepts. The first concept was that the Egyptianshad a thorough knowledge of the twice-times table. The second conceptwas that they had the ability to find two-thirds of any number (Gillings3). This number could be either integral or fractional.
The Egyptiansused the fraction 2/3 used with sums of unit fractions (1/n) to expressall other fractions. Using this system, they were able to solve allproblems of arithmetic that involved fractions, as well as some elementaryproblems in algebra (Berggren). The science of mathematics was furtheradvanced in Egypt in the fourth millennium BC than it was anywhere elsein the world at this time. The Egyptian calendar was introduced about4241 BC.
Their year consisted of 12 months of 30 days each with 5festival days at the end of the year. These festival days were dedicatedto the gods Osiris, Horus, Seth, Isis, and Nephthys (Gillings 235). Osiris was the god of nature and vegetation and was instrumental in civilizingthe 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. Inundationwas the sowing period, coming-forth was the growing period, and summerwas the harvest period. They also determined a year to be 365 daysso they were very close to the actual year of 365 ? days (Gillings235). When studying the history of algebra, youfind that it started back in Egypt and Babylon.
The Egyptians knewhow to solve linear (ax=b) and quadratic (ax2+bx=c) equations, as wellas indeterminate equations such as x2+y2=z2 where several unknowns areinvolved (Dauben). The earliest Egyptian texts were writtenaround 1800 BC. They consisted of a decimal numeration system withseparate 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, andso 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 threetimes. Addition was done by totaling separately the units-1s, 10s,100s, and so forth-in the numbers to be added. Multiplication wasbased on successive doublings, and division was based on the inverse ofthis process (Berggren). The original of the oldest elaborate manuscripton mathematics was written in Egypt about 1825 BC.
It was calledthe Ahmes treatise. The Ahmes manuscript was not written to be atextbook, but for use as a practical handbook. It contained materialon linear equations of such types as x+1/7x=19 and dealt extensively onunit fractions. It also had a considerable amount of work on mensuration,the act, process, or art of measuring, and includes problems in elementaryseries (Smith 45-48).
The Egyptians discovered hundreds of rulesfor the determination of areas and volumes, but they never showed how theyestablished these rules or formulas. They also never showed how theyarrived at their methods in dealing with specific values of the variable,but they nearly always proved that the numerical solution to the problemat hand was indeed correct for the particular value or values they hadchosen. This constituted both method and proof. The Egyptiansnever stated formulas, but used examples to explain what they were talkingabout. If they found some exact method on how to do something, theynever asked why it worked. They never sought to establish its universaltruth by an argument that would show clearly and logically their thoughtprocesses.
Instead, what they did was explain and define in an orderedsequence the steps necessary to do it again, and at the conclusion theyadded a verification or proof that the steps outlined did lead to a correctsolution of the problem (Gillings 232-234). Maybe this is why theEgyptians were able to discover so many mathematical formulas. They never argued why something worked, they just believed it did. BIBLIOGRAPHYBerggren, 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. Mathematicsin 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 Noteson Mythology. Lincoln, Nebraska: Cliffs Notes, Inc. , 1991.
