Egyptian Math
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 t...
... middle of paper ...
...alking 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.
Works Cited:
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
Millions of Americans work full-time, day in and day out, making near and sometimes just minimum wage. In 1998, Barbara Ehrenreich decided to join them in part by the welfare claim, which promises that any job equals a better life. Barbara wondered how anyone can survive, let alone prosper, on $6-$7 an hour. Barbara moved from Florida to Maine to Minnesota, working in the cheapest lodgings available and accepting work as a waitress, hotel maid, house cleaner, nursing home aide, and Wal-Mart salesperson. She soon realizes that even the lowliest occupations require exhausting mental and physical efforts and in most cases more than one job was needed to make ends meet. Nickel and Dimed reveals low-wage America in all of its glory, consisting of
It’s hard to believe that a civilization consisting of once illiterate nomadic warriors could have a profound impact on the field of mathematics. Yet, many scholars credit the Arabs with preserving much of ancient wisdom. After conquering much of Eastern Europe and Northern Africa the Islamic based Abbasid Empire transitioned away from military conquest into intellectual enlightenment. Florian Cajori speaks of this transition in A History of Mathematics. He states, “Astounding as was the grand march of conquest by the Arabs, still more so was the ease hit which they put aside their former nomadic life adopted a higher civilization, and assumed the sovereignty over cultivated peoples” (Cajori 99). Due to this change in culture,t he Abbasid Empire was able to bridge the gap between two of the most dominant civilizations in mathematic history; the Greeks and the Italians. At the time of Islamic expansion, much of the world had fallen into massive intellectual decline. The quest for knowledge had faltered as civilizations were forced to fight for survival. Islamic scholars played a critical role in retrieving scholarly works from these civilizations and preserving them for future use. According to to Carl Boyer in his book, also titled A History of Mathematics, “Had it not been for the sudden cultural awakening in Islam during the second half of the eighth century, considerably more of ancient science and mathematics would have been lost” (Boyer 227). Islamic scholars did more than just preserve mathematical history. Persian mathematicians, Abu Ja’far Muhammad ibn Musa Al-Khwarizmi, Abu Bakr al-Karaji, and Omar Khayyam, attached rules and provided logical proofs to Grecian geometry thus creating a new field of mathematics called algeb...
The culture of Ancient Egypt is identified and very well known for many aspects of their ways of life. Considering the time period, they were very technologically advanced. This can especially be seen through the great pyramids and hieroglyphs that elaborately decorate the walls of them. Pyramids were not small structures. In fact the largest one was over fifty stories high. In addition they were also built completely by manual labor. Labor consisted of moving limestone blocks that weighed on average 2.5 metric tons and could weigh up to 15 metric tons. In addition they had to form these blocks, move them, and sculpt them into the great structures known as the Pyramids. As you can imagine they took several decades of day in and day out work to complete these massive structures. The hieroglyphs were also an important part of not only the Ancient Egyptian culture but the pyramids especially. They provided pictorial descriptions for burial chambers, temples, jewelry, and important statues. Ways to decipher them were unknown until the discovery of what is known as the Rosetta Stone. It was a stone that showed the same text in three different languages. Then early in the 19th century a French scholar name Jean Francois Champollion was able to decipher it and later on aid in learning the language of the dead language of hieroglyphs. Hieroglyphs are still being deciphered to this day.
Egyptians, or more accurately, Pharaohs, did not write fractions in the formula that we are accustomed to seeing and using, today. The hieroglyphs, as explained on page 20, chapter three of, Mathematics in the Time of the Pharaohs, were not as efficient, then, because it did not allow for certa...
The math of the Ancient Egyptians is both simple and complex. With their methods of math usage, they could find complex and definite solutions to any problem. This especially came in handy for everyday challenges, not just record keeping and pyramid building. The math of the Egyptians is both extensive and accurate.
Egypt is one of the oldest civilizations in the world that appeared before writing and chronicling history. It was settled by primitive peoples from ancient times back to the Late Stone Age (110 thousand years BC). Egypt is also famous for archeology and art, most notably the pyramids.
Henrik Ibsen’s A Doll’s House is a three-act play significant for its attitude toward marriage norms. In the drama, Ibsen explores idealism between the wife Nora and her husband Helmer. Nora’s and Helmer’s idealism forces the pair to see themselves and each other starring in various idealist scenarios of female sacrifice and heroic male rescue. As a play, the scenes are act out on stage. The staging of a house reveals the dramaturgical aspects and dynamics of the play. The presence of the house is significant to the depiction of women on stage. The action of the play traces Nora’s relationship to the house. Ibsen’s play focuses on the aspect of the expected idealism of the wife and husband, and how the domestic abode can hinder freedom.
The enforcement of specific gender roles by societal standards in 19th century married life proved to be suffocating. Women were objects to perform those duties for which their gender was thought to have been created: to remain complacent, readily accept any chore and complete it “gracefully” (Ibsen 213). Contrarily, men were the absolute monarchs over their respective homes and all that dwelled within. In Henrik Ibsen’s play, A Doll’s House, Nora is subjected to moral degradation through her familial role, the consistent patronization of her husband and her own assumed subordinance. Ibsen belittles the role of the housewife through means of stage direction, diminutive pet names and through Nora’s interaction with her morally ultimate husband, Torvald. Nora parades the façade of being naïve and frivolous, deteriorating her character from being a seemingly ignorant child-wife to a desperate woman in order to preserve her illusion of the security of home and ironically her own sanity. A Doll’s House ‘s depiction of the entrapment of the average 19th century housewife and the societal pressures placed upon her displays a woman’s gradual descent into madness. Ibsen illustrates this descent through Torvald’s progressive infantilization of Nora and the pressure on Nora to adhere to societal norms. Nora is a woman pressured by 19th century societal standards and their oppressive nature result in the gradual degradation of her character that destroys all semblances of family and identity.Nora’s role in her family is initially portrayed as being background, often “laughing quietly and happily to herself” (Ibsen 148) because of her isolation in not only space, but also person. Ibsen’s character rarely ventures from the main set of the drawi...
A Doll’s House is a modern drama written in 1879 by Henrick Ibsen that takes place in Norway during Christmas time. According to Kate Millett Ibsen is the first writer since the “Greeks to challenge the myth of male dominance,” (Durbach5) which is clearly demonstrated in this particular drama. The plays protagonist is Nora Helmer who is being blackmailed for a past decision. Nora, had to get enough money in order to take a trip to Italy that would save her husband’s life, without him knowing. The intent of this drama was to show the obligations and the role that a woman plays, specifically relating to her family. Henrik’s character, Nora Helmer has stirred up some major controversy. Critics disagree on if Nora Helmer is a good or a bad wife
The Allegory poem tells a story while having a deeper meaning this makes a poem intriguing as it makes the reader interpret the meaning in various ways. Robert Frost was a master of poetry he used figurative language to guide the reader on a journey through imagery. One of the most misunderstood poems by Frost is The Road Not Taken, Frost uses an introspection on life choices and not regretting taking the road less traveled.
There have been many prosperous civilizations throughout the history of the world. Many of them became very large, and lasted for a countless number of years. The most successful and large scale civilization, however, was that of Ancient Egypt. Although it lies in the middle of the largest desert in the world, egyptians were able to use their intelligence to utilize the Nile River and cultivate the surrounding land for farming. They came up with very unique conceptual ideas that benefitted them greatly, and discovered many new things that would impact society around the world to this day. For all of these reasons and many more, Ancient Egypt was the most advanced civilization of its time.
The history of mathematics has its roots on the African continent. The oldest mathematical object was found in Swaziland Africa. The oldest example of arithmetic was found in Zaire. The 4000 year old, Moscow papyrus, contains geometry, from the Middle Kingdom of Egypt, Egypt was the cradle of mathematics. The great Greek mathematicians, including Pythagoras, Thales, and Exodus all acquired much of their mathematics from Egypt, including the notion of zero. This paper will discuss a brief history of mathematics in Africa. Starting with the Lebombo bone and the Ishango Bone, I will then present Egyptian mathematics and end with a discourse on Muslim mathematics in African. “Most histories of mathematics devote only a few pages to Africa and Ancient Egypt... Generally they ignore the history of mathematics in Africa … and give the impression that this history either did not exist or, at least …is not knowable.”
Some similar techniques used by Frost in ‘Stopping By Woods’ and ‘The Road Not Taken’ are repetition and metaphors. The continual use of metaphors in both of these poems adds a certain depth to the poems, another layer of meaning. For example, “And miles to go before I sleep.” This line is the closing line of the poem ‘Stopping By Woods’, it may seem like the persona is talking about the length he has to travel before he can rest or before he reaches his destination, but this last line is repeated. This repetition reinforces Frost’s metaphoric connotations of sleep for death, linking this to the main things the persona has to do before he dies. Similarly, metaphors are used in ‘The Road Not Taken’ also, “Two roads diverged in a yellow wood,” is the opening line in this poem. It has special significance because it hints to the main meaning of the poem. It may seem like the persona is talking about a fork that occurred in the road that he was travelling along in autumn, but there is underlying meaning. “Two roads diverged in a yellow wood,” shows that he had a choice about what direction to take in life, or a decision to make. This gives a deeper meaning to Frost’s poetry so that ...
In conclusion, it is clear that while their ancient civilization perished long ago, the contributions that the Egyptians made to mathematics have lived on. The Egyptians were practical in their approach to mathematics, and developed arithmetic and geometry in response to transactions they carried out in business and agriculture on a daily basis. Therefore, as a civilization that created hieroglyphs, the decimal system, and hieratic writing and numerals, the contributions of the Egyptians to the study of mathematics cannot and should not be overlooked.
The basic of mathematics was inherited by the Greeks and independent by the Greeks beg the major Greek progress in mathematics was from 300 BC to 200 AD. After this time progress continued in Islamic countries Unlike the Babylonians, the Egyptians did not develop fully their understanding of mathematics. Instead, they concerned themselves with practical applications of mathematics. Mathematics flourished in particular in Iran, Syria and India from 450B.C. Major progress in mathematics in Europe began again at the beginning of the 16th Century.