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Ancient Egyptian Mathematics Essay Example For Students

Ancient Egyptian Mathematics Essay 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 Osiriss wife and their son was Horus. Seth was Osiriss evil brother and Nephthys was Seths 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. .u94c5b61f5f2cbe1559af25bb26072815 , .u94c5b61f5f2cbe1559af25bb26072815 .postImageUrl , .u94c5b61f5f2cbe1559af25bb26072815 .centered-text-area { min-height: 80px; position: relative; } .u94c5b61f5f2cbe1559af25bb26072815 , .u94c5b61f5f2cbe1559af25bb26072815:hover , .u94c5b61f5f2cbe1559af25bb26072815:visited , .u94c5b61f5f2cbe1559af25bb26072815:active { border:0!important; } .u94c5b61f5f2cbe1559af25bb26072815 .clearfix:after { content: ""; display: table; clear: both; } .u94c5b61f5f2cbe1559af25bb26072815 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u94c5b61f5f2cbe1559af25bb26072815:active , .u94c5b61f5f2cbe1559af25bb26072815:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u94c5b61f5f2cbe1559af25bb26072815 .centered-text-area { width: 100%; position: relative ; } .u94c5b61f5f2cbe1559af25bb26072815 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u94c5b61f5f2cbe1559af25bb26072815 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u94c5b61f5f2cbe1559af25bb26072815 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u94c5b61f5f2cbe1559af25bb26072815:hover .ctaButton { background-color: #34495E!important; } .u94c5b61f5f2cbe1559af25bb26072815 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u94c5b61f5f2cbe1559af25bb26072815 .u94c5b61f5f2cbe1559af25bb26072815-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u94c5b61f5f2cbe1559af25bb26072815:after { content: ""; display: block; clear: both; } READ: Vegetarianism EssayNumbers 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.

Acid And Base Lab Report Essay Example

Acid And Base Lab Report Paper My hypothesis for these solutions is ammonia is acid, vinegar is neutral, rain cleaner is base, soft drink is base, baking soda is base, detergent is base, and lemon juice is an acid. For the red cabbage it would be the same as using red and blue litmus. If the pH number of the solutions is less than 7 then lemon juice is the only that is acid but it’s weak. If the pH number of the solutions is greater than 7 then ammonia, drain cleaner, soft drink, baking soda, and detergent are bases. If a solution equals 7 then vinegar is neutral. Some of the materials are red litmus paper, blue litmus paper, hydration paper, pipettes, and 12 well spot plates. The other materials that are chemicals or solutions are red cabbage juice, drain cleaner (Noah), detergent, baking soda (Enhance), ammonia (NH), soft drink, distilled water, vinegar (CHICHI), and lemon juice. For Part A the first step is on a paper towel lay-out seven pieces of red litmus paper, seven pieces of blue litmus paper, and seven pieces of hydration paper. Second step is use the pipette place one drop of the first solution on the red litmus paper and record observations. Third step is use the pipette place one drop of the first solution on the blue litmus paper and record observations. Acid And Base Lab Report Essay Sample We will write a custom essay sample on Acid And Base Lab Report specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Acid And Base Lab Report specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Acid And Base Lab Report specifically for you FOR ONLY $16.38 $13.9/page Hire Writer Acid and Base Lab Report Acid and Base Lab Report Acid and Base Lab Report The fourth and last step is repeat steps 2-4 with the remaining solutions. For Part B the first step is on a sheet of paper draw a diagram of a spot plate and decide which well will be used for each solution, then place a spot on the paper diagram. The second step is add 10 drops of each of the solutions to their own well in the spot plate. The third and last step is add 5 drops of the red cabbage indicator and record observations. My data is that with the red litmus the solutions that turn blue are ammonia, drain cleaner, baking soda, detergent, and lemon juice. The solutions that stayed the same when the solution makes contact with red litmus are vinegar and soft drink. For the blue litmus the mostly stayed the same except lemon juice it turned pink. I have learned how to use the pH scale and also how to determine if the solutions are acids, bases, and neutral. For my hypothesis I was right I didn’t mess because basically studied my notes before doing the lab. This lab made me learn more because I didn’t really how to use the pH scale but now I do because had to use it in this lab.