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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.

Issues over the Presidency essays

Issues over the Presidency essays While I was reading through the issues, there was two that really struck home with me that the two presidential candidates talked about. The first issue that they talked about was Drugs. President Bush believes that we need to be more aggressive in teaching drug education, providing treatment and enforcement of laws. Presidential candidate John Kerry admitted he has smoked marijuana and believes that we should target the traffickers as well as reducing the need for it at home. Kerry voted no for funding drug control and for higher drug penalties. The second issue talked about by the candidates was education. President Bush Says we nee to progress ourselves toward achieving excellence for every child to succeed. He says we should raise the standards and focus on the results for our schools. In return for the high standards and results from the students efforts will come freedom and flexibility. He also says he will fund early intervention programs to help high-schoolers in their educational needs. John Kerry on the other hand says we need to invest are money into the child not the prison system. He nails President Bush with saying he did not fully fund the No Child Left Behind Act. He Says we need to roll back tax cuts for the rich so that they can fund the educational needs. He claims we should measure learning but with a flexible standard. He also claims that providing student loans for college kids is an ethical issue. ...

Regulating Cross Media Ownership Essays

Regulating Cross Media Ownership Essays Regulating Cross Media Ownership Essay Regulating Cross Media Ownership Essay Regulating Cross-Media Ownership According to political theorists Noam Chomsky and Edward Herman The media is unable to satisfy our democratic needs because: They are profit-seeking businesses, owned by very wealthy people (or other companies); they are funded largely by advertisers who are also profit-seeking entities, and who want their ads to appear in a supportive selling environment. The media are also dependent on government and major business firms as information sources, and both efficiency and political considerations, and frequently overlapping interests, cause a certain degree of solidarity to prevail among the government (as cited in Levin 39). Therefore, with aforementioned factors, large corporations and government entities control the flow of information. The fact is much of the information audiences receive via media outlets, provide us with the â€Å"successes and failures of government† (Levin 39), meaning the media tells us what to think and how to take action. It is crucial for viewers alike to obtain a variety of news, opinions, and freely expressed ideas. The media has the power to greatly influence; much like the three branches of U. S. government, the media must have check-and-balance provisions set in place so to alleviate any possible abuses made by those with majority power. Similarly, the media must ensure that â€Å"proprietors’ pursuit of their private interests correspond to the public good†¦(which) produces a press which is diverse, accountable and representative [of its viewers, respectively],† (Levin 39). The fact is, those who have the control matter. â€Å"Media ownership regulations focus on who controls the particular media company,† therefore, they have control over editorial content, and utilize the media outlets by promoting their own â€Å"commercial or political interests† (Levin 39). And, because most enterprising media players have â€Å"friends in high places† e. g. politicians, lobbyists, etc. messages are presented in a biased manner, rather than remaining impartial to their allies and presenting all possible facts with all possible sides. One way to remedy this situation would be to â€Å"separate editorial leadership within each commonly owned media outlet† (Levin 40), so as to secure an unguarded democracy guided by competition, diversity, and localism. In 1996, the Telecommunications Act required the Federal Communications Commission (FCC) to review its media ownership rules, seeing that all rules are still relevant to the technologically advancing times, while remaining in the public interests of its viewers, which is the first and foremost principle to be â€Å"protected above all remains†¦ to which these proceedings must refer† (Obar 521). As well, Congress allowed the FCC â€Å"to take deregulatory steps to eliminate barriers that discouraged entry by new competition† (â€Å"Limits on Media Concentration† 2003). Essentially, the premise behind the rules of media ownership are that they provide a safeguard for the American populace and subsequently ensure our First Amendment rights establishing not only a diverse media market, but one with driving competitive forces, vital for any form of democracy (â€Å"Limits on Media Concentration†). Again, rules have and always will change with society’s modern advances; for example, â€Å"Efforts are underway to drop the rules allowing television broadcasters to own more local stations and to permit media cross-ownership in a single market†, and â€Å"Opponents say that the rules would give giant corporations too much clout at the expense of communities†¦quashing opportunities for independent companies† (Limits of Media Concentration†). In addition, rising media market shares providing its viewers with less varied news sources and journalistic quality, leaving us with a vertically homogenized media model, ignoring community interests, diversity, and values. Given the efforts, as previously stated, it is vital for smaller media players to have a voice so that viewers may be presented with diverse regional and local content, allowing us to make our own decisions, rather than being told which side to reason with. In whole-hearted agreement with Levin, â€Å"It is crucial that we continue to scrutinize what is presented to us for underlying context and perspective (or lack of it), regardless of who owns the media outlet that presents it. † For years, the views we are presented have been consolidated by a handful of high playing media corporations; limited information is being carried through to its audience, and of which, it is presented in a biased fashion. If society does not scrutinize the content its being served and by whom, varied political, social, and cultural perspectives will be restricted causing a one-way, carbon copy of chosen information. Society must lobby for more media dissemination; however, â€Å"Media policy makers have struggled to construct policies that will widen the available viewpoints to include those of minorities, women, and individuals representing [varied social and cultural perspectives]†¦Ã¢â‚¬  (Hillard 56). Promoting diversity within the media will comes through greater ownership restrictions, promotion of ownership by women and minorities, â€Å"the Fairness Doctrine, [and] equal time requirements†, therefore impeding the parochial media model as set forth today. According to Hillard, â€Å"†¦ the need to preserve public policies favoring diversity and antitrust provisions that restrict monopolization of markets by media companies is clear†, hence the reason why we must limit monopolizing media mergers and create opportunities for independently owned outlets in television, radio, and the newspapers. As Walter Lippman once wrote, â€Å"The theory of the free press is that truth will emerge from free discussion, not that it will be presented perfectly and instantly in any one account. † Bibliography Compaine, Ben. Domination Fantasies. (Cover story). Reason 35. 8 (2004): 26-33. Academic Search Premier. EBSCO. Web. 9 Dec. 2010. Hillard, Robert and Picard, Robert. â€Å"Plurality, Diversity, and Prohibitions on Television- Newspaper Crossownership. Journal of Media Economics Vol. 2 Issue 1 (1989): 55-65. Communication Mass Media Complete. EBSCO. Web. 9 Dec. 2010. Levin, Jane. CROSS-MEDIA OWNERSHIP: THE DEBATE CONTINUES. Australian Screen Education 33 (2004): 38-41. Academic Search Premier. EBSCO. Web. 7 Dec. 2010. Limits on Media Concentration. Congressional Digest 82. 8 (2003): 230. Academic Search Premier. EBSCO. Web. 8 Dec. 2010. Marks, Alexandra. Media future: Risk of monopoly? Christian Science Monitor 19 Sept. 2002: 2. Academic Search Premier. EBSCO. Web. 12 Dec. 2 010. Media Ownership. Congressional Digest 82. 8 (2003): 225. Academic Search Premier. EBSCO. Web. 6 Dec. 2010. Obar, Jonathan A. Beyond Cynicism: A Review of the FCCs Reasoning for Modifying The Newspaper/Broadcast Cross-Ownership Rule. Communication Law Policy 14. 4 (2009): 479-525. Academic Search Premier. EBSCO. Web. 9 Dec. 2010.

Evidence for (or against) water on Mars Research Paper

Evidence for (or against) water on Mars - Research Paper Example Scientists pondered the possibility of life on the red planet, while artists and dreamers such as H.G. Wells took the notion even further, imagining a Martian conquest of Earth in his 1898 book "War of the Worlds."† (Doydey and Lamb). Some astronomers argue that water exists on mars planet in the form of water ice. Many scientists claim that Mars contains water because it supports life of all forms. The Mars volcanic activities that lead to freezing and melting of ice can be another example of underground water existence. Polar ice caps can exemplify water existence on Mars because of carbon dioxide ice. Therefore, volcanic activities, the existence of polar ice caps and presence of chemical compounds on the Martian surface rocks confirm water in the Mars planet. Notwithstanding that there were hundreds of investigation held, the issue is still controversial and needs further research. However, this research can be implemented only with the help of further technological achieve ments. The planet Mars consists of water in the form of ice. Mars planet has two polar ice caps, which are constant. The Martian pole in winter is in constant darkness and the surface is chilled. This contributes to approximately 30 percent of the atmosphere, which is in the form of carbon dioxide ice (dry ice).... Dowdey and Lamb agree with his â€Å"Mars is replete with water, but most (if not all) of it is in frozen or vapor form. For instance, ice caps the planet's poles, and patches of ice lie over dunes in craters† (Dowdey and Lamb).The Martian surface rocks occur in high latitude areas, which are known as permafrost, which is in a freezing state below the 0 °C. Most permafrost areas are located in high latitudes, and ice is not always present, but they occur due to hydraulic saturation of the bedrock materials. Water vapor is always presented in the atmosphere but the permafrost is lacking of liquid water. The present condition of the surface of many planets does no longer support the existence of water in liquid form for a longer period. This is because the atmospheric temperature is too low. In this case immediate freezing and sublimation processes occur. The research study indicates that the liquid water exists in liquid water flow on the earth’s surfaces thus creating larger surface areas for oceans or seas. There are varied proofs about the presence of water in Mars. With increased technology, the scientists are now able to use advanced cameras of Mars orbiters including the mars odyssey, global mass surveyor and reconnaissance orbiters for visual confirmation of the presence of water in the mars planet. With the help of different technical tools modern scientists are very much focused on possible effective ways of water finding on Mars. Quality of water is another important issue for their concern. Further on we will focus on different theories and hypotheses about water existence on Mars planet. NASA's  charge  to  researchers  on  the  mission  has  been  simple:  Ã¢â‚¬Å"Follow the water," meaning examine all aspects of water-or ice on Mars. No water