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How do we find the the two farthest points  on a 3D object? For example, we know that on a circle, any two points that are diametrically opposite will be the  farthest from each other than from any other points on the circle. Which two points will be the farthest from each other on a square? The diagonally opposite vertices. Now here is a trickier question which two points are farthest from each other on a rectangular solid? Again, they will be diagonally opposite, but the question is, which diagonal? A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box? (A) 15 (B) 20 (C) 25 (D) 10 * √(2) (E) 10 * √(3) There are various different diagonals in a rectangular solid. Look at the given figure: BE is a diagonal, BG is a diagonal, GE is a diagonal, and BH is a diagonal. So which two points are farthest from each other? B and E, G and E, B and G, or B and H? The inside diagonal BH can be seen as the hypotenuse of the right triangle BEH. So both BE and EH will be shorter in length than BH. The inside diagonal BH can also be seen as the hypotenuse of the right triangle BHG. So both HG and BG will also be shorter in length than BH. The inside diagonal BH can also be seen as the hypotenuse of the right triangle BDH. So both BD and DH will also be shorter in length than BH. Thus, we see that BH will be longer than all other diagonals, meaning B and H are the points that are the farthest from each other. Solving for the exact value of BH then should not be difficult. In our question we know that: l = 10 inches w = 10 inches h = 5 inches Let’s consider the right triangle DHB. DH is the length, so it is 10 inches. DB is the diagonal of the right triangle DBC. If DC = w = 10 and BC = h = 5, then we can solve for DB^2 using the Pythagorian Theorem: DB^2 = DC^2 + BC^2 DB^2 = 10^2 + 5^2 = 125 Going back to  triangle DHB, we can now say that: BH^2 = HD^2 + DB^2 BH^2 = 10^2 + 125 BH = √(225) = 15 Thus, our answer to this question is A. Similarly, which two points on a cylinder will be the farthest from each other? Lets examine the following practice GMAT question to find out: The radius of cylinder C is 5 inches, and the height of cylinder C is 5 inches. What is the greatest possible straight line distance, in inches, between any two points on a cylinder C? (A) 5 * √2 (B) 5 * √3 (C) 5 * √5 (D) 10 (E) 15 Look at where the farthest points will lie diametrically opposite from each other and also at the opposite sides of the length of the cylinder: The diameter, the height and the distance between the points forms a right triangle. Using the given measurements, we can now solve for the distance between the two points: Diameter^2 + Height^2 = Distance^2 10^2 + 5^2 = Distance^2 Distance = 5 * √5 Thus, our answer is C. In both cases, if we start from one extreme point and traverse every length once, we reach the farthest point. For example, in case of the rectangular solid, say we start from H, cover length l and reach D from D, we cover length w and reach C, and from C, we cover length h and reach B. These two are the farthest points. Getting ready to take the GMAT? We have  free online GMAT seminars  running all the time. And, be sure to follow us on  Facebook,  YouTube,  Google+, and  Twitter! Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the  GMAT  for Veritas Prep and regularly participates in content development projects such as  this blog!

Copyright Infringement Of The Happy Birthday Song, Along...

Copyright is set out to protect the original artists’ creative work from imitations for a limited time, until it enters the Public Domain. Creators may view this as a much needed law to prevent infringement, which grants the lawful artist the rights to their respective work. However, continuing this practice is redundant as copyright does not accomplish what it has been set out to do. The Blurred Lines Case is used to convey how the Lay Listener Test fails to determine copyright infringement. Adele’s plagiarism allegation is reviewed to show the copies of other work, suggesting that copyright cannot determine who holds original authorship. The invalid copyright of The Happy Birthday Song, along with The Walt Disney Company’s lobbying†¦show more content†¦This showed that jurors were unable to determine if songs were guilty of copyright infringement; since a large majority of Jurors (84.8%) wrongfully stated that the original and the copied song were diff erent in composition. Elements of a Civil Copyright Infringement Claim consists of proving Ownership of a Valid Copyright, Actual Copying, and Misappropriation. Actual Copying is proven through direct or indirect evidence that shows a â€Å"striking similarity† between the two works. In the Blurred Lines Case, indirect â€Å"evidence† was used in â€Å"proving† music recording’s two copyright protections were infringement upon: (1) a copyright in the underlying composition and (2) a copyright in the sound recording. This is problematic as Blurred Lines did not infringe on the Actual Copying claim; jurors confused the underlying composition and sound recording for style, when style is not protectable copyright for music recordings. Copyright fails to determine composition and sound recordings in a Lay Listener Test, and give Thicke and William’s exclusive rights to their respective creations, illustrating how copyright is unreliable. Copyright law encourages the creation of â€Å"original† creative work. Yet, creation requires influence. It is not realistic to say that a song can be completely original, containing innovating composition and sound recording. Artists gain influence from other artists, who have adopted the style of the

Essay about Sight and Blindness in Oedipus Rex - 730 Words

Sight and Blindness in Oedipus Rex Oedipus Rex is a play about the way we blind ourselves to painful truths that we can’t bear to see. Physical sight and blindness are used throughout the play, often ironically, as a metaphor for mental sight and blindness. The play ends with the hero Oedipus literally blinding himself to avoid seeing the result of his terrible fate. But as the play demonstrates, Oedipus, the man who killed his father and impregnated his mother, has been blind all along, and is partly responsible for his own blindness. When the play opens, the people of the town are asking Oedipus for help. A curse has been cast upon the city and the only way to remove it, is to find the murderer of the last king, Laios.†¦show more content†¦It is ironic that the one individual, who comes to help the city, is the individual that has been the cause of the curse. Oedipus is the illness. Oedipus and Jocasta both don’t want to see the truth. Although it may occur to them at some point, but the y don’t give it a second thought because they think it is absurd and it isn’t possible. â€Å"Why should anyone in this world be afraid, since fate rules us and nothing van be forseen? A man should live only for the present day. Have no more fear of sleeping with your mother: How many men, in dreams, have lain with their mothers! No reasonable man is troubled by such things.† Jocasta is further from believing than Oedipus, she constantly tells him not to worry about it, don’t get worked up, and to just forget what you were told. Oedipus cannot forget what the oracle has said and goes on to pursue the case. Through the course of the play Oedipus is the detective, the judge, and the jury. He investigates, decides a verdict, and carries out his own punishment. When Tiresias arrives at Thebes Oedipus questions him looking for answers. Tiresias is a blind man, who ironically can see the future and truths of people’s lives. It is Tiresias who is the first person to tell Oedipus that he has killed his own father. He tells Oedipus â€Å"you do not see the evil in which you live.† Oedipus doubts Tiresias’ ability to see the truths because of his physical blindness and states, â€Å" YouShow MoreRelatedEssay on Sight and Blindness in Oedipus Rex1311 Words   |  6 PagesIn the play Oedipus Rex by Sophocles, the themes of sight and blindness are developed in a way to communicate to the reader that it is not eyesight itself, but insight that holds the key to truth and, without it, no amount of knowledge can help uncover that truth. Some may define insight as the abilit y to intuitively know what is going to happen, or simply as the capacity to understand the true nature of a situation. Both definitions hold a significant role in the play, not only for more obviousRead MoreOedipus Rex: Imagery of Blindness and Sight as a Medium to the Themes1218 Words   |  5 PagesIn the play, Oedipus Rex, written by Sophocles, an honourable and admirable Greek king named Oedipus rules the town of Thebes. He is left in mental turmoil and decay as his unknown, corrupt and immoral past is slowly revealed during his quest to find the culprit who murdered King Laius. The newly exposed past suddenly transforms his glory and respect into shame and humiliation. After he learns about his wicked past he stabs his eyes, which lead to his blindness. During the course of the play, referencesRead More Blindness and Sight - Sight Versus Insight in Oedipus the King (Oedipus Rex)1357 Words   |  6 PagesSight Versus Insight in Oedipus the King      Ã‚  Ã‚   Anyone who has common sense will remember that the bewilderments of the eye are of two kinds, and arise from two causes, either from coming out of the light or from going into the light,which is true of the minds eye, quite as much as the bodily eye; and he who remembers this when he sees anyone whose vision is perplexed and weak, will not be too ready to laugh; he will ask whether that soul of man has come out of the brighter life, and is unableRead MoreThroughout most famous Greek literature, a great hero usually saves the day. In the story of900 Words   |  4 Pagesusually saves the day. In the story of Oedipus though, the good man with one minor flaw goes through great pain. This pain in the play Oedipus Rex is the focal point for the whole play. Almost every aspect of the play builds up and foreshadows Oedipus’ fall from power, and entry into pain. Sophocles in his tragedy Oedipus Rex creates a mood of dramatic irony using the dualities of sight and bli ndness, and light and darkness. This dramatic irony highlights Oedipus’ hamartia and in doing so SophoclesRead MoreOedipus Rex Is A Greek Tragedy Written By Sophocles1177 Words   |  5 PagesOedipus Rex is a Greek tragedy written by Sophocles. Sophocles, through writing this work along with Antigone and Oedipus at Colonus, became a legendary tragedian, and went off to produce several other works. This classic tragedy held great influence over Aristotle’s six components in his work, the Poetics, more specifically, over the component of plot and character. The birth of Oedipus Rex since spurred countless famous interpretations, including ones by the father of psychoanalysis himself, SigmundRead More The Role of Teiresias in Sophocles Oedipus Rex Essay1410 Words   |  6 PagesSophoclesOedipus Rex (the King) Teiresias uses his psychic abilities to foreshadow the anguish and destruction that Oedipus will encounter after he learns the truths of his life. Teiresias is also responsible for further developing the theme of blindness by using his own physical blindness to reveal to Oedipus his mental blindness. Lastly, Teiresias is ultimately responsible for imposing dramatic irony because of his great knowledge of the truth of Oedipus. In the play, Oedipus Rex, by SophoclesRead MoreHuman Will and the Power of the Gods: Oedipus Rex by Sophocles1363 Words   |  6 Pagesaccomplished only by some. Sophocles’ Oedipus Rex is considered today as one of the greatest tragedies produced by an author during this time. Carefully crafted motifs, character-developing monologues, and poignant irony all combine to create a tragedy that leaves readers stunned and grieving for poor Oedipus. Throughout Oedipus Rex, the motif of blindness and sight emphasizes the struggle between the power of free wi ll and the power of the gods made evident in Oedipus’ interactions with Tiresias, Jokasta’sRead MoreThe True Vision of Blindness in Oedipus Rex by Sophocles Essay959 Words   |  4 Pagesthey are blind to it. In Oedipus Rex by Sophocles it is easy to see how blindness affects the transition of the story. It is said that blind people see â€Å"in a different manner† because they sense the world in a totally diferent way, such as Teiresias in the play. Oedipus Rex is a tragedy due to the content the Sophocles, the playwright, decided to include, first, murdering his father, king Laius, then marrying his mother, Jocasta, and ending by blinding himself. Oedipus has been blinded to the truthRead MoreThe Value Of Leadership In Oedipus Rex By Sophocles1326 Words   |  6 PagesBased on evidence, Athenians valued bravery, confidence and heroic strength in their leaders. For example, the entire reason Oedipus from Oedipus Rex by Sophocles became king of Thebes is beca use he defeated the Sphinx that was guarding the city, saving the citizens (info from the backstory). On page 11, a senator makes the comment, â€Å"if his bosom holds a grain of fear, curses like yours he never will abide.† The reader can assume the Athenians valued bravery because the senator makes a comment againstRead MoreOedipus the King and The Tragedy of King Lear Essay1272 Words   |  6 PagesSophocles’ Oedipus Rex and William Shakespeare’s The Tragedy of King Lear One of the key themes in both Shakespeare’s The Tragedy of King Lear and Sophocles’ Oedipus Rex is the importance of having a good understanding of our condition as human beings – knowing ourselves, the world that surrounds us and our place in it. At the same time, however, both authors recognize the fact that blindness to this knowledge of the human condition is a basic mortal trait. Thus, before we can have an

Solar Cells Essay Research Paper Example For Students

Solar Cells Essay Research Paper Word Count: 1045 today are mostly made of silicon, oneof the most common elements on Earth. Thecrystalline silicon solar cell was one of the firsttypes to be developed and it is still the mostcommon type in use today. They do not pollutethe atmosphere and they leave behind no harmfulwaste products. Photovoltaic cells workeffectively even in cloudy weather and unlike solarheaters, are more efficient at low temperatures. They do their job silently and there are no movingparts to wear out. It is no wonder that one marvelson how such a device would function. Tounderstand how a solar cell works, it is necessaryto go back to some basic atomic concepts. In thesimplest model of the atom, electrons orbit acentral nucleus, composed of protons andneutrons. each electron carries one negativecharge and each proton one positive charge. Neutrons carry no charge. Every atom has thesame number of electrons as there are protons, so,on the whole, it is electrically neutral. Theelectrons have discrete kinetic energy levels, whichincrease with the orbital radius. When atoms bondtogether to form a solid, the electron energy levelsmerge into bands. In electrical conductors, thesebands are continuous but in insulators andsemiconductors there is an energy gap, in whichno electron orbits can exist, between the innervalence band and outer conduction band Book1. Valence electrons help to bind together theatoms in a solid by orbiting 2 adjacent nucleii,while conduction electrons, being less closelybound to the nucleii, are free to move in responseto an applied voltage or electric field. The fewerconduction electrons there are, the higher theelectrical resistivity of the material. Insemiconductors, the materials from which solarsells are made, the energy gap Eg is fairly small. Because of this, electrons in the valence band caneasily be made to jump to the conduction band bythe injection of energy, either in the form of heat orlight Book 4. This explains why the highresistivity of semiconductors decreases as thetemperature is raised or the material illuminated. The excitation of valence electrons to theconduction band is best accomplished when thesemiconductor is in the crystalline state, i.e. whenthe atoms are arranged in a precise geometricalformation or lattice. At room temperature andlow illumination, pure or so-called intrinsicsemiconductors have a high resistivity. But theresistivity can be greatly reduced by doping, i.e. introducing a very small amount of impurity, of theorder of one in a million atoms. There are 2 kindsof dopant. Those which have more valenceelectrons that the semiconductor itself are calleddonors and those which have fewer are termedacceptors Book 2. In a silicon crystal, eachatom has 4 valence electrons, which are sharedwith a neighbouring atom to form a stabletetrahedral structure. Phosphorus, which has 5valence electrons, is a donor and causes extraelectrons to appear in the conduction band. Siliconso doped is called n-type Book 5. On theother hand, boron, with a valence of 3, is anacceptor, leaving so-called holes in the lattice,which act like positive charges and render thesilicon p-typeBook 5. The drawings in Figure1.2 are 2-dimensional representations of n- andp-type silicon crystals, in which the atomic nucleiiin the lattice are indicated by circles and thebonding valence electrons are shown as linesbetween the atoms. Holes, like electrons, willremove under the influence of an applied voltagebut, as the mechanism of their movement isvalence electron substitution from atom to atom,they are less mobile than the free conductionelectrons Book 2. In a n-on-p crystalline siliconsolar cell, a shadow junction is formed by diffusingphosphorus into a boron-based base. At thejunction, conduction electrons from donor atomsin the n-region diffuse into the p-region andcombine with holes in acceptor atoms, producinga layer of negatively-charged impurity atoms. Theopposite action also takes place, holes fromacceptor atoms in the p-region crossing into then-region, combining with electrons and producingpositively-charged impurity atoms Book 4. Thenet result of these movements is the disappearanceof conduction electrons and holes from the vicinityof the junction and the establishment there of areverse electric field, which is positive on then-side and negative on the p-side. This reversefield plays a vital part in the functioning of thedevice. The area in which it is s et up is called thedepletion area or barrier layerBook 4. Whenlight falls on the front surface, photons with energyin excess of the energy gap (1.1 eV in crystallinesilicon) interact with valence electrons and lift themto the conduction band. This movement leavesbehind holes, so each photon is said to generatean electron-hole pair Book 2. In the crystallinesilicon, electron-hole generation takes placethroughout the thickness of the cell, inconcentrations depending on the irradiance andthe spectral composition of the light. Photonenergy is inversely proportional to wavelength. .udd589f6a8781cc73ba54363732e57486 , .udd589f6a8781cc73ba54363732e57486 .postImageUrl , .udd589f6a8781cc73ba54363732e57486 .centered-text-area { min-height: 80px; position: relative; } .udd589f6a8781cc73ba54363732e57486 , .udd589f6a8781cc73ba54363732e57486:hover , .udd589f6a8781cc73ba54363732e57486:visited , .udd589f6a8781cc73ba54363732e57486:active { border:0!important; } .udd589f6a8781cc73ba54363732e57486 .clearfix:after { content: ""; display: table; clear: both; } .udd589f6a8781cc73ba54363732e57486 { 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; } .udd589f6a8781cc73ba54363732e57486:active , .udd589f6a8781cc73ba54363732e57486:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .udd589f6a8781cc73ba54363732e57486 .centered-text-area { width: 100%; position: relative ; } .udd589f6a8781cc73ba54363732e57486 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .udd589f6a8781cc73ba54363732e57486 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .udd589f6a8781cc73ba54363732e57486 .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; } .udd589f6a8781cc73ba54363732e57486:hover .ctaButton { background-color: #34495E!important; } .udd589f6a8781cc73ba54363732e57486 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .udd589f6a8781cc73ba54363732e57486 .udd589f6a8781cc73ba54363732e57486-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .udd589f6a8781cc73ba54363732e57486:after { content: ""; display: block; clear: both; } READ: State and Church EssayThe highly energetic photons in the ultra-violet andblue part of the spectrum are absorbed very nearthe surface, while the less energetic longer wavephotons in the red and infrared are absorbeddeeper in the crystal and further from the junctionBook 4. Most are absorbed within a thicknessof 100 ?m. The electrons and holes diffusethrough the crystal in an effort to produce an evendistribution. Some recombine after a lifetime of theorder of one millisecond, neutralizing their chargesand giving up energy in the form of heat. Othersreach the junction before their lifetime has expired. There they are separated by the reverse field, theelectrons being accelerated towards the negativecontact and the holes towards the positive Book5. If the cell is connected to a load, electrons willbe pushed from the negative contact through theload to the positive contact, where they willrecombine with holes. This constitutes an electriccurrent. In crystalline silicon cells, the currentgenerated by radiation of a particular spectralcomposition is directly proportional to theirradiance Book 2. Some types of solar cell,however, do not exhibit this linear relationship. The silicon solar cell has many advantages such ashigh reliability, photovoltaic power plants can beput up easily and quickly, photovoltaic powerplants are quite modular and can respond tosudden changes in solar input which occur whenclouds pass by. However there are still somemajor problems with them. They still cost toomuch for mass use and are relatively inefficientwith conversion efficiencies of 20% to 30%. Withtime, both of these problems will be solvedthrough mass production and new technologicaladvances in semiconductors. Bibliography 1)Green, Martin Solar Cells, Operating Principles,Technology and System Applications. NewJersey, Prentice-Hall, 1989. pg 104-106 2)Hovel, Howard Solar Cells, Semiconductors andSemimetals. New York, Academic Press, 1990. pg 334-339 3) Newham, Michael ,Photovoltaics,The Sunrise Industry, Solar Energy, October 1,1989, pp 253-256 4) Pulfrey, DonaldPhotovoltaic Power Generation. Oxford, VanNorstrand Co., 1988. pg 56-61 5) Treble,Fredrick Generating Electricity from the Sun. NewYork, Pergamon Press, 1991. pg 192-195