Greek Achievement essays

Greek Achievement expositions While examining old human advancements, one of the most unmistakable must be the Greek development. Under the standard of different rulers, Greece saw a change from an agnostic loving society that was nearly canceled, to a suffering development that strived on theory, and scholarly idea. As the Greeks apportioned the divine beings in political life, they put together government with respect to human insight. The advancement of the Greek polis, or city-state, from an innate strict foundation to a mainstream normal organization, that is viewed as one of the best throughout the entire existence of humanity, was just a piece of the general change of the Greek brain from fantasy to reason. What isolated the Greeks from other Near Eastern civic establishments, just as gave it suffering centrality, was the Greeks steady acknowledgment that political issues are brought about by man and require natural arrangements. The Greeks additionally had a solid confidence in their arrangement of the city-state yet it in the end would add to their end. These city-states took into consideration much partition inside their political life, and in this way was the reason for much affliction. Greece would persevere through two significant wars, which would shape their development, and have an enduring impact. First was the Persian Wars with Sparta. Since Sparta was a walled city, and couldnt rival the Athenian culture, Athens in the end triumphed. One of the most interesting complexities in this war is the manner by which distinctive the two city-states could be. Athens was situated on the promontory of Attica, close to the coast, had an incredible naval force, and was a business head for the Greeks. Sparta was a land power and was only agrarian. Spartas pioneers sought after an independent international strategy, and had faith in keeping their opportunity on the country. The Athenians had such things as popular government, and broadened their authority over the Greeks. Sadly, after the long fights among Athens and Sparta were at long last laid ... <!

Business Regulation Law

When directing business whether it is nearby and worldwide, enormous or little associations need to comply with state and government laws. Contingent upon the idea of the business distinctive association needs to consent to specific laws and guidelines. For instance, retailers like Wal-Mart, Target and Kroger need to consent to the Department of Labor and an assembling organization like LM Fiberglass and Toyota would need to conform to the Environmental Protection Agency and Occupational Safety and Health Administration (OSHA). At the point when an association don't follow the state and government guideline the organization can confront fines or become made up for lost time in significant case, costing the organization significant costs. In this notice I will distinguish regular tort and hazard found in the association of Alumina, and depict various measures to oversee chance. Some regular torts found at Alumina are carelessness, criticism/criticize/slander, Freedom of Information Act (FOIA), and exacting obligation is tort liabilities revealed. Alumina Violation Alumina is an aluminum producer base in the United States and has activity in eight nations. The aluminum creator is on Lake Dira in the province of Erehwon. Alumina is under the locale of district six under the Environmental Protection Agency. A couple of years back Alumina was found in infringement with the Environmental Protection Agency for ecological release standards in an Environmental Protection Agency consistence assessment. The PAH levels were above recommend limits. Alumina was organization to tidy up the issue in which they went along too rapidly. As a result of this episode Alumina has keep up a decent consistence record. As of late an occupant name Kelly Bates claims that Alumina constant tainting of Lake Dira with toxins. Bates takes steps to document a suit against the organization for correctional harms and recuperation harms. She accepts that the occurrence that happened quite a while prior is the reason for her daughter’s leukemia. Tort Liability A tort is a â€Å"civil wrong that is an obstruction with someone’s individual or property to such an extent that a physical issue results† (Jennings, 2006, p. 367). Torts can be sorted as deliberate torts, torts of carelessness, and exacting obligation torts. Deliberate torts are those that bring about a mischief not coincidental. Torts of carelessness are incidental damages that outcome from an inability to act properly in a given circumstance. Severe risk torts relegate supreme obligation and offer not many guards. Criticism of Character An organization or an individual notoriety is an important resource. The tort of criticism of character necessitates that an offended party demonstrate that: the litigant offered a false expression about the offended party or the announcement was purposefully distributed by an outsider (Cheeseman, 2010). Composed False explanations are alluded to as criticism and verbal proclamation are alluded to as defamation. Bates made a defamation proclamation in the paper about Alumina and the infringement that happened years back. This criticism can negatively affect the organization. Alumina can lose business with an awful notoriety and once the notoriety has turned sour it is difficult to recover the great name. Opportunity of Information Act A neighborhood journalist and Kelly Bates moved toward the EPA to acquire ecological review reports that archived Alumina infringement of the Clean Water Act. Bates mentioned the archives under the Freedom of Information Act; this demonstration was established in Congress in 1966 to the American open extraordinary access to the Federal Government records (Federal Communication Commission, 2010) . The Company decides to discharge fractional review data from the infringement from years back. Alumina has the option to retain instructive this qualifies under the Confidential Business Information, which is accessible under exclusion four of the Freedom of data Act. Severe obligation Negligence and Strict risk Carelessness, the most well-known tort, is clarified as lead that falls underneath measures of conduct built up by the law for the assurance others against outlandish hazard hurt (Cheeseman, 2010). For this situation of carelessness Bates must demonstrate that Alumina had an obligation to keep the PAH levels contained. For a situation Alumina breaks that obligation by not remaining in consistence with the EPA guideline quite a while back. Bates expect that the utilization of the water cause the damage of her girl to have leukemia. Accordingly Alumina decided to lead a free site concentrate for new infringement. The reports return great the PAH levels were well underneath the norm. In the wake of discharging a fractional review report Bates has take steps to document a claim against Alumina of individual injury to recuperate pay and reformatory harms. Alumina careless direct of â€Å"serious infringement of ecological laws five years prior is the reason for her girl leukemia,† affirmed by Bates (Business Regulations Simulation, 2010). The best goals for this circumstance is intervention by an impartial outsider, by picking this choices Alumina can furnish Bates with a classified settlement. The settlement incorporates that Alumina furnishes Bates with repayment of clinical costs for her little girl treatment a single amount for future medications and a school finance put in a safe spot if her little girls recuperates from the leukemia (Business Regulations Simulation, 2010). In spite of the fact that tort obligation is established on expected mischief severe risk is appended despite the fact that the litigant has been sensible. In the Article titled â€Å" The American Influence on Canadian Tort Law† writer Allen M. Linden states â€Å" One individual might be require to repay another for injury or harms despite the fact that the misfortune was neither purposefully or carelessly perpetrated. In the event that Alumina had prosecuted the case, the organization would have been in a long case process costing the organization thousands and even a great many dollar. The intercession procedure is a large portion of the expense of a court preliminary and there is no assurance that the jury would concur with Alumina despite the fact that the organization may have had evidence that the charge against the organization was bogus. The jury will in general side with the people in question. Safeguard, Detective, and Corrective Measures In an association it will be difficult to forestall claim against the organization, yet the organization needs to plan for such issues when they emerge. A precaution plan ought to be established. The organization should focus on it that the representatives of the organization mindful of the standards and guidelines of the state and government laws. The organization ought to know about the contenders who have damaged any administration guidelines and improve their procedure with the goal that the organization won't disregard indistinguishable guidelines from the opposition. Wellbeing hazard that might be opens to the staff, clients, and other ought to be remembered for the record moreover. End Alumina needs to keep state and government manages these laws are set up to improve ecological wellbeing. The office that directs Alumina was the Environmental Protection Agency this organization implements natural laws. Alumina must know and agree to the state and government guidelines at unequaled or it can influence the business a lot. Keeping up a positive picture in the network is likewise significant when an emergency happens the help of the network can be a major assistance in decide issues. The choice mage by Alumina were astute, the organization adopted the correct strategy to keep up its great name in the network and the serious market and spare expense on prosecution.

Tenure of Office Act

Tenure of Office Act Tenure of Office Act, in U.S. history, measure passed on Mar. 2, 1867, by Congress over the veto of President Andrew Johnson ; it forbade the President to remove any federal officeholder appointed by and with the advice and consent of the Senate without the further approval of the Senate. It also provided that members of the President's cabinet should hold office for the full term of the President who appointed them and one month thereafter, subject to removal by the Senate. With this measure the radical Republicans in Congress hoped to assure the continuance in office of Secretary of War Edwin M. Stanton and thus prevent any interference with the military occupation of the South in their Reconstruction plan. In order to bring about a court test of the constitutionality of the act, Johnson dismissed Stanton, but the Supreme Court, intimidated by the radicals, refused to pass on the case. Gen. Ulysses S. Grant , whom Johnson appointed Secretary ad interim, turned the office bac k to Stanton when the Senate refused to approve his dismissal. Johnson then appointed Gen. Lorenzo Thomas Secretary of War, but Stanton, barricading himself in the department, refused to yield. Johnson's alleged violation of the Tenure of Office Act was the principal charge in the impeachment proceedings against him. When this move failed (May, 1868), Stanton finally gave up. The act, considerably modified in Grant's administration, was in large part repealed in 1887, and in 1926 the Supreme Court declared its principles unconstitutional. The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved. See more Encyclopedia articles on: U.S. History

The Civil War On Drugs - 1310 Words

The prison system in the United States is broken. There are many reasons why it is broken, but the main source of the problem is from the privatization of prisons. The United States has a capitalistic economy, which means our society driven by acquiring capital. Every person’s goal is to make money and live the â€Å"American Dream†, including big corporations. Since privatizing markets like healthcare, television, and banking worked for their favor, companies realized that prisons could produce large sums of capital. The war on drugs solidified that belief. Since the start of Ronald Reagan s â€Å"War on Drugs† in the 1970’s, prisons have been privatized and exploited for monetary gain. The public thinks that this so called â€Å"War on Drugs† is†¦show more content†¦Another problem with privatized prisons is that they do not focus on rehabilitating prisoners. There are no preventative measures enforced to keep felons from going back to pr ison once they get out. Since keeping prisons full makes more money, the private prisons plan to keep them full. The prison system is broken and it needs to be fixed. Our class collaborated and made a five point plan that we think will fix the majority of the problems that privatized prisons have caused. Our first point is to â€Å"abolish all policies and laws in place that discriminate against those that have been convicted. We want the judicial system to lead with fairness toward all†(1). Our second point is to â€Å"protect the interests of prisoners [by letting the federal government run prisons] and not private institutions [so that inmates safety is not sacrificed] for the sake of corporate profit†(2). Our third point is to â€Å"equip prisoners with the skills that they need to be successful when they get out of prison through correspondence programs, rehabilitation programs, and ridding the public of the negative stigma that prisoners carry†(3). Our fou rth point is to put â€Å"programs in place to prevent at risk communities from being forced into prison. This can be enforced by putting police through programs to teach them how to catch criminals without racial profiling. We want programs in at risk communities that teach skills

The Cask of Amontillado by Edgar Allan Poe - 888 Words

The Cask of Amontillado by Edgar Allan Poe In ?The Cask of Amontillado?, Edgar Allan Poe takes us on a trip into the mind of a mad man. Poe uses certain elements to convey an emotional impact. He utilizes irony, descriptive detail of setting, and dark character traits to create the search of sinful deceit. Poe also uses first person, where the narrator is the protagonist who is deeply involved. The purpose is to get the reader to no longer be the observer. He wants them to see with Montressor?s eyes, hear with his ears, and to react as he would. There is no real violence in the modern sense of the word. However, it is more horrifying because rather than seeing it through our eyes, we feel it through words. This short story is a great†¦show more content†¦This false sense of friendship and care is the ultimate deception trait found in Montressor. The setting Poe chooses for the story adds to the horror. The details of the environment help to increase the feeling of sinful darkness. His use of descriptive imagery help us experience the catacombs ourselves. He sets most of the story in the dark, damp series of winding tunnels of the catacombs. The weather is an example of the sinfulness that exist in the catacombs. Drops of moisture trickle among the bones, and the ground is constantly damp. Poe use these illustrations to remind us the sliminess nature of the catacombs. Through Poe?s use of descriptive detail we get the feeling as if it is us, the reader, who is being led through the crazed corridors of Montressor?s mind. Poe uses several different types of irony throughout the story. Dramatic irony, where the reader perceives something that a character in the story does not, is seen in the plot of the story. It is Fortunato?s obsession for wine that dramatically lures him to his death. Fortunate approached Montressor with a lot of warmth from his heavy wine drinking. The search for the Amontillado (Spanish sherry) delivers the plot for the murder. The thing that provides Fortunato with warmth, is also the thing that helps cause the murder. The irony of the carnival setting, and Fortunato?s attire illustrate aShow MoreRelatedThe Cask of Amontillado by Edgar Allan Poe836 Words   |  3 Pagesqualities in the story. In the story many things are used as symbols such as the actual cask of amontillado, the trowel, the jester costume and the setting in which there is two in the story. Another literary technique used significantly in the story is irony. Irony is the expression of ones meaning by using language that normally signifies the opposite. In the short story â€Å"The Cask of Amontillado,† Montresor a very troubled man who plans to seek revenge on another man named FortunatoRead MoreEdgar Allan Poe And The Cask Of Amontillado1384 Words   |  6 PagesWhat makes Edgar Allan Poe work unique? Other than being a strange individual, Poe has become a remarkable literature writer. The Raven, Annabel Lee, and The Cask of Amontillado are just a few of Poe’s work that staples the theme of gothic literature. This essay will allow you to see the gothic elements Edgar Allan Poe uses through his most common poems. Gothic literature has many elements which play into its definition. The actual definition is a style of writing that is characterized by elementsRead MoreThe Cask Of Amontillado By Edgar Allan Poe906 Words   |  4 Pages â€Å"The Cask of Amontillado† â€Å"The Cask of Amontillado† was written in 1846, by Edgar Allan Poe. Born in 1809, Poe never knew any of his parents. At the age of three, his mother died of tuberculosis, and his father deserted the family before he was born. Taking care of him was his foster parents in Richmond, Virginia. They loved Poe, but were not supportive of his decisions and kept Poe poor. Having debt and not being able to provide food and clothes for himself caused Poe to quit school. Later, heRead MoreThe Cask Of Amontillado By Edgar Allan Poe920 Words   |  4 Pageswhen that trust no longer exists? In â€Å"The Cask of Amontillado† written by Edgar Allan Poe, Fortunato is about to find the answer to this question. On the surface, Montresor seems friendly with Fortunato, but deep down he feels nothing but hate for him. Could this hatred have an irrationality that only Montresor understands? In different ways, both of these men are proud and affluent, yet both have downfalls that will l ead to a tragic ending. Edgar Allan Poe’s use of language contributes to the understandingRead MoreThe Cask Of Amontillado By Edgar Allan Poe1555 Words   |  7 PagesIn his writing, Edgar Allan Poe has multiple uses of direct and indirect characterization. In The Cask of Amontillado, Montresor had rules such as â€Å"I must not only punish but punish with impunity. A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong† (Poe, 2). Poe used indirect characterization to show the reader that Montresor is an unreliable narrator because he justified hisRead MoreThe Cask Of Amontillado By Edgar Allan Poe1303 Words   |  6 PagesIn Edgar Allan Poe’s â€Å"The Cask of Amontillado,† the narrator recalls an extremely significant time in his life, and takes the reader along with him. Throughout the story, one experiences a perfectly planned murder which took place over fifty years ago, and still no one has discovered what truly happened to poor Fortunato as he was chained to a wall in a room that was then closed off, and torched to death due to all the nitre in the walls. As the story goes on, the reader can see some of Poe’s unfortunateRead MoreThe Cask Of Amontillado By Edgar Allan Poe1076 Words   |  5 PagesThe short story, The Cask of Amontillado, written by Edgar Allan Poe is a story of terror and betrayal. Like many of Poe’s literary works, the story has a dark undertone with a theme of terror and depression. More than half a century ago, Marshall McLuhan argued that though Poe was fascinated by evil, the evil that he had in mind was not that of Calvinism, but that of the split man and the split civilization. In general, McLuhan was right, but in this instance Calvinism, and its God, provided a darkRead MoreThe Cask Of Amontillado By Edgar Allan Poe707 Words   |  3 PagesIn the short story of The Ca sk of Amontillado, Edgar Allan Poe writes in first person point of view from the perspective of Montresor who seeks revenge against Fortunato. Montresor began to develop the perfect plan for revenge. During the carnival season, Montresor meets with Fortunato and decides to implement his plan carefully through irony. Poe s story describes the murderer s mind which has lived as a memory of Fortunato s death for fifty years. Poe uses different types of irony and symbolismRead MoreThe Cask Of Amontillado By Edgar Allan Poe985 Words   |  4 PagesEdgar Allen Poe is a well known author of short stories and poetry from the 19th century. He is known especially for his stories of horror and suspense. The Cask of Amontillado is one of his more famous pieces. The story follows the narrator, Montresor, as he exacts revenge on Fortunato. Montressor draws Fortunato into the wine cellar where eventually he chains Fortunato to the wall and encloses him inside it. Throughout the story the narrator continually proves that he is not the most reliable sourceRead MoreThe Cask Of Amontillado By Edgar Allan Poe1575 Words   |  7 Pagescommitted the perfect murder in just such a tale, â€Å"The Cask of Amontillado.† Montresor plots and kills an unwary friend/foe during carnival time for motives that are unclear. The author of this tale, Edgar Allan Poe, influenced by his somewhat tragic life and one of the most influential Gothic writers, uses symbolism and irony to show the multitude of complicated motives of the narrator in his famous horror story. Upon examining Edgar Allan Poe’s life, one is not surprised that he chooses to write

Alcohol’s Effects on Teenagers Free Essays

The number of teenagers who are into â€Å"alcohol† nowadays is increasingly alarming. The physiological effects, as well as, the physical and behavioral consequences are equally disturbing as well. â€Å"Permanent brain damage, depression, poor school performance, psychological distress / serious behavioral problems, and attention deficit disorder† are some of the physiological effects on teenagers who drink alcohol (The Marin Institute, n. We will write a custom essay sample on Alcohol’s Effects on Teenagers or any similar topic only for you Order Now d., n.p.). On the other hand, the physical and behavioral consequences include the following: â€Å"in-denial, self-pity, excessive anger, blaming others, and hurting oneself other individuals† (Garrett, 2002, n.p.). Physiological Effects Teenagers who are into too much drinking may experience â€Å"permanent brain damage† (The Marin Institute, n.d., n.p.). This claim is backed up by an expert named â€Å"Dr. John Nelson†, a member of the American Medical Association (The Marin Institute, n.d., n.p.). Moreover, according to the â€Å"National Health and Nutrition Survey† girls who drink experience depression â€Å"four times more likely than those who do not engage in drinking† (The Marin Institute, n.d., n.p.). Furthermore, teenagers who drink also suffer from low grades; in fact, according to the â€Å"American Medical Association†, those who drink get lower scores on â€Å"vocabulary, visual-spatial, as well as, memory tests† as compared with those who do not engage in drinking (The Marin Institute, n.d., n.p.). In addition to that, some teenagers who drink develop â€Å"psychological distress†, as well as, â€Å"serious behavioral problems†; this is according to the statistical information gathered by the â€Å"Substance Abuse and Mental Health Services Administration† (The Marin Institute, n.d., n.p.). Last but not least, a study conducted by the â€Å"Substance Abuse and Mental Health Services Administration† confirms that teenagers who are regularly drinking may develop â€Å"attention-deficit disorder† (The Marin Institute, n.d., n.p.). Physical and Behavioral Effects Teenagers who engage themselves in alcohol drinking may also suffer from the following physical and behavioral effects: First of all, teenagers may develop problems accepting unfortunate occurrences in their lives (Garrett, 2002, n.p.). They may turn â€Å"in-denial† and make use of alcohol as a â€Å"defense mechanism† every time he or she is reminded of the truth especially in cases where he or she gets offended (Garrett, 2002, n.p.). Second, some teenagers may feel pity for themselves while some tend to get excessively angry which may actually result in severe drinking (Garrett, 2002, n.p.). Third, some teenagers drinking severely may experience troubles accepting their faults (Garrett, 2002, n.p.). Thus eventually, they blame somebody else for the untoward incidents that occurred to them (Garrett, 2002, n.p.). Finally, some teenagers who drink too much may experience hurting other people or even oneself (Garrett, 2002, n.p.). Summary / Conclusion Indeed, teenagers who engage themselves in drinking alcohol are faced with dangers including physiological and behavioral/physical ones (The Marin Institute, n.d., n.p.). â€Å"Physiological effects† include the following: â€Å"permanent brain damage, depression, poor school performance, psychological distress / serious behavioral problems, and attention deficit disorder† (The Marin Institute, n.d., n.p.). Meanwhile, physical ones include: â€Å"in-denial, self-pity, excessive anger, blaming others, and   hurting oneself other individuals† (Garrett, 2002, n.p.). References Garrett, F.P. (2002). Excuses Alcoholics Make. Retrieved April 1, 2009 from http://www.bma-wellness.com/papers/Excuses_Alcoholics.html The Marin Institute. (n.d.). Physiological Effects of Alcohol on Teenagers. Retrieved April 1, 2009 from http://www.marininstitute.org/Youth/teen_alcohol_use.htm    How to cite Alcohol’s Effects on Teenagers, Papers

Isoperimetric Quotients Essay Example

Isoperimetric Quotients Essay Isoperimetric Quotients of plane shapes are calculated using the formula: I.Q. = 4? x Area of shape (Perimeter of shape)à ¯Ã‚ ¿Ã‚ ½ I am going to investigate isoperimetric quotients of plane shapes and interpret my findings. We will write a custom essay sample on Isoperimetric Quotients specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Isoperimetric Quotients specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Isoperimetric Quotients specifically for you FOR ONLY $16.38 $13.9/page Hire Writer Firstly, I am going to look at flat shapes. Using the formula, I will calculate the isoperimetric quotients of the shapes. Starting with the smallest 2D shape- a triangle- I will calculate the I.Q s of right-angled triangles. I will also do this with isosceles and equilateral triangles. I will move on to quadrilaterals and look at the I.Q s. Maybe there will be something about the results that will help me with further plane shapes; pentagon, hexagon, heptagon, nonagon, decagon and possibly a circle. With comparison, the results might show something about the shapes, such as a pattern. Triangles I am now going to study right-angled triangles. Right-angled triangles I will first look at the 3, 4, 5 right-angled triangles and then enlargements of it. 1. Perimeter= 3+4+5= 12 cm Area= 1/2 x 4 x 3= 6cmà ¯Ã‚ ¿Ã‚ ½ I.Q. = 4 x ? x 6 12à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.5236 I will look at similar enlarged right-angled triangles, based on the 3, 4, 5 triangle. 2. Perimeter= 6+8+10= 24 cm Area= 1/2 x 6 x 8= 24 cm à ¯Ã‚ ¿Ã‚ ½ I.Q= 4 x ? x 24 24à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.5236 3. Perimeter= 16+20+12=48 cm Area= 1/2 x 16 x 12= 96 cmà ¯Ã‚ ¿Ã‚ ½ I.Q. = 4 x ? x 96 48à ¯Ã‚ ¿Ã‚ ½ =0.5236 Similar 345 right-angled triangles have the same I.Q. The answers are all the same. I predict that similar enlarged shapes make the same I.Q. answer. I am now going to look at other right-angled triangles that are not versions of the 3, 4, 5. Other right angled triangles Firstly, in these triangles, I will need to find the hypotenuse length so I will use Pythagoras theorem. 4. Hypotenuse = 4à ¯Ã‚ ¿Ã‚ ½ + 6à ¯Ã‚ ¿Ã‚ ½ = 52 = V52 = 7. 2111 cm Perimeter = 4+6+7.2111 = 17.2111 cm Area= 1/2 x 4 x 6 = 12 cm à ¯Ã‚ ¿Ã‚ ½ I.Q. = 4 x ? x 12 17.2111à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.5090 5. H = 8à ¯Ã‚ ¿Ã‚ ½ + 12à ¯Ã‚ ¿Ã‚ ½ = 208 = V 208 = 14.422 cm P = 12+8+14.422 = 34.422 A = 1/2 x 8 x 12 = 48 I.Q. = 4 x ? x 48 34.422à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.5090 6. H = 3à ¯Ã‚ ¿Ã‚ ½ + 2à ¯Ã‚ ¿Ã‚ ½ = 13 = V13 = 3.6 P = 3+2+3.6 = 8.6 A= 1/2 x 2 x 3 = 3 I.Q. = 4 x ? x 3 8.6à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.5097 7. H = 6à ¯Ã‚ ¿Ã‚ ½+4à ¯Ã‚ ¿Ã‚ ½ = 52 =V52 = 7.211 P = 6+4+7.211 = 17.211 A= 1/2 x 4 x 6 = 12 I.Q. = 4 x ? x 12 17.211à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.5091 8. H = 7à ¯Ã‚ ¿Ã‚ ½+9à ¯Ã‚ ¿Ã‚ ½ = 130 = V130 = 11.4018 P = 7+9+11.4018 = 27.4018 A = 1/2 x 7 x 9 = 31.5 I.Q. = 4 x ? x 31.5 27.4018à ¯Ã‚ ¿Ã‚ ½ I.Q.= 0.5271 9. H = 18à ¯Ã‚ ¿Ã‚ ½+14à ¯Ã‚ ¿Ã‚ ½= 520 = V520 = 22.8035 cm P = 18+14+22.8035 = 54.8035 cm A= 1/2 x 14 x 18 = 126 cmà ¯Ã‚ ¿Ã‚ ½ I.Q. = 4 x ? x 126 54.8035à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.5271 Different right-angled triangles have different I.Q. s but enlarged versions have the same I.Q. s as smaller triangles. Isosceles Triangles 1. P = 6+6+4 = 16 cm H = cà ¯Ã‚ ¿Ã‚ ½=aà ¯Ã‚ ¿Ã‚ ½+b à ¯Ã‚ ¿Ã‚ ½ 6à ¯Ã‚ ¿Ã‚ ½ = aà ¯Ã‚ ¿Ã‚ ½ + 2à ¯Ã‚ ¿Ã‚ ½ 6à ¯Ã‚ ¿Ã‚ ½ 2à ¯Ã‚ ¿Ã‚ ½ = aà ¯Ã‚ ¿Ã‚ ½ 32=aà ¯Ã‚ ¿Ã‚ ½ V32 = a 5.66 = a A of isosceles= 1/2 x 4 x 5.66 = 11.32 cmà ¯Ã‚ ¿Ã‚ ½ I.Q. = 4 x ? x 11.32 16à ¯Ã‚ ¿Ã‚ ½ I.Q.= 0.556 I predict that an enlarged version of the isosceles triangle will have the same I.Q. 2. P = 8+12+12 = 32 H = cà ¯Ã‚ ¿Ã‚ ½=aà ¯Ã‚ ¿Ã‚ ½+b à ¯Ã‚ ¿Ã‚ ½ 12à ¯Ã‚ ¿Ã‚ ½ = aà ¯Ã‚ ¿Ã‚ ½ + 4à ¯Ã‚ ¿Ã‚ ½ 12à ¯Ã‚ ¿Ã‚ ½ 4à ¯Ã‚ ¿Ã‚ ½ = aà ¯Ã‚ ¿Ã‚ ½ 128= aà ¯Ã‚ ¿Ã‚ ½ V128 = a 11.314 cm = a A of isosceles= 1/2 x 8 x 11.314 = 45.256 I.Q. = 4 x ? x 45.256 32à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.55537 The answers were the same my prediction was correct. (Do not round for more accurate answers.) I will now look at a different isosceles and an enlarged version. 3. P= 8+8+5 = 21 H = cà ¯Ã‚ ¿Ã‚ ½=aà ¯Ã‚ ¿Ã‚ ½+b à ¯Ã‚ ¿Ã‚ ½ 8à ¯Ã‚ ¿Ã‚ ½ = aà ¯Ã‚ ¿Ã‚ ½ + 2.5à ¯Ã‚ ¿Ã‚ ½ 8à ¯Ã‚ ¿Ã‚ ½ 2.5à ¯Ã‚ ¿Ã‚ ½ = aà ¯Ã‚ ¿Ã‚ ½ 57.75= aà ¯Ã‚ ¿Ã‚ ½ V57.75 = a 7.599342077 cm = a A= 1/2 x 5 x 7.599342077 = 18.99835519 I.Q. = 4 x ? x 18.99835519 21à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.541361388 I am now looking at an enlarged version of the above triangle; I predict that the I.Q. will be 0.54136188. 4. P= 16+16+10 = 42cmà ¯Ã‚ ¿Ã‚ ½ H = cà ¯Ã‚ ¿Ã‚ ½=aà ¯Ã‚ ¿Ã‚ ½+b à ¯Ã‚ ¿Ã‚ ½ 16à ¯Ã‚ ¿Ã‚ ½ = aà ¯Ã‚ ¿Ã‚ ½ + 5à ¯Ã‚ ¿Ã‚ ½ 16à ¯Ã‚ ¿Ã‚ ½ 5à ¯Ã‚ ¿Ã‚ ½ = aà ¯Ã‚ ¿Ã‚ ½ 231= aà ¯Ã‚ ¿Ã‚ ½ V231 = a 15.19868415 cm = a A= 1/2 x 10 x 15.19868415 = 75.99342075 cm à ¯Ã‚ ¿Ã‚ ½ I.Q. = 4 x ? x 75.99342075 42à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.541361388 The I.Q. s of the isosceles enlarged triangle is equal to the smaller triangle, therefore my prediction was correct. The I.Q. s of enlarged isosceles triangles are equal. However, when they are not similar or enlarged isosceles triangles they have different I.Q. s Equilateral Triangles I think that all equilateral triangles will have the same I.Q. because each one is an enlargement of another; they are all similar. 1. I am going to us 1/2absinC to find the area because all the angles in an equilateral triangle are 60à ¯Ã‚ ¿Ã‚ ½. A= 1/2 x absinC = 1/2 x 3 x 3 x sin 60 = 3.897114317 P= 3+3+3 = 9 I.Q. = 4 x ? x 3.897114317 9à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.604599788 I will now look at other similar enlarged versions. 2. A= 1/2 x absinC = 1/2 x 5 x 5 x sin 60 = 10.82531755 P= 5+5+5 = 15 I.Q. = 4 x ? x 10.82531755 15à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.604599788 3. A= 1/2 x absinC = 1/2 x 11 x 11 x sin 60 = 52.39453693 P= 11+11+11 = 33 I.Q. = 4 x ? x 52.39453693 33à ¯Ã‚ ¿Ã‚ ½ I.Q. = 0.604599788 The I.Q. for each triangle was 0.604599788. They were all equal. I will now construct a table comparing all of the isoperimetric quotients I have found. I will use this to try and discover a pattern between the I.Q. s.