The Recovery Rate Of The Male Is Significantly Faster Thna The Female :: essays research papers

THE RECOVERY RATE OF THE MALE IS SIGNIFICANTLY   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  FASTER THAN THAT OF THE FEMALE.   Ã‚  Ã‚  Ã‚  Ã‚   Abstract:   Ã‚  Ã‚  Ã‚  Ã‚  This experiment is designed to test whether or not gender is a major contributing factor to the recovery heart rate in humans. Most would assume that the male heart rate would be considerably faster in recovery time than that of the female. This experiment furthers that assumption by eliminating uncontrolled variables such as age, build, and health conditions. Introduction:   Ã‚  Ã‚  Ã‚  Ã‚  The male human has always had certain physical advantages over the female human such as increased muscle mass, larger bones, and superb aggressiveness in times where deemed necessary. But is recovery rate (or, how long it takes for the heart rate to return to its resting rate) an advantage possessed by males also? The question posed in this experiment is whether or not the heart rate of the male will recover faster than that of a female. The hypothesis tested was that the male's heart rate would fall considerably faster than the female's after one minute of intense physical activity.   Ã‚  Ã‚  Ã‚  Ã‚  It is known already that males dominate females in the physical world in most cases. Males have much larger natural muscle mass, less body fat, and a physique that is designed for superiority in the physical world. Therefore it can only be assumed that the most important muscle of all (the heart) would also be superior in its performance. Mariotti 2   Ã‚  Ã‚  Ã‚  Ã‚  Many factors can influence the results of testing this hypothesis. All variables have been controlled except for the variable gender. Both the male and female subjects are close in age (< two years difference), both are nonsmokers, both possess small body builds for their respective gender, and both have no debilitating medical conditions (e.g., asthma, diabetes, heart condition). Controlling these factors allowed for the testing of the hypothesis, which is focused strictly on gender. Materials and Methods:   Ã‚  Ã‚  Ã‚  Ã‚  The materials used: one wristwatch (with second hand), two variably indifferent humans (one male, one female), and a standard staircase at CCC. The method was simple: two test subjects were exposed to two trials involving one minute of physical activity and x minutes needed for the recovery of the heart rate. Before the experiment began, each subject's resting heart rate was taken. This would become the controlled variable. Next, each subject ran up one set of stairs at CCC, one stair at a time, for one minute. After one minute of activity, the subjects stopped and began taking his or her heart rate.

A New Nation of Individuals :: Literature Papers

A New Nation of Individuals Abstract As John Savage articulates, â€Å"Nothing costs enough here,† in Huxley’s Brave New World (1932) of bottled automata, where maelstroms of soma-ingesting, Malthusian orgies casually toss human life about (239). Nothing is dear when the freedom to choose disappears because individuals â€Å"don’t know what it’s like being anything else† (74). Removing choice is simply a method of brainwashing that only subdues human nature for the short-run. Consider Sigmund Freud's views of private property: In abolishing private property we deprive the human love of aggression, certainly a strong one, though certainly not the strongest; but we have in no way altered the differences in power and influence which are misused by aggressiveness, nor have we altered anything in its nature. Aggressiveness was not created by property. (Kumar 384) Aggressiveness, too, was not created by choice. This essay proposes a utopia based on individual freedom, derived from a laissez-faire economy and semi-socialist meritocracy. A New Nation of Individuals First existed the individual; then a group of individuals established government via a social contract. Thus, as Percy Bysshe Shelley writes, "(g)overnment has no rights; it is a delegation from several individuals for the purpose of securing their own. It is therefore just, only so far as it exists by their consent, useful only so far as it operates to their well-being" (qtd. in Chianese 282). Such basic democracy founded the United States of America—yet modern democracy has gone terribly awry, and power now lies in the hands of few rather than many. Ideally, "(t)he highest purpose of Nature, which is the development of all the capacities which can be achieved by mankind, is attainable only in society, and more specifically in the society with the greatest freedom," and the greatest freedom can only be obtained, as Thoreau believed, through a government that governs least (202). In order for the individual to maintain full rights and a completely separate, private sphere of self, government must be just large enough to protect man's unalienable rights, Thomas Jefferson's "life, liberty and pursuit of happiness," but not overstep its boundaries onto the slippery slope of tyranny or oppression. A utopian society should thus stem from a meritocracy that allows for maximum individuality and freedom of choice while protecting man from one another, specifically through universal education and healthcare, and a laissez-faire economy founded on a flat-rate sales tax. A New Nation of Individuals :: Literature Papers A New Nation of Individuals Abstract As John Savage articulates, â€Å"Nothing costs enough here,† in Huxley’s Brave New World (1932) of bottled automata, where maelstroms of soma-ingesting, Malthusian orgies casually toss human life about (239). Nothing is dear when the freedom to choose disappears because individuals â€Å"don’t know what it’s like being anything else† (74). Removing choice is simply a method of brainwashing that only subdues human nature for the short-run. Consider Sigmund Freud's views of private property: In abolishing private property we deprive the human love of aggression, certainly a strong one, though certainly not the strongest; but we have in no way altered the differences in power and influence which are misused by aggressiveness, nor have we altered anything in its nature. Aggressiveness was not created by property. (Kumar 384) Aggressiveness, too, was not created by choice. This essay proposes a utopia based on individual freedom, derived from a laissez-faire economy and semi-socialist meritocracy. A New Nation of Individuals First existed the individual; then a group of individuals established government via a social contract. Thus, as Percy Bysshe Shelley writes, "(g)overnment has no rights; it is a delegation from several individuals for the purpose of securing their own. It is therefore just, only so far as it exists by their consent, useful only so far as it operates to their well-being" (qtd. in Chianese 282). Such basic democracy founded the United States of America—yet modern democracy has gone terribly awry, and power now lies in the hands of few rather than many. Ideally, "(t)he highest purpose of Nature, which is the development of all the capacities which can be achieved by mankind, is attainable only in society, and more specifically in the society with the greatest freedom," and the greatest freedom can only be obtained, as Thoreau believed, through a government that governs least (202). In order for the individual to maintain full rights and a completely separate, private sphere of self, government must be just large enough to protect man's unalienable rights, Thomas Jefferson's "life, liberty and pursuit of happiness," but not overstep its boundaries onto the slippery slope of tyranny or oppression. A utopian society should thus stem from a meritocracy that allows for maximum individuality and freedom of choice while protecting man from one another, specifically through universal education and healthcare, and a laissez-faire economy founded on a flat-rate sales tax.

Why Might The Enron Collapse Make A Good Play Accounting Essay

Question 10:Fix a concern study ( as if for senior direction ) on two of the followers. Use the Internet as a resource. Length about 200-300 words each excepting any appendices. Use right referencing and include a bibliography. a. Digital Dashboards. Include in your study definitions, types, history, benefits, disadvantages, and screenshots of illustrations and an account of how splashboards could be used to show corporate societal duty. OR b. Bounded reason in determination devising. OR c. Critically measure ‘predictably irrational ‘ ( Dan Ariely ) OR d. Why might the Enron prostration make a good drama ) ( Google Enron – the Play )Question 1:15-35:Formula position:In this exercising, we do n't cognize precisely how $ 78,000 in dealing ( a ) was paid. In this instance, we assumed that this money is account collectible. If it is paid by hard currency, the operating income for Cash BASIC would be $ 56,800 – $ 78,000 = $ -21,200, a loss of $ 21,200.2.From my position, the accrual footing should be considered as the step of Dr. Sanchez ‘s public presentation in 20X1. Because it includes all assets and liabilities looking in all minutess, while the hard currency footing contains merely hard currency which was used in this twelvemonth. So the accrual footing can reflect the efficiency of Dr. Sanchez ‘s concern more precisely than the hard currency BASIC. For illustration, in dealing ( vitamin D ) , $ 20,000 fee billed have been earned and we can merely see this money in the accrual footing but non in the hard c urrency footing. The authorities normally uses accrual footing for the income revenue enhancement intent in companies. In instance the authorities uses hard currency BASIC, it will be better for the companies in which hard currency BASIC is less than accrual basic. Normally these companies have little concern and different intents.Question 2:15-1, 15-3, 15-4, 15-13, 15-1615-1:The income statement ( besides called a net income and loss statement ) replies inquiries about company ‘s fiscal public presentation during a period of clip. The income statement provides information about a company ‘s net income or loss. The balance sheet ( or a province of fiscal place ) replies inquiries about concern ‘ fiscal position at a specific minute in clip. A balance sheet encompasses assets, liabilities, and proprietors ‘ or shareholders ‘ equity.15-3:A company ‘s income statement shows the net income or loss over a span of clip, while balance sheet is a snapshot of the fiscal position at an blink of an eye of clip. Therefore, the income statement is the major nexus between balance sheets. In add-on, the income statement = hard currency flow statement + balance sheet.15-4:â€Å" Net income is the difference in the ownership capital history balances at two points in clip † . This statement is erroneous because net income is the surplus of grosss over disbursals. There are other factors which affect the ownership capital history but non the net income, such as dividends or ownership investing.15-13:â€Å" Dividends are distribution of net incomes † . This statement is no n truly precisely. Although profitable operations create the ability to pay dividends, dividends are distributions of assets to shareholders.15-16:Ethical motives and unity are of import to comptrollers because they are the hallmark of the accounting profession. Accountants have to do users rely on their information. Furthermore, assurance in fiscal statements depends on the competency and unity of comptrollers and hearers.Question 3:16-A1:Formula ViewQuestion 4:15-42:Formula View:Inventories: $ 10,895.1 – $ 315.1 – $ 1,057.4 – $ 2,661.6 – $ 6,141.3 = $ 719.7 Entire Stockholders ‘ equity: $ 173.2 + $ 1,995.8 = $ 2,169.0 ( degree Celsius ) Entire liabilities: $ 2,317.8 + $ 681.7 + $ 4,507.0 + $ 1,219.6= $ 8,726.1 or $ 10,895.1 – $ 2,169.0 = $ 8,726.1Question 5:16-4:â€Å" Accrued depreciation is a amount of hard currency being accumulated for the replacing of fixed assets † . I think this statement is non rather precisely. Depreciation is an allotment of an historical cost to write off ( Horngren, 2008, p754 ) . Accumulated depreciation sum expresses merely the expired value of an plus and it is non hard currency or any other assortment of assets that can be used to purchase another plus.16-7:â€Å" To capitalise an sum spent means that it will non be charged as an disbursal † . I do n't hold with this statement. â€Å" To capitalise an sum means to enter it as an plus instead as an disbursal † ( Horngren, 2008, p732 ) . Therefore it will non be immediately charged as an disbursal but it will be charged as an disbursal when capitalized plus is used.16-8:â€Å" Good will may hold nil to make with the personality of the director or employees † . I agree with this statement. Harmonizing to Horngren ( 2008, p733 ) , â€Å" good will is the surplus of the cost of an acquired company over the amount of the just market values of it identifiable single assets less its liabilities † .16-16:The statement of hard currency flows illustrates alterations in hard currency grosss and hard currency payments of an organisation during a period. This statement shows the relationship of net income to alterations in hard currency balances. Furthermore, it reports pas hard currency flows in order to foretell future hard currency flows, evaluate direction ‘s coevals and usage of hard currency and find whether company can pay involvement, dividends and debts on clip ( Horngren, 2008, p740 ) .16-29:â€Å" Depreciation is an built-in portion of a statement of hard currency flows. † I do non hold with this statement. Depreciation is added to net income to calculate hard currency flow but it does non impact hard currency and it does non imply a cu rrent escape of hard currency ( Horngren, 2008, p754 ) .Question 6:16-56:Formula ViewQuestion 7:What went incorrect at One Tel?One Tel failed because of an expensive error, they failed to pull off receivables and liabilities. They spent excessively much clip on advancing and spread outing One Tel but non adequate clip concentrating on operation of the concern system. In 2000, One Tel spent $ 525.6 million on buying Australia spectrum licence in order to spread out their web and take the market from Optus. However there was a job with their system so they could non sell this web at its existent value, and it did non do net income. One Tel was cleared bank bill of exchange in 2001.What are the major fiscal studies?The major fiscal studies are: – Statement of finance public presentation – Statement of finance place – Statement of hard currency flow. – Mugwump Audit Report.3. Why are net incomes of import? Why is hard currency flow of import?Net incomes are of import because the function of capitalist economic system is to do a net income or travel out of concern. Net incomes show how a company operates efficaciously and productively every bit good as the return of investing. Cash flow is of import because it is one of the most primary grounds which make the concern fails. If companies want to better their concern and net incomes, they have to guarantee precise hard currency flow to do right fiscal programs.4. How did One Tel show a positive hard currency balance?One Tel showed a positive hard currency balance by the wages on sale volume. By advancing the selling, One Tel wanted clients to utilize more profitable services One Tel offered them.5. What are the features of a good internal control system?Harmonizing to the COSO ( Committee of Sponsoring Organizations of the Treadway Commission ) , internal control can be defined as â€Å" a procedure, effected by an entity ‘s board of managers, direction and other forces, designed to supply sensible confidence sing the accomplishment of aims in the undermentioned classs: effectivity and efficiency of operations, dependability of fiscal coverage and conformity with applicable Torahs and ordinances. â₠¬  ( Internal Control-Integrated Framework, Executive Summary, 1992 ) The features of a good control system consists five cardinal constituents: The Control Environment: the most of import one because if sets the tone for the organisation, and contributes the ordinance and construction for the other constituents. Hazard Appraisal: used to place, analyse and manage relevant hazards to the accomplishment of aims. Information and Communication: used to place, gaining control, and exchange fiscal, operational, and conformity information in a timely mode in order to enable people to transport out their duties. Control Activities: included policies and processs that make certain direction directives are implemented. Monitoring-processes: used to measure the quality of internal control public presentation over clip. ( Internal Control-Integrated Framework, Executive Summary, 1992 )Question 8:17-11:â€Å" It is better to acknowledge good will than to compose up assets to their just market values † . In a amalgamate statement, we have to compose up assets to their just market values at the clip of the acquisition. However if it is possible, acknowledging good will can cut down the depreciation of the single assets.17-15:The two ratios which are multiplied together to give the pretax operating rate of return on mean entire assets are runing income per centum on gross revenues and entire plus turnover. The pretax operating rate of return on mean entire assets = runing income per centum on gross revenues * entire plus turnover.17-19:â€Å" If IBM had been forced to write off ( the package development cost of ) $ 785 million, its net incomes would hold been cut by 72 cents a portion. With IBM selling at 14 times gaining, write offing the cost might hold knocked over $ 10 off IBM ‘s portion monetary value. † The citation assumes that the ratio of monetary value net incomes is fixed. If the package development cost of $ 785 million, it means that there was a lessening in net income about $ 785 million, so the net incomes per portion was cut by 72 cents. Price gaining ratio is calculated by the market monetary value per portion / net incomes per portion. IBM monetary value gaining ratio is stable at 14 times and the net incomes per portion was cut by 72 cents are the grounds why the IBM ‘s portion monetary value reduced $ 10.17-20:Suppose the president of your company wanted to exchange depreciation methods to increase reported net income: â€Å" Our stock monetary value is 10 % below what I think it should be ; altering depreciation method will increase income by 10 % , therefore acquiring our portion monetary value up to its proper degree † . From my position, altering the depreciation methods is non a good manner. It can do income addition but it will make a incorrect value of the assets in the hereafter. Furthermore, we can non be certain that increasing reported net income will do the stock monetary value to lift, because the stock market does non wholly depend on the reported net income.Question 9:17-36Formula ViewQuestion 10:Digital splashboardsExecutive Summary This study provides inside informations about digital splashboards, includes the definition, types, history, benefits and disadvantages of digital splashboards. In add-on, it gives an illustration of digital splashboards screenshot every bit good as how splashboards could be used to show corporate societal duty. Introduction Digital splashboards play an of import function in direction information system as they are really utile to find the departmental public presentation of a company. Definition A splashboard is described as an executive information system which is easy to be read. Digital splashboards can be known as † existent clip visual image tools of critical concern indexs that help in determination devising † ( Dursteler, 2004 ) . They are the direction of all informations base within an organisation, so they can mensurate the departmental public presentation. Types There are three chief types of digital splashboards: stand entirely package applications, web-browser based applications, and desktop applications. History The thought of digital splashboards was based on the survey of determination support systems in 1970s. However, digital splashboards were appeared in the late of 1990s, with the rush of the web. Digital splashboard is one portion of Digital Nervous System concept which was developed by Microsoft in the same this period of clip ( From Wikipedia – Splashboards ) . Benefits There are many benefits of digital splashboards as they help directors command the varied sections in their companies. These are the other maps of digital splashboards: – Ocular presentation of public presentation steps – Identify and right negative tendencies – Measure efficiencies/inefficiencies – Generate elaborate studies demoing new tendencies – Brand determinations based on concern intelligence – Align schemes and organisational ends – Save clip over running multiple studies – Addition entire visibleness of all systems immediately ( From Wikipedia – Splashboards ) Disadvantages Digital splashboards measure the public presentation based on input informations of companies. Therefore, if the information is non precisely, there will be a bad consequence in the measuring of digital splashboards and it will do a bad determination. Companies have to pass money to keep their information system in order to guarantee that digital splashboards can roll up available informations from all sections. Screenshot As we can see, this is the screen shooting of digital splashboards, which illustrates the day-to-day gross revenues of an organisation in October 2003. We can see the sum of day-to-day units sold every bit good as the day-to-day cargos ( Dursteler, 2004 ) . How splashboards could be used to show corporate societal duty Splashboards monitor the public presentation of an organisation so it could be used to show corporate societal duty. Splashboards reflect the duty of an organisation which has to run into the community aspirations. Decision and Recommendations In decision, based on available informations, digital splashboards are really utile for organisations to supervise their concern public presentation and doing determinations. Digital splashboards should be used loosely in companies in order to assist companies develop in the right manner.d. Why might the Enron prostration make a good drama?Executive Summary The dislocation of Enron is really celebrated over the universe and there is a drama about this dirt. This study gives information about the history of Enron and the Enron drama, the accounting job which made Enron autumn and the lesson we can larn from this company. Introduction Enron Corporation used to be the most powerful American energy companies in Houston, Texas. However, the rapid prostration of Enron created a large dirt in the fiscal history. In 2009, the drama – Enron was written by the British dramatist Lucy Prebble, based on the Enron dirt. It won many awards for best new drama every bit good as best manager and best histrion ( From Wikipedia – Enron, the drama ) . So why might the Enron prostration make a good drama? History Enron was established in 1985 by the amalgamation between Houston Natural Gas and InterNorth. There were about 21,000 employees in this company and it was one of the universe ‘s taking in electricity, natural gas, mush and paper. In 2000, it reported the grosss of $ 111 billion dollars. However, in the terminal of 2001, it collapsed so rapidly in an incredible manner. ( Healy and Palepu, 2003, p4 ) The prostration of Enron The autumn of Enron was started in August 2001, when CEO Jeffrey Skilling resigned for unrevealed grounds. After that, it fell into loss and debt. Finally, on December 2, 2001, the company declared bankruptcy. The accounting job One of the chief grounds why Enron collapsed is the accounting issues. Mark Jickling ( 2002, p3 ) , Coordinator Specialist in Public Finance Government and Finance Division, mentioned in his study that Enron ‘s operations and fundss position were non been shown clearly in the fiscal statements to stockholders and analysts. In late 2001, Enron recognized that some new concerns were non runing every bit good as expected. It had to sell its electric power works, Portland General Corp. , at a loss of $ 1.1 billion on October 5, 2001. ( Healy and Palepu, 2003, p12 ) With these accounting jobs, the Enron ‘s stock monetary value was halved while its adoption costs were increased. On November 28, Enron ‘s accepted to be acquired by its rival, Dynergy, in order to avoid bankruptcy. On November 28, Enron ‘s public debt was dropped to debris bond position, so Dynergy drew back. ( Healy and Palepu, 2003, p12 ) As a consequence, on December 2, 2001, Enron led for bankruptcy with its stock monetary value at merely $ 0.26. ( Healy and Palepu, 2003, p12 ) Lesson from Enron dirt The autumn of Enron in a short-time created a lesson for all companies in the universe. One of the most of import for all companies to do a concern viable is the direction of their fiscal coverage so companies can guarantee everything is right. The lesson from many fiscal errors of Enron made a good drama, Enron – the Play.Mentions:Committee of Sponsoring Organizations of the Treadway Committee ( COSO ) . ( 1992 ) . Internal Control- Integrated Framework, Executive Summary. www.coso.org. Juan C. Dursteler ( 2004 ) . Digital Dashboards. The digital magazine of InfoVis.net.Retrieved April 12th 2004 from hypertext transfer protocol: //www.infovis.net/printMag.php? num=143 & A ; lang=2 Horngren, et Al. ( 2008 ) . Introduction to direction accounting ( 14th Ed. ) . Pearson: Prentice Hall Wikipedia – Splashboards. Retrieved from: hypertext transfer protocol: //en.wikipedia.org/wiki/Dashboards_ % 28management_information_systems % 29 Wikipedia – Enron, the drama Retrieved from: hypertext transfer protocol: //en.wikipedia.org/wiki/ENRON_ % 28play % 29

History of Trigonometry

Running Head: History of Trigonometry History of Trigonometry Rome Fiedler History of Mathematics 501 University of Akron April 29, 2012 History of Trigonometry: An Introduction Trigonometry is useful in our world. By exploring where these concepts come from provides an understanding in putting this mathematics to use. The term Trigonometry comes from the Greek word trigon, meaning triangle and the Greek word meatria meaning measurement. However it is not native to Greek in origin. The mathematics comes from multiple people over a span of thousands of years and has touched over every major civilization.It is a combination of geometry, and astronomy and has many practical applications over history. Trigonometry is a branch of math first created by 2nd century BC by the Greek mathematician Hipparchus. The history of trigonometry and of trigonometric functions sticks to the general lines of the history of math. Early research of triangles could be found in the 2nd millennium BC, in Egyp tian and Babylonian math. Methodical research of trigonometric functions started in Greek math, and it reached India as part of Greek astronomy.In Indian astronomy, the research of trigonometric functions flourished in the Gupta dynasty, particularly as a result of Aryabhata. Throughout the Middle Ages, the research of trigonometry continued in Islamic math, while it was implemented as a discrete subject in the Latin West beginning in the Renaissance with Regiomontanus. The growth of contemporary trigonometry shifted in the western Age of Enlightenment, starting with 17th-century math and reaching its contemporary type with Leonhard Euler (1748) Etymology The word â€Å"trigonometry† originates from the Greek â€Å"trigonometria†, implying â€Å"triangle measuring†, from triangle + to measure.The name developed from the study of right triangles by applying the relation ships between the measures of its sides and angles to the study of similar triangles (Gullberg , 1996). The word was introduced by Barthoolomus ptiticus in the title of his work Trigonometria sice de solutione triangularumtractus brevis et perspicius†¦ in 1595. The contemporary word â€Å"sine†, is originated from the Latin word sinus, which implied â€Å"bay†, â€Å"bosom† or â€Å"fold†, translation from Arabic word jayb. The Arabic word is in origin of version of Sanskrit jiva â€Å"chord†.Sanskrit jiva in learned used was a synonym of jya â€Å"chord†, primarily the word for â€Å"bow-string†. Sanskrit jiva was taken into Arabic as jiba (Boyer, 1991). This word was then changed into the real Arabic word jayb, implying â€Å"bosom, fold, bay†, either by the Arabs or erroneously of the European translators such as Robert of Chester, who translated jayb into Latin as sinus. In particular Fibonacci's sinus rectus arcus was significant in creating the word sinus. Early Beginnings The origin of the subject has rich di versity. Trigonometry is not the work of one particular person or place but rather a development over time.The primitive Egyptians and Babylonians had known of theorems on the ratios of the sides of analogous triangles for many centuries. However pre-Greek societies were deficient of the concept of an angle measure and as a result, the sides of triangles were analyzed rather, a field that would be better known as â€Å"trilaterometry†(Boyer, 1991). The Babylonian astronomers kept comprehensive records on the rising and setting of stars, the movement of the planets, and the solar and lunar eclipses, all of which needed knowledge with angular distances measured on the celestial sphere.Founded on one explanation of the Plimpton 322 cuneiform tablet, some have even claimed that the primitive Babylonians had a table of secants. There was, on the other hand, much discussion as to whether it is a table of Pythagorean triples, a solution of quadratic equations, or a trigonometric tab le. The Egyptians, in contrast, applied an ancient kind of trigonometry for construction of pyramids and surveying the land in the 2nd millennium BC. The early beginnings of trigonometry ar thought to be the first numerical sequences correlating shadow lengths to time of day.Shadow tables were simple sequences of numbers which applied the shadow of a vertical stick, called a gnomon, is long in the morning and shortens to a minimum at noon. Then becomes longer and longer as the afternoon progresses (Kennedy, 1969). The shadow tables would correlate a particular hour to a particular length and were used as early as 1500 BC by the Egyptians. Similar tables were developed by other civilizations such as the Indians and Greeks. Greek mathematics Shadow tables were the primary development in creation of trigonometry however the Greeks really developed Trigonometry into an ordered science.The Greeks continued as the Babylonians astronomers did and studied the relation between angles and cir cles in lengths of chords to develop their theories on planetary position and motion (Mankiewicz, 2001). [pic] The chord of an angle subtends the arc of the angle. Ancient Greek mathematicians used the chord. Given a circle and an arc on the circle, the chord is the line that subtends the arc. A chord's perpendicular bisector traverses the center of the circle and bisects the angle. One half of the bisected chord is the sine of the bisected angle, that is, [pic] nd consequently the sine function is also known as the â€Å"half-chord†. As a result of this relationship, several trigonometric identities and theorems that are known at present were also known to Greek mathematicians, however in their equivalent chord form. Though there is no trigonometry in the works of Euclid and Archimedes, there are theorems presented in a geometric method that are similar to particular trigonometric laws or rules. Theorems on the lengths of chords are applications of the law of sines. In addit ion Archimedes' theorem on broken chords is similar to rules for sines of sums and differences of angles.From the primitive landmarks of shadow tables and the Greeks’ gain and expansion of astronomical knowledge from the Babylonians, there was a gap in the improvement of trigonometry until the time of Hipparchus. Hipparchus The first trigonometric table was in fact compiled by Hipparchus of, who is known as an as â€Å"the father of trigonometry†(Boyer, 1991). Hipparchus was the first to put into a table the corresponding values of arc and chord for a series of angles. He did this by considering every triangle was inscribed in a circle of fixed radius. Each side of the triangle became a chord, a straight line drawn between two points on a circle.To find the parts of the triangle he needed to find the length of the chord as a function of the central angle. [pic] For Example, in the diagram triangle ACB is? inscribed in circle O. So the sides of the triangle become chord ? AC, chord CB and chord AB. Hipparchus would have sought to? find the length of the chord, AC, as a function of the central? angle. He deduced a trigonometric formula for the? length of a chord sketched from one point on the circumference of? a circle to another (Motz, 1993). This could therefore be used to help understand the positioning of the planets on the sphere.Though it is not known when the methodical use of the 360 ° circle came into math, it is known that the methodical introduction of the 360 ° circle introduced a little after Aristarchus of Samos comprised of On the Sizes and Distances of the Sun and Moon, since he measured an angle a part of a quadrant. It seemed that the systematic used of the 360 ° circle was mainly as a result of Hipparchus and his table of chords. Hipparchus might have taken the idea of that division from Hypsicles who had previously divided the day into 360 parts, a division of the day that might have been recommended by Babylonian astronomy .In primeval astronomy, the zodiac had been divided into twelve â€Å"signs† or thirty-six â€Å"decans†. A recurring cycle of approximately 360 days could have corresponded to the signs and decans of the zodiac by dividing each sign into 30 parts and each decan into 10 parts. It was as a result of the Babylonian sexagesimal numeral system that each degree was divided into 60 minutes and each minute was divided into 60 seconds. Though Hipparchus is attributed as the father of trigonometry all of his work is lost except one but we gain knowledge of his work through Ptolemy. [pic] http://www. ies. co. p/math/java/vector/menela/menela. html Menelaus Menelaus of Alexandria wrote in three books his Sphaerica. In Book I, he created a basis for spherical triangles analogous to the Euclidean basis for plane triangles. He established a theorem that is without Euclidean analogue, that two spherical triangles were similar if corresponding angles are equal, however he did not diff erentiate between congruent and symmetric spherical triangles. Another theorem that he established was that the sum of the angles of a spherical triangle is more than 180 °. Book II of Sphaerica applied spherical geometry to astronomy.In addition Book III contained the â€Å"theorem of Menelaus†(Boyer, 1991). He further gave his well-known â€Å"rule of six quantities†(Needham, 1986). This theorem came to paly a major role in spherical trigonometry and astronomy. It was also believed that Melaus mya have developed a second table of chords based on Hipparchus works, however these were lost (Smith, 1958). Ptolemy Afterwards, Claudius Ptolemy developed upon Hipparchus' Chords in a Circle in his Almagest, or the Mathematical Syntaxis. The Almagest was mainly a work on astronomy, and astronomy relied on trigonometry.The 13 books of the Almagest were the most prominent and important trigonometric work of ancient times. This book was a composition of both astronomy and trig onometry and was derived from the work of Hipparchus and Menelaus. Almagest contains a table of lengths of chords in a circle and a detailed set of instructions on how to construct the table. These instructions contain some of the earliest derivtions of trigonometry. Ptolemy distinguished that Menelaus started by dividing a circle into 360o, and the diameter into 120 parts. He did this because 3 x 120 = 360, using the previous application of 3 for pi.Then each part is divided into sixty parts, each of these again into sixty parts, and so on. This system of parts was based on the Babylonian sexagesimal or base 60-numeration system, which was the only system available at the time for handling fractions (Maor, 1998). This system was based on 60 so that the number of degrees corresponding to the circumference of a circle would be the same as the number of days in a year, which the Babylonians believed to be 360 days (Ball 1960). From Menlaus Ptolemy developed the concept that the sine i s half of a chord.Ptolemy took Menelaus’ construction _ crd  · 2_ and said that the complement angle could be written as _ crd  · (180 o -2_), since 180o was half the circumference of the circle. Since today, cos_ = sin(90 o -_), it can be shown that cos_ = _ crd  · (180 o -2_), using a similar argument as the one shown above (van Brummelen, 2009). From these two expressions, one of the greatest identities known today was created. That is, (_ crd  · 2_) 2 + {_ crd  · (180 o -2_)} 2 = 1 which is exactly sin2_ + cos2_ = 1 (van Brummelen, 2009). [pic]http://nrich. maths. org/6853 [pic] http://en. ikipedia. org/wiki/Ptolemy's_table_of_chords Using his table, Ptolemy believed that one could solve any planar triangle, if given at least one side of the triangle (Maor, 1998). A theorem that was fundamental to Ptolemy's calculation of chords was what was still known at present as Ptolemy's theorem, that the sum of the products of the opposite sides of a recurring quadrilater al was equivalent to the product of the diagonals. Ptolemy used these results to develop his trigonometric tables; however whether these tables were originated from Hipparchus' work could not be proved.Neither the tables of Hipparchus nor those of Ptolemy had survived to the present day, though descriptions by other ancient authors exhibits they existed. In his work, Ptolemy founded formulas for the chord of? difference and an equivalent for our modern day half-angle? formulas. Because of Ptolemy’s discoveries, given a chord of? an arc in a circle, the chord of half an arc can be determined as? well. Ptolemy also discovered chords of sum and difference, chords of half an arc, and chords of half degree, from which he then built up his tables to the nearest second of chords of arcs from half degree.In the Almagest, a true distinction was made between plane and spherical trigonometry. Plane trigonometry is the branch of trigonometry which applies its principles to plane triangle s; Spherical trigonometry, on the other hand, is the branch of trigonometry in which its principles are applied to spherical triangles, which are triangles on the surface of the sphere. Ptolemy began with spherical trigonometry, for he worked with spherical triangles in many of his theorems and proofs. However, when calculating the chords of arcs, he unintentionally developed a theory for plane trigonometry. Trigonometry was created for use in astronomy; and because spherical trigonometry was for this purpose the more useful tool, it was the first to be developed. The use of plane trigonometry†¦ is foreign to Greek mathematicians† (Kline, 1972). Spherical trigonometry was developed out of necessity for the interest and application of astronomers. In fact, spherical trigonometry was the most prevalent branch of trigonometry until the 1450s, even though Ptolemy did introduce a basis for plane trigonometry in the Almagest in 150 A. D. IndiaThe next major contribution to trig onometry came from India. The trigonometry of Ptolemy was based on the functional relationship between chords of a circle and central angles they subtend. The Siddhantas, a book thought to be written by Hindu scholars in late fourth century, early fifth century A. D. , changed Ptolemy’s trigonometry to the study of the relationship between half of a chord of a circle and half of the angle subtended at he center by the whole chord (Kennedy, 1969). This came from the basis for the modern trigonometric function known as the sine.The Siddhantas introduction to the sine function is the chief contribution from India and marks a transformation in trigonometry. Indian mathematicians also contributed by creating their own sine table. Arya-Bhata, born in 476, was a great Indian mathematician and astronomer (Ball, 1960). He composed a book called Aryabhathiya, which contained most of the essential ideas we associate with sine and cosine. His most outstanding contribution to the topic, w hich distinguishes him from the other mathematicians of this time, was his work on sine differences (van Brummelen, 2009).His definition of sine was literally â€Å"half chord† and was abbreviated jya or jiva, which simply meant, â€Å"chord† (Smith 615). Sines were given in minutes, at intervals of 225 minutes. This measurement was not of the sines themselves, but instead, it was the measurement of the differences between the sines. His method of calculating them was as follows. The first sine was equal to 225. The second sine was defined as any particular sine being worked with in order to calculate the sine that directly follows (Clark 29).It was found using the following pattern: (225 – the previous sine) + (225 + the previous sine) 225 this total was then subtracted from 225 to obtain the sine table. Second sine: 225 – 225 = 0 225 / 225 = 1 0 + 1= 1 225 – 1 = 224 Third sine:? 225 – 224 = 1 (225 + 224) / 225 ? 2 225 – 2 = 222 (van Brummelen, 2009). Arya-Bhata concluded that dividing a quarter of the circumference of a circle (essentially one quadrant of the unit circle) into as many equal parts, with the resulting triangles and quadrilaterals would have, on the radius, the same amount of sines of equal arcs.Doing this, he was able to form a table of natural sines corresponding to the angles in the first quadrant (van Brummelen, 2009). Although much of his work had the right idea, many of Arya-Bhata’s calculations were inaccurate. Later, in 1150AD, an Indian mathematician known as Bhaskara gave a more accurate method of constructing a table of sines, which considered sines in every degree (van Brummelen, 2009). Although the Indian mathematicians made attempts at creating a table to help with astronomy, their table of sines was not as accurate as that of the Greeks. Islamic mathematicsThe ancient works were translated and developed in the medieval Islamic world by Muslim mathematicians of mostly Persian and Arab descent, who explained a large number of theorems which freed the subject of trigonometry from reliance upon the complete quadrilateral, as was the case in Greek mathematics as a result of the application of Menelaus' theorem. In accordance with E. S. Kennedy, it was following that development in Islamic math that â€Å"the first real trigonometry appeared, in the sense that only then did the object of study become the spherical or plane triangle, its sides and angles† (Kennedy, 1969).E. S. Kennedy pointed out that whilst it was possible in pre-Islamic math to calculate the magnitudes of a spherical figure, in theory, by use of the table of chords and Menelaus' theorem, the application of the theorem to spherical problems was very complex actually (Kennedy, 1969). With the aim of observing holy days on the Islamic calendar in which timings were established by phases of the moon, astronomers at first used Menalaus' method to compute the place of the moon and stars, a lthough that method proved to be ungainly and complex.It engaged creation of two intersecting right triangles; by applying Menelaus' theorem it was possible to solve one of the 6 sides, however only if the other 5 sides were known. To tell the time from the sun's elevation, for example, repeated applications of Menelaus' theorem were needed. For medieval Islamic astronomers, there was a clear challenge to find a simpler trigonometric rule (Gingerich, 1986). In the early 9th century, Muhammad ibn Musa al-Khwarizmi c a Persian Mathematician, was an early pioneer in spherical trigonometry and wrote a treatise on the subject creating accurate sine and cosine tables.By the 10th century, in the work of Abu al-Wafa' al-Buzjani, another Persian Mathematician established the angle addition formulas, e. g. , sin(a + b), and discovered the sine formula for spherical trigonometry. Abu’l-Wafa is believed to have helped introduced the concept of the tangent function. He also may have had s omething to do with the development of secant and cosecant. His trigonometry took on a more systematic form in which he proved theorems for double and half angle formulas. The law of sines, is also attributed to Abu’l-Wafa, even? hough it was first introduced by Ptolemy. This is in part? due to the fact that Abu’l-Wafa presented a? straightforward formulation of the law of sines for? spherical triangles, which states [pic] where A, B, and C are surface angles of the spherical? triangle and a, b, and c are the central angles of the? spherical triangle. In 830, Habash al-Hasib al-Marwazi created the first table of cotangents. Muhammad ibn Jabir al-Harrani al-Battani found the reciprocal functions of secant and cosecant, and created the first table of cosecants for each degree from 1 ° to 90 °.By 1151 AD, the ideas of the six trigonometric functions existed, they were just not named as we know them today. Europe It is from the Arabic influence that trigonometry reache d Europe. Western Europe favored Arabic mathematics over Greek geometry. Arabic arithmetic and algebra were on a more elementary level than Greek geometry had been during the time of the Roman Empire. Romans did not display much interest in Greek trigonometry or any facets of Greek math. Therefore, Arabic math appealed to them since it was easier for them to comprehend.Leonardo Fibonacci was one mathematician who became acquainted with trigonometry during his extensive travels in Arab countries. He then presented the knowledge he gained in Practica geometriae in 1220 AD (Gullberg, 1996). The first distinction of trigonometry as a science separate from astronomy is credited to the Persian, Nasir Eddin. He helped to differentiate plane trigonometry and spherical trigonometry. Other than that, little development occurred from the time of the 1200’s to the 1500’s, aside for the developments of the Germans in the late 15th and early 16th century.Germany was becoming a prosp erous nation at the time and was engaged in much trade. Their interests also developed in navigation, calendar formation, and astronomy. This interest in astronomy precipitated a general interest and need for trigonometry (Kline, 1972). Included in this movement around the time of 1464, the German astronomer and mathematician, Regiomontanus (also known as Iohannes Molitoris) formulated a work known as De Triangulis Omnimodis, a compilation of the trigonometry of that time.When it was finally printed in 1533, it became an important medium of spreading the knowledge of trigonometry throughout Europe (Gullberg, 1996). The first book began with fifty propositions on the solutions of triangles using the properties of right triangles. Although the word â€Å"sine† was derived from the Arabs, Regiomontanus read the term in an Arabic manuscript in Vienna and was the first to use it in Europe. The second book began with a proof of the law of sines and then included problems involving how to determine sides, angles, and areas of plane triangles.The third book contained theorems found on Greek spherics before the use of trigonometry, and the fourth was based on spherical trigonometry. In the sixteenth century, Nicholas Copernicus was a revolutionary astronomer who could also be deemed as a trigonometer. He studied law, medicine and astronomy. He completed a treatise, known as De revolutionibus orbium coelestium, the year he died in 1543. This work-contained information on trigonometry and it was similar to that of Regiomontanus, although it is not clear if they were connected or not.While this was a great achievement, Copernicus’ student, Rheticus, an Indian mathematician, who lived during the years 1514-1576, went further and combined the work of both these men and published a two-volume work, Opus palatinum de triangulus. Trigonometry really began to expand and formalize at this point as the functions with respect to arcs of circles were disregarded. Fran cois Viete who practiced law and spent his leisure time devoted to mathematics also . contributed trigonometry around this time. He came to be known as â€Å"the father of the generalized analytic approach to trigonometry† (Boyer, 1991).He thought of trigonometry as? an independent branch of mathematics, and he worked? without direct reference to chords in a circle. He made? tables for all six trigonometric functions for angles to the? nearest minute. Viete was also one of the first to use the? formula for the law of tangents, which states the following: [pic] Viete was one of the first mathematicians to focus on analytical trigonometry, the branch of trigonometry which focuses on the relations and properties of the trigonometric functions.This form of trigonometry became more prevalent around the time of 1635 with the work of Roberval and Torricelli. They developed the first sketch of half an arch of a sine curve. This important development assisted in the progression of tri gonometry from a computational emphasis to a functional approach. This formed the basis of the European contribution of trigonometry. From the influence of oriental scientists, the Europeans focused on the computation of tables and the discovery of functional relations between parts of triangles.Europe developed appropriate symbols, which replaced the verbal rules and ordinary language in which the subject was usually presented. Previously, trigonometry was expressed in lengthy passages of confusing words, but the Europeans introduced such symbols as sin, cos, tan, etc. to simplify the subject and make it more concise. Prior to the analytic approach, the main usage of trigonometry was to measure geometric figures, but the transition of its influence from geometry to calculus began with the discovery of infinite series representations for the trigonometric functions.Trigonometric series became useful in the theory of astronomy, around the time of the eighteenth century. Since astrono mical phenomena are periodic, it was useful to have trigonometric series because they are periodic functions as well. The use of trigonometric series was introduced to determine the positions of the planets and interpolation, which is a mathematical procedure that estimates the values of a function at positions between given values (Kline, 1972). Many continued to make contributions to Trigonometry looking for more accurate tables to determine the six functions.These works continued up until the invention of the Scientific Calculator in 1968. In society today, trigonometry is used in physics to aide in the understanding of space, engineering and chemistry. Within mathematics it is typically seen in mainly in calculus, but also in linear algebra and statistics. Despite the minimal information available on the history of Trigonometry it is still a vital part of mathematics. The History shows progression from astronomy and geometry and the movement from spherical to plane geometry.Toda y, Trigonometry is used to understand space, engineering, chemistry as well as mathematics. By exploring the history of trigonometry we see the importance of it in our world. References Boyer, Carl B. (1991), A History of Mathematics (Second ed. ). John Wiley & Sons, Inc. 3 Bressoud, D. M. (2010). Historical Refelctions on Teaching Trigonometry. Mathematics Teacher, 104 (2), 106-112. Brummelen, G. V. (2009). The Mathematics of the Heavens and the Earth. Princeton, NJ: Princeton University Press. Gingerich, Owen (1986), â€Å"Islamic astronomy†. Scientific American 254 (10): 74.Gullberg, Jan. (1996)Mathematics from the Birth Of Numbers. New York:W. W. Norton and Company, Inc. Joyce, D. E. (n. d. ). History of Trigonometry Outline. Retrieved 3 21, 2012, from History of Trigonometry Outline: http://aleph0. clarku. edu/~djoyce/ma105/trighist. html Kennedy, E. S. (1969), â€Å"The History of Trigonometry†. 31st Yearbook (National Council of Teachers of Mathematics, Washingt on DC) (cf. Haq, Syed Nomanul. The Indian and Persian background. pp. 60–3, in Seyyed Hossein Nasr, Oliver Leaman (1996). History of Islamic Philosophy. Routledge. pp. 52–70.Kline, Morris. (1972) Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press. Kluemper, A. (2010, 3 24). History of Trigonometry. Retrieved 3 5, 2012, from www. xtimeline. com: http://www. xtimeline. com/timeline/History-of-Trigonometry Mankiewicz, Richard. (2001)The Story of Mathematics. New Jersy:Princetion University Press. Maor, E. (1998). Trigonometric Delights. New Jersey: Princeton University Press. Miller, S. (2001). Understanding Transformations of Periodic Functions through Art. Mathematics Teacher , 94 (8), 632-635.Moussa, Ali (2011), â€Å"Mathematical Methods in Abu al-Wafa's Almagest and the Qibla Determinations†. Arabic Sciences and Philosophy. Cambridge University Press. 21 (1): 1–56. Needham, Joseph (1986), Science and Civilization in Chi na: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Taipei: Caves Books, Ltd. Rogers, L. (n. d. ). The History of Trigonometry- Part 1. Retrieved 3 1, 2012, from Enriching Mathematics: http://nrich. maths. org/6843/index Suzuki, J. (2009). Mathematics in Historical Context. Washington D. C. : The Mathematical Association of America.Smith, D. E. (1958)History of Mathematics. New York:Dover Publications, Inc. Toomer, G. J. (1998), Ptolemy's Almagest, Princeton University Press. Weber, K. (2005). Students Understanding of Trigonometric Functions. Mathematics Education Research Journal , 17 (3), 91-112. www. cartage. org. (n. d. ). Trigonometry History. Retrieved 3 5, 2012, from Trigonometry History: http://www. cartage. org. lb/en/themes/sciences/Mathematics/Trigonometry/history/History%20. html van Brummelen, G. (2009)The Mathematics of the Heavens and Earth. Princeton University Press. Princeton and Oxford.

Is Police Brutality a Serious Problem in the US? Essay

Introduction In the article, â€Å"Police Brutality is Over-Sensationalizedâ€Å", Auerback made plenty of logical arguments about the issue of police brutality. But, the statistics he showed was from the city of Chicago. For example the Rodney King case was the first major case tried in court. The Rodney King case was about an African American being pulled over for no apparent reason. Eventually the officer was acquitted of all charges. Why do police officers just feel that they are above the law? Are they above the law? Despite Auerback showing many valid points throughout the article, his argument was very one sided or biased. Summary The article ‘’the article police brutality is Over-Sensationalized’’, (Auerback, 2010) is about police brutality not being as big of a problem as the media makes it out to be. According to Auerback (2010) he claims’’ police brutality is not as commonplace as Americans claim’’. The author uses many statistics but they are only from the city of Chicago. But throughout the entire article he continuously was saying that police are put in challenging positions. 1st major point In the paragraph â€Å"The Thin Lineâ€Å", the author spoke about how excessive force by a police officer was a big problem. Auerback explained that police officers deal with dangerous situations through their regular day. Also, he described cases such as the Rodney King beating in Los Angeles being some of the reason police brutality was widespread. He said that the statistics he used couldn’t explicate a significant reason. In the paragraph â€Å"The Evidence Suggests Otherwiseâ€Å", Auerback clarified statistics showing that  police brutality was not as bad as the media makes it out to be. For example, there was a study done by the Urbana – Champaign independent Media Center on police brutality. The results showed that in Illinois 2854 police officers had complaints about police brutality, but surprisingly only 7 percent of the officers were regulated. Later on in the paragraph Auerback argued that police officers have the right to use excessive force to a certain extent. Basically in this paragraph the author is arguing that there isn’t enough evidence to prove police brutality isn’t a big deal. The paragraph â€Å"having the Opposite Effectâ€Å", Auerback explained how the media portrays the police sometimes makes the job harder, and hurts he communities. Throughout the paragraph he showed that police brutality was a very huge charge. Also the author showed that not all police officers are bad guys as the media portrays them. 2nd Major Point There were many logical arguments and valid questions to ask during the article â€Å"Police Brutality is Over Sensationalizedâ€Å". One logical argument about the article would be why were there only a few arguments? If the author would have made the article a two-way debate about police brutality. The article would be drastically changed. Auerback did explain police brutality could be a problem but, he explained police are always in the right basically. Another question I had that wasn’t answered was are all police officers bad? There are valid examples that some police officers take their authority too far. Such as the Rodney King beating in Los Angeles made police brutality come to the light. But, because of some police officers making bad decisions and using excessive force, they give police a bad name. Lastly, another argument would be that a police officers` is very dangerous, but are they above the law? Most police officers are some of the nicest people you will meet. They put their lives on the line to serve and protect us citizens. However when you look at the statistics shown in the article they show cops get away a lot of crimes. Such as in the article the statistics done in Chicago. Throughout five years Chicago saw 1774 complains per year with only 5% of the officer having the complaints. But, in the identical survey done only 1 percent had enough evidence to start a case. That is very disturbing to hear. Why do the police officers get away with  such crimes? The reason is there is just not much evidence to prove the point. The three logical points made by the article would be the police was above the law, and why do they have so much power. 3rd Major Point Auerbacks` angle of vision was very demanded by his background which gives him ethos or credibility but also shows he could be biased. His background gives him a lot of credibility. For example he had seventeen years of experience in public policy and political science. He graduated from Boston College Graduate School of Arts and Sciences, also working as a federal contractor. With all being said his perspective is biased by him working with the government. The governments’ perspective is that the government is always right. Which Auerbacks’ angle of vision is basically police are always in the right no matter what. If the author would have shown both sides of the issue of police brutality the article would be more credible. Also, the statistics shown in the article was only from the city of Chicago. If Auerback showed statistics of the entire country instead of using just a metropolitan city then the article wouldn’t be so biased. Auerbacks` angle of vision discredited the article. The author made it seem like officers always has a reason to use excessive force. Conclusion In conclusion, the article â€Å"Police Brutality is Over Sensationalizedâ€Å", spoke about how police officers use excessive force and how it was a huge problem. The author tried to downplay the issue by using examples of cases where the police officers was in the right. But, in reality there are plenty of examples of police officers using excessive force for no reason at all. His argument throughout the article was that the media over-exposes the issue. Auerback used only a certain amount of logical arguments. Despite Auerback showing many valid points throughout the article, his argument was very one-sided or biased. Works Cited Auerback, Michael. â€Å"Police Brutality is Over Sensationalizedâ€Å". John D. Ramage, John C. Bean, June Johnson. â€Å"The Allyn & Bacon Guide to Writingâ€Å" 7th Edition

The Pennsylvania Academy of Fine Art Essay Example | Topics and Well Written Essays - 1250 words

The Pennsylvania Academy of Fine Art - Essay Example The building rises to a height of about 70 feet, and the whole structure is made of iron, stones, brick, with no wood being used anywhere in its construction. (Fairman Rogers, published in ‘The Philadelphia Inquirer’, on April 24, 1876) In keeping with the high Victorian Gothic style, the building is made of richly colored materials, the faà §ade being made of green and red sandstone along with purplish Bluestone. The architectural style is an eclectic mix of Gothic and Classical architecture, and it is revolutionary in the context that, until then, there was no other building that could boast of a â€Å"13th century Gothic arch on a 17th-century mansarded pavilion.† The building opens onto Broad Street, with the faà §ade 65 inches high. The North is flanked by Cherry Street, Burnt Street on to the east and Apple tree Street towards the South. The building is planned with a central corridor which is about 15 feet wide, with rooms on either side. The first floor of the building, houses the library, art studios and offices, while a mezzanine floor has a conservation laboratory, the boardroom and the plumbing. The museum’s collection or the artworks are housed on the second floor, called the Gallery, where the corridor is intersected by a Rotunda which is about 52'6" x 38'2". Pennsylvania, being an industrial city, Frank Furness could freely use â€Å"riveted iron truss that held aloft the great weight of the blind wall of the north faà §ade.† (Lewis)Above the Gallery is the attic made up of iron trusses.

CORPORATE AND SECURITIES LAW Case Study Example | Topics and Well Written Essays - 500 words

CORPORATE AND SECURITIES LAW - Case Study Example The paper applies both corporate and securities law to solve the issue existing at Bagofglass, Inc. (BofG). Peter, the petitioner in the case, seeks compensation for damages caused by Bog as provided under section 11 of corporate law. Bagofglass Inc., through its CEO, Mr. Erwin Mainway, signed the registration statement. The statement took effect on January 1, 2011 after its successful filing on December 10, 2010. In the statement, Bagofglass Inc declared public offering of its shares. Mr. Peter bought shares after the statement became effective. Each share sold at ten dollars; Peter purchased a thousand shares. On January 15, the Company violated the agreement stipulated in the statement by selling its shares at fifteen dollars per share. Peter, the plaintiff, therefore, alleges that Bagofglass violated the law by omitting the facts stated in the registration statement. Therefore, the registration statement signed by Erwin was misleading. In this case, Bagofglass Inc’s CEO is liable as the signatory and director of the corporation. Corporate Law provides that if an individual purchases the shares not in the initial offer, except when from a third party, the plaintiff may seek compensation for damages caused by false statements as provided under section 11. Therefore, it is possible for Mr. Peter to recover against Bagofglass and its staff involved in giving a misleading registration statement. The staff includes Mr. Ewin Mainway (Bagofglass Inc.’s CEO), the law firm representing Bagofglass Inc., Dewy, Cheat hem and How (DUCHY) and the accounting firm representing BofG, Ernest and Ernest, LLP (E&E). The law firm, DC&H is liable if they expertise the portion of the initial public offering of Bagofglass, Inc. The aforementioned statement takes effect only if the conducted reasonable investigations provide facts beyond reasonable doubt that DUCHY participated at the time when the registration statement thereon was untrue. However, DC&H are not liable in