The History And Contributions :: essays research papers

Greek Geometry Although the original roots of geometry can be traced to the Egyptians, the Greeks built on most Egyptian theories that we use today. Greek astronomy and Greek geometry were both used in order to answer many difficult questions of the time. Without geometry, the study of astronomy would have been almost impossible, and vice versa. Even though many Greek theorems and principles were later built on by geniuses such as Einstein and Lobachevsky, the basis still remains the same. The development of Greek geometry is said to be started by Thales of Miletus. Thales came from Egypt with a number of geometric principles that the Greeks were able to use for practical purposes. He lived towards the beginning of the sixth century B.C, and has been credited with many geometric theorems. Some of the most important theorems developed by Thales included: -  Ã‚  Ã‚  Ã‚  Ã‚  If two triangles have two angles and one side is respectively equal, then both triangles are congruent to each other. -  Ã‚  Ã‚  Ã‚  Ã‚  Angles at the base of any isosceles triangle are equal. -  Ã‚  Ã‚  Ã‚  Ã‚  If two straight lines intersect, then the opposite angles formed are equal. Thales also did much work with the height of pyramids by measuring the height of the pyramid's shadow only at a specific time of the day. While most of his theorems were proven, some that were not pertained to a ship's distance from shore and the bisector of a circle. His discoveries led to the formation of many other theorems by later Greeks such as Pythagoras and Plato. These two men (next to Thales) contributed the most to Greek geometry. Pythagoras discovered and proved many different theorems and ideas that contributed greatly to the development of geometry. Some of Pythagoras's proven discoveries included: -  Ã‚  Ã‚  Ã‚  Ã‚  All of the angles in a triangle add up to the sum of two right angles. -  Ã‚  Ã‚  Ã‚  Ã‚  The development and use of geometrical algebra. -  Ã‚  Ã‚  Ã‚  Ã‚  The theorem of Pythagoras. a^2 + b^2 = c^2 Pythagoras also did many studies with triangles and developing or editing shapes. His most famous discovery was the Pythagorean theorem (listed above). This theorem combined the sides of a right triangle, and this led to the development of irrational numbers by Pythagoras later on. Pythagoras discovered that the square root of 2 was an irrational number. Plato, another great mind of Greece, did more than just develop theorems for geometry, he stressed that geometry was essential. Plato believed that everyone should be well educated in mathematics as well as geometry.

Mintzberg †the Fall and Rise of Strategic Planning Essay

The Fall and Rise of Strategic Planning by Henry Mintzberg When strategic planning arrived on the scene in the mid- ­? 1960s, corporate leaders embraced it as â€Å"the one best way† to devise and implement strategies that would enhance the competitiveness of each business unit. True to the scientific management pioneered by Frederick Taylor, this one best way involved separating thinking from doing and creating a new function staffed by specialists: strategic planners. Planning systems were expected to produce the best strategies as well as step- ­? by- ­? step instructions for arrying out those strategies so that the doers, the managers of businesses, could not get them wrong. As we now know, planning has not exactly worked out that way. While certainly not dead, strategic planning has long since fallen from its pedestal. But even now, few people fully understand the reason: strategic planning is not strategic thinking. Indeed, strategic planning often spoils strategic thinking, causing managers to confuse real vision with the manipulation of numbers. And this confusion lies at the heart of the issue: the most successful strategies are visions, not plans. Strategic planning, as it has een practiced, has really been strategic programming, the articulation and elaboration of strategies, or visions, that already exist. When companies understand the difference between planning and strategic thinking, they can get back to what the strategy- ­? making process should be: capturing what the manager learns from all sources (both the soft insights from his or her personal experiences and the experiences of others throughout the organization and the hard data from market research and the like) and then synthesizing that learning into a vision of the direction that the business should pursue. Organizations isenchanted with strategic planning should not get rid of their planners or conclude that there is no need for programming. Rather, organizations should transform the conventional planning job. Planners should make their contribution around the strategy- ­? making process rather than inside it. They should supply the formal analyses or hard data that strategic thinking requires, as long as they do it to broaden the consideration of issues rather than to discover the one right answer. They should act as catalysts who support strategy making by aiding and encouraging managers to think strategically. And, finally, they an be programmers of a strategy, helping to specify the series of concrete steps needed to carry out the vision. By redefining the planner’s job, companies will acknowledge the difference between planning and strategic thinking. Planning has always been about analysis—about breaking down a goal or set of intentions into steps, formalizing tho se steps so that they can be implemented almost automatically, and articulating the anticipated consequences or results of each step. â€Å"I favour a set of analytical techniques for developing strategy,† Michael 1 Porter, probably the most widely read writer on strategy, wrote in he Economist. The label â€Å"strategic planning† has been applied to all kinds of activities, such as going off to an informal retreat in the mountains to talk about strategy. But call that activity â€Å"planning,† let conventional planners organize it, and watch how quickly the event becomes formalized (mission statements in the morning, assessment of corporate strengths and weaknesses in the afternoon, strategies carefully articulated by 5 p. m. ). Strategic thinking, in contrast, is about synthesis.

Definition and Examples of Amphiboly in English

Amphiboly is a  fallacy  of relevance that relies on an ambiguous word or grammatical structure to confuse or mislead an audience. Adjective: amphibolous. Also known as  amphibology. More broadly, amphiboly may refer to a fallacy that results from a faulty sentence structure of any kind. Etymology From the Greek, irregular speech Pronunciation:  am-FIB-o-lee Examples and Observations [T]he 2003 election reform law demanded that politicians acknowledge in their own voices their responsibility for advertisements they run on public airwaves. But five years later, the I approved has become a pivotal device in commercials for Congress and the White House, a place for candidates to make a declaration of intent, summarize the message or take a parting shot. . . .A University of New Hampshire rhetoric professor, James Farrell, was irked as far back as the 2004 Democratic primary campaign, the first time the disclaimers were required. Then, as now, he said, advertisement writers were coming up with awkward non-sequiturs just to slip in something extra.Mr. Farrell noted a current commercial for Representative Don Cazayoux, Democrat of Louisiana, in which the candidate said, I’m Don Cazayoux and I approved this message because that’s who I’m fighting for. That, Mr. Farrell said, is an amphiboly, a logical confusion created by a grammatical ambiguity.Of course, if asked, the candidate will say he means he’s fighting for the middle class, said Mr. Farrell, of the spot’s theme. However, one could easily conclude that the disclaimer addition refers to the candidate himself, as in, I’m Don and that’s who I’m fighting for.(Steve Friess, Candidates ‘Approve’ Ads and Get a Bit Creative. The New York Times, Sep. 30, 2008) Humorous Amphibolies Amphiboly is usually so recognizable that it is rarely used in real-life situations to make a claim seem stronger than it is. Instead, it more often leads to humorous misunderstandings and confusions. Newspaper headlines are one common source of amphiboly. Here are a few examples: Prostitutes Appeal to Pope -- Farmer Bill Dies in House -- Dr. Ruth to Talk About Sex With Newspaper Editors -- Burglar  Gets Nine Months in Violin Case -- Juvenile  Court to Try Shooting Defendant -- Red Tape Holds Up New Bridge -- Marijuana Issues Sent to a Joint Committee -- Two Convicts Evade Noose: Jury Hung. . . . Most of these cases of amphiboly are the result of a poorly constructed sentence: I like chocolate cake better than you. Although we normally try to avoid them, intentional amphiboly may prove useful when we feel obligated to say something we would rather not have to say, yet want to avoid saying something that is patently not true. Here are lines from letters of recommendation: In my opinion, you will be very fortunate to get this person to work for you. I am pleased to say that this candidate is a former colleague of mine. From a professor on receiving a late paper from a student: I shall waste no time in reading this. (John Capps and Donald Capps, Youve Got To Be Kidding!: How Jokes Can Help You Think. Wiley-Blackwell, 2009) Amphiboly in a Classified Ad Sometimes the amphiboly is more subtle. Take this newspaper classified ad that appears under Furnished Apartments for Rent: 3 rooms, river view, private phone, bath, kitchen, utilities included Your interest is aroused. But when you visit the apartment, there is neither a bathroom nor a kitchen. You challenge the landlord. He remarks that there are common bathroom and kitchen facilities at the end of the hall. But what about the private bath and kitchen that the ad mentioned? you query. What are you talking about? the landlord replies. The ad didnt say anything about a private bath or a private kitchen. All the ad said was private phone. The advertisement was amphibolous. One cannot tell from the printed words whether private modifies only phone or whether it also modifies bath and kitchen. (Robert J. Gula, Nonsense: Red Herrings, Straw Men and Sacred Cows: How We Abuse Logic in Our Everyday Language. Axios, 2007) Characteristics of Amphibolies To become a skilled perpetrator of amphibolies you must acquire a certain nonchalance toward punctuation, especially commas. You must learn to toss off lines such as I heard cathedral bells tripping through the alleyways, as if it mattered not a whit whether you or the bells were doing the tripping. You should acquire a vocabulary of nouns which can be verbs and a grammatical style which easily accommodates misplaced pronouns and confusions over subject and predicate. The astrology columns in popular newspapers provide excellent source material. (Madsen Pirie, How to Win Every Argument: The Use and Abuse of Logic. Continuum, 2006) The Lighter Side of Amphiboly Some amphibolous sentences are not without their humorous aspects, as in posters urging us to Save Soap and Waste Paper, or when anthropology is defined as The science of man embracing woman. We should be mistaken if we inferred immodest dress on the woman described in a story: . . . loosely wrapped in a newspaper, she carried three dresses. Amphiboly is often exhibited by newspaper headings and brief items, as in The farmer blew out his brains after taking affectionate farewell of his family with a shotgun. (Richard E. Young, Alton L. Becker, and Kenneth L. Pike, Rhetoric: Discovery and Change. Harcourt, 1970)