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Centered on Geometry (Euclid)
The ancient Greeks have contributed much to the development of the Western World as we know it today. The Greeks questioned all and yearned for the answers to many of lifes questions. Their society revolved around learning, which allowed them to devote the majority of their time to enlightenment. In answering their questions, they developed systematic activities such as philosophy, psychology, astronomy, mathematics, and a great deal more. Socrates (469-399 BC) was an ancient Greek philosopher whose ideas mark the turning point in the history of knowledge and formal thought. Plato (428-347:348 BC) one of Socrates students founded the Academy. The Academy was key in spreading thought and knowledge because of its devotion to teaching the sciences. Aristotle (384-322 BC), Platos brightest student, founded Biology and is given credit for his accomplishments in varying fields. Out of all of the great Greek accomplishments which influence the world today, I chose the one which I believe is the most important, Euclidean Geometry and its effects.
Euclid (365-300 BC) is often considered synonymous with geometry. Euclids works have been so influential that they serve as the basis for most geometrical teachings for the past 2000 years. His works supercede all other works of its kind. Euclids interests in spatial knowledge lead him to detailed definitions, postulates, and axioms that are used today. Data is a collection of given measurements and postulates that Euclid collected. Data expresses that lines, angles, and ratios can be given in magnitude; rectilinear figures may be given in species or form; and points and lines may be given in position. Euclids 94 propositions state that when certain aspects of a figure are given, other aspects can be found by using concrete formulas. For example, proposition 66 states, If a triangle have one angle given, the area of the rectangle contained by the sides including the angle has to the area of that triangle a given ratio. Divisions of Figures consists of 36 propositions concerning the divisions of various figures into two or more equal parts in given ratios. Optics is an elaboration on Platonic thought stating that discrete rays cause vision, and that vision can be explained by geometry. Euclid states that, Things seen under a greater angle appear greater, and those under a lesser angle appear less, while those under equal angles appear equal. Euclid used this statement and his mathematical formulas to explain elusions in size comparison. Conics, Porisms, Psiedese, and Surface Loci are lost works attributed to Euclid. These four works are the link between elementary geometry, and higher mathematics. Catoptrica explains the theory of mirrors and brought about Euclids Elements of Music. Elements of Music is a brief excursion into the uses of mathematics in music and sound.
Euclids most important works are summarized in the Elements, which consists of 13 detailed books. Elements presents all of the Greek geometrical knowledge of Euclids day in a logical fashion. These books give us a little insight into Euclid and were designed and are used as learning tools. Including theorems and constructions of plane geometry, solid geometry theory of proportions, incommensurable, commensurable, number theory, and the basis for what is known as geometrical algebra. Proclus (Greek Philosopher) defined Elements as those theorem whose understanding leads to knowledge of the rest. Elements is a detailed explanation of geometric shapes, and measurements using the number theory. The impact of the Elements has been so great that translated forms are widely studied today. Since Euclid based his entire geometric study on points, straight lines, and circles, his work leaves three main geometrical questions open. The three famous problems left unsolved were squaring a circle, doubling the cube, and trisecting the angle. But the Greeks say other Greek philosophers later solved these unsolved mysteries. Euclidean Geometry was not elaborated upon greatly until 1667 when Girolamo Saccheri wrote Euclid Freed of Every Flaw. Girolamo Saccheri through his works started the basis for elliptical geometry (obtuse angles) and hyperbolic geometry (acute angles) which was a continuation on Euclids work eventually forming Non Euclidean Geometry.
Although a large part of mathematics can be attributed to Euclid, there are other Greek philosophers who have also contributed greatly to the ... more
Find essay on Lesser Extent In
The Un And Environmental Issues
The UN attempts to follow universal ideals, but at this point it is not fully universal and still reflects some great power interests because of economic situations. This can be clearly seen in the environmental issues. The problem is that the UN does not have enough power internationally to fully contain the issue. The trouble is that the developing countries and the developed countries do not agree on main points, and this leads to a division.
When the UN was first established, the UN Charter makes no mention of environmental protection (Roberts and Kingsbury, 327). One of the shortcomings of the League, which the UN was founded on, was the lack of environmental interest. The turning point was in the 1972 Conference of Human Environment. This conference stated that all human beings had the right to live in a clean world. This was the beginning of environmental awareness in the UN.
After this the UN attempted to integrate environmental concern into the system. The UN was equipped with five economic commissions for different regional areas; Africa, Latin America, Western Asia, Asia and the Pacific, and Europe. Along with promoting economic development they also dealt with environmental issues. The European branch has been the most active. This shows the beginning of great power interests.
By 1972 many countries had begun to establish their own environmental organizations. The separate states decided that at this time they should try to unite under the UN to make policies international. One of the main problems was that the governments had different thoughts on environmental concerns verses developmental concerns. The developing countries were concerned that the economic costs would slow their developments, along with the restrictions placed on them that developed countries did not have to deal with when they were developing.
In the past, the greater powers were able to develop more freely as there were no restrictions placed on them. They had the freedom to pollute the world, as they did not know the harm they were causing the environment. Now, because of greater knowledge and damage around the world, restrictions need to be placed on all the countries in the world. The problem with environmental issues is that one country can damage something like the ozone layer, which ends up affecting the whole world and not just that one country.
The 1992 conference, UNCED, on environment was a landmark. It recognized dangers of deforestation and global warming. Both of these are global problems that need to be solved, making environmental issues international concerns. One of the main problems with the UNCED was that its sponsorship was by donor governments along with major companies and foundations. This gave greater powers more say as they donated more money, while the lesser powers disagreed with many of the issues.
The UNCED was not as successful as it had hoped to be. The main problem was that the greater powers saw environmental issues as not that big of problems, easily solved by restricting certain tests, chemical usage, and the destruction of nature. The countries had developed enough that they did not need to do extensive research in potentially dangerous areas. The developing countries saw these movements as a great threat on their advancements. Without being able to learn for themselves they felt that they were being treated unfairly. Along with that, they wanted to spend their money on furthering their country instead of helping solve environmental issues that did not need to be solved immediately.
These problems created a divide between northern and southern countries. The South felt that their sovereignty was being threatened by the North, as the North had more technology, more knowledge, more access to natural resources, and most importantly, more economic power. The lesser-developed countries did not see it as fair that they had to help and spend money on issues such as global climate control as it was the more industrial countries that created the damage. Also the developing countries have not had the chance to acquire the experience that the other countries have.
The latest attempt at universal environmental reform was at Kyoto. The countries gathered together and formed the Kyoto treaty. The treaty did not address issues such as when or ... more
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