Rene Descartes Analytic Geometry Essays - Analytic Geometry

Rene' Descartes Analytic Geometry Essays - Analytic Geometry Rene' Descartes Analytic Geometry Analytic geometry was brought fourth by the famous French mathematician Rene' Descartes in 1637. Descartes did not start his studying and working with geometry until after he had retired out of the army and settled down. If not for Descartes great discovery then Sir Isaac Newton might not have ever invented the concept of calculus. Descartes concept let to calculus and Newton and G.W. Leibniz would not be know as well as they are today if it were not for the famous mathematician Rene' Descartes. Analytic geometry is a, branch of geometry in which points are represented with respect to a coordinate system, such as Cartesian coordinates, and in which the approach to geometric problems is primarily algebraic. (Analytic Geometry) Analytic geometry is used to find distances, slopes, midpoints, and many many other things using special equations and formulas to determine what a person is looking for. Analytic geometry concentrates very much on algebra, generally, it is taught to students in algebra classes and becomes very helpful when being used in geometry. It is not very often when geometry is taught not using the algebra to solve the problems, unless proving statements, analytic geometry is used most often when speaking of geometry, it is the guidelines of geometry. It is a set way to find out answers to problems. There are many simple formulas to analytic geometry, but some of them get very complex and difficult. Analytic geometry is not only used in math, it is very common to see it being used in any kind of science, logic, and any other mathematical subjects. There are formulas in this form of mathematics in which the volume of a gas is measured, and other formulas along those lines (Encyclopedia.com). Some formulas and equations of analytic geometry are: The midpoint formula- (change in x/2, change in y/2) Distance formula- square root of (change in x) squared -(change in y) squared Formula for slope- (Change in y)/(Change in x) Formula for a line- y=mx+b where m is the slope of the line and b is the y intercept. Equation of a line- ax+by+c=0 (Fuller, Gordon) To find perpendicular lines you take to slope of each line and multiply them together, if the result is one then the lines are said to be perpendicular. To find parallel lines the Slope must be exactly the same. These are just some simple facts about analytic geometry, it actually can get very complicated. When finding out about parabolas and ellipse's it gets difficult, there are many difficult and extended formulas in analytic geometry (Fuller, Gordon 7, 12, 18). Obviously these are just a few examples and analytic geometry goes on much further than what you see in these formulas. There are so many geometric formulas and theorems that they are almost impossible to put in a list. Analytic geometry has been combined with many other branches of geometry, now there are some things that are hard to decide wheater to label them algebraic or otherwise. Analytic geometry is broken up into two sections, finding an equation to match points and finding points to match equations. (Geometry) There are many other kinds of geometry such as demonstrative geometry that involves measuring fields and right angles. The early Egyptians developed this kind of geometry when building. There is descriptive geometry that involves using shapes that do not change when moved, they are definite, defined shapes. Another is non-three- dimensional geometry that uses analytic and projective geometry to study four dimensional figures. All of these kinds of geometry are commonly used (Geometry). Analytic geometry is used every day, it is defiantly something that can be extremely helpful if learned. Analytic geometry is used in architecture, surveying, and even business. In business analytic geometry can be used to find the maximum profit that can be made from a sale or event. As with all skills that are generally learned, analytic geometry is a great thing to know. Even the simple things, the basics, are very helpful. This subject can be broken down into the simplest things, such as having to walk to say Wal-mart and knowing when you are about half way, that is taking the distance from the starting point to the destination and dividing it by two

Invention of Polystyrene and Styrofoam

Invention of Polystyrene and Styrofoam Polystyrene is a strong plastic created from erethylene and benzine. It can be injected, extruded or blow molded. This makes it a very useful and versatile manufacturing material.   Most of us recognize polystyrene in the form of styrofoam used for beverage cups and packaging peanuts. However, polystyrene is also used as a building material, with electrical appliances (light switches and plates) and in other household items. Eduard Simon Hermann Staudinger Polymer Research Keystone/Stringer/Getty Images German apothecary Eduard Simon discovered polystyrene in 1839 when he isolated the substance from natural resin. However, he did not know what he had discovered.  It took another organic chemist named Hermann Staudinger to realize that Simons discovery, comprised of long chains of styrene molecules, was a plastic polymer. In 1922, Staudinger published his theories on polymers. They stated that natural rubbers were made up of long repetitive chains of monomers that gave rubber its elasticity. He went on to write that the materials manufactured by the thermal processing of styrene were similar to rubber. They were the high polymers, including polystyrene. In 1953, Staudinger won the Nobel Prize for Chemistry for his research. BASF Commercial Use of Polystyrene Badische Anilin Soda-Fabrik or BASF was founded in 1861. BASF has a long history of being innovative due to having invented synthetic coal tar dyes, ammonia, nitrogenous fertilizers as well as developing polystyrene, PVC, magnetic tape and synthetic rubber. In 1930, the scientists at BASF developed a way to commercially manufacture polystyrene. A company called I.G. Farben is often listed as the developer of polystyrene because BASF was under trust to I G. Farben in 1930. In 1937, the Dow Chemical company introduced polystyrene products to the U.S. market. What we commonly call styrofoam, is actually the most recognizable form of foam polystyrene packaging. Styrofoam is the trademark of the Dow Chemical Company while the technical name of the product is foamed polystyrene. Ray McIntire - Styrofoam Inventor Dow Chemical Company scientist  Ray McIntire invented foamed polystyrene aka Styrofoam. McIntire said his invention of foamed polystyrene was purely accidental. His invention came about as he was trying to find a flexible electrical insulator around the time of World War II. Polystyrene, which already had been invented, was a good insulator but too brittle. McIntire tried to make a new rubber-like polymer by combining styrene with a volatile liquid called isobutylene  under pressure. The result was a foam polystyrene with bubble and was 30 times lighter than regular polystyrene. The Dow Chemical Company introduced Styrofoam products to the United State in 1954. How Are Foamed Polystyrene or Styrofoam Products Made? Foamed polystyrene starts as small spherical beads that contain an expanding agent called hydrocarbon.The polystyrene beads are heated with steam. As the expanding agent boils, the beads soften and expand up to forty times their original size.The expanded beads are left to cool down before being heated again. However, this time the beads are expanded within a mold.The molds are designed in a variety of  shapes  depending on the desired end product.  Examples are things such as styrofoam  cups, cartons, wig stands and more.The beads completely fill the mold and also fuse together.Styrofoam is about 98% percent air.

Diversity in Canada Research Paper Example | Topics and Well Written Essays - 2000 words

Diversity in Canada - Research Paper Example The research paper "Diversity in Canada" analyzes the opportunities and challenges brought by the cultural diversity in Canada. The employment rate of the indigenous people in Canada that were aged between 25 and 54 years increased from 61.2 percent in the year 2001 to 65.8 per cent in the year 2006. On the other hand, 80.3 percent of the immigrants In Canada were employed in 2001 and in 2006, they employed population increased to 81.6 percent. The local Canadian market is quite diverse culturally just like the global market. Thus, businesses in Canada need to perceive and deal with the cultural diversity as well as the way it affects the economic behavior, market trends, and demands. To encourage the creation and sharing of Canadian stories, both at home and abroad, which reflect Canada's cultural mosaic, Canadian Heritage is pursuing a number of strategic objectives. One of the most cardinal strategic objectives is the realization of the significance of cultural diversity for Canada. There has been a huge debate about the usefulness of multiculturalism in Canada and the potential ways it is impacting the lifestyle of both the indigenous and the immigrant population in the country. The current state of cultural diversity in Canada can best be described as, â€Å"the best of times, it was the worst of times†. Canada has not only seen increased comparative advantage into the society but also has witnessed more evidence of the important role of the Canadian multiculturalism policy in the achievement of comparative success.