Analytic Geometry Essay, Research Paper
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
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 to find out how far half way is. That could be considered part of the midpoint formula. Some of the formulas are a bit complex to use in everyday life, but in some working careers, it is very common for a person to use these highly complicated equations.
Rene’ Descartes was a famous French mathematician, he came up with the theory of analytic geometry using the Cartesian coordinates (Instant Essays). The Cartesian coordinates that are a plane made of two intersecting lines where numbers, (x, y) are used to find the relative distance from the intersecting lines. These lines have 4 different sections and go on forever, there is no end to Cartesian’s coordinates (Cartesian Coordinates). Descartes got his education fist from Jesuit College and then the University of Poitiers. After he left school Descartes liked to party until he joined the army of Prince Maurice of Nassu. In 1628, after Descartes had retired, he contributed his life to “Scientific research and philosophic reflection.” (Descartes, Rene’) In Descartes life he wrote many essays in which he became famous for. Compendium Musicae and Discourse on Method are two of Descartes famous essays. In 1637 a group of his essays was published, after years of having the essays, they caused Descartes to finally become well known. Descartes did not make amazing accomplishments until after he was retired from the army. A little over then years after his essay’s were published Rene’ was invited to
Sweden by Queen Christina because she wanted to meet the person with the brilliant mind, shortly after arriving in Sweden Descartes fell ill and died (Descartes, Rene’).
Rene’ Descartes contributed not only to math but also to science, and many other things. Rene’ followed the scientific method, he loved to build off others’ idea’s and make them more interesting and informational. He followed Francis Bacon’s method, but based his results on “rationalization and theory, rather than experiences.” (Descartes, Rene’) He was very dedicated to everything that he studied, and that is why he had accomplished so much in his lifetime (Descartes, Rene’). Descartes was the originator of Cartesian coordinates and curves. As it has been stated many times already, he is known as the creator of analytic geometry. He also contributed the imaginary number i to the math of algebra, this is used in result of negative roots to a number.
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