# Essay, Research Paper: Analytic Geometry

## Mathematics

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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 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.

Bibliography"Analytic Geometry." 21 Nov. 99

. "Cartesian Coordinates." 2 Dec. 99

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