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

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

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