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 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
Publishing, 1962. "Geometry.
Encarta. CD-ROM. 1996-1997. "Results of
Analytic Geometry." 1 Jan. 95. 12
Dec. 99
. "The Life of Rene' Descartes." 12 Dec. 99