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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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