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### Purpose of Algebra

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Date: 10/15/96 at 8:23:59
From: Landon Stuckey
Subject: Purpose of Algebra

What is the purpose of algebra and who came up with the idea of
algebra?

Sincerely,
Landon Stuckey
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Date: 10/16/96 at 14:0:42
From: Doctor Ceeks
Subject: Re: Purpose of Algebra

Hi,

one.  The idea of algebra has occurred to many in the past, and it is
unclear who was the very first to come up with the idea.

Okay, now to your first question.

Algebra is useful for many things.

It's like this.  You're studying some objects and how they behave and
interact.  You notice some patterns that happen over and over.  You
try to eliminate all the unnecessary details and grasp the essence of
what is going on. You find out that you can describe what is going on
by explaining some rules. You discover that these rules describe
many, many things and imply some things you never thought of before.
You end up explaining lots of new things.  You have then created an
algebra and used it with purpose.

(Technically, the word "algebra" is now used by mathematicians to mean
a very special kind of thing, but that won't matter unless you go to

Here's an example of the above.

You're playing with a square. You notice that you can move the square
some ways without making it seem like you moved the square. For
instance, you can flip it around one of its diagonals. Or, you can
rotate it 90 degrees clockwise (or counter-clockwise). You notice
that sometimes, you can follow such a motion by another such motion
and get something new which doesn't affect the square.

You want to understand these motions. You decide to simplify things
by simply denoting the rotation by 90 degrees clockwise by R and the
90 degree counter-clockwise rotation by L. You decide to write RR for
the motion you get when you do R twice. You find that RRRR is really
the same as doing absolutely nothing. You notice that RRR is the same
as L, and LLL=R. You find that RR=LL. You find that you can't get the
flip about the diagonal using just R and L, so you call it F.

You keep exploring, and "algebra" just naturally pours forth!
Eventually you may discover everything you can do to a square. You
may see that with just R and F, you can get everything! You may try
to do this for a regular pentagon, then a regular hexagon...even, a
regular n-gon! Are they really so different?

If you have fun doing this, and you do it a lot, welcome to the world
of algebra... you're an algebraist.

Usually, people first encounter algebra when they study the algebra
of numbers. So you may be more used to seeing things like 3x+5=y,
where x and y stand for numbers. The algebraic rules numbers obey are

commutativity:     x+y = y+x,
associativity: (x+y)+z = x+(y+z), and
distributivity:  x(y+z) = xy+xz.

There's also a special number, called zero, and denoted 0.  It has the
property that x+0=x.)

-Doctor Ceeks,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Basic Algebra