History Of Algebra Essay, Research Paper

Algebra is defined by Webster?s New Collegiate Dictionary

as a generalization of arithmetic in which letters

representing numbers are combined according to the rules of

arithmetic. This is not a good definition of algebra. It

would take a thick book to really explain it. In fact, to

this day it is still being added to. There are always new

things to be discovered about it. It has been added to by

many different people over the centuries. Algebra has a

long interesting history.

The first work describing algebra was called

Arithmetica, a treatise by Diophantus of Alexandria. It

was a collection of 130 problem and numerical solutions.

Only 6 of the 13 books have been found, the others were

believed to have been destroyed soon after their creation.

Diophantus was known as the father of algebra. The way he

solved problems algebraically was know as Diophantine

analysis. He lived from about 200 AD to about 284 AD He

was the first to use an algebraic symbolism, in which

symbols and letters represented the unknown. He refused to

believe that there was any such thing as a negative number.

He reasoned this by saying it is impossible to have

negative four objects. He did much work with quadratic

equations and even equations with variables to the sixth

power. Diophantus also seemed to know that any whole

number could be written as the sum of four squares. Pierre

de Fermat did some work with this but it was not proved

until later when Joseph Louis Lagrange worked with it.

Despite all of Diophantus?s work algebra had a long way to

go before general problems could be written down and

solved.

There were many other influential people in the

history of mathematics. One such man was named Theon of

Alexandria. He wrote commentaries on many other works of

mathematics in his time. In many cases he added extra

steps into others proofs. He never really did anything

original but he added much to other mathematicians works.

His daughter Hypatia grew up around mathematics. As she

grew she picked up on it and eventually she even helped her

father on several works. She became the head of a

Plotinost school in Alexandria. There she lectured on

subjects such as mathematics and philosophy. Platonusts

believed that there was an ultimate reality in which humans

could never fully understand. Hypatia only lived to be

about forty five because she was brutally murdered by

Christians who felt threatened by her scholarship. One of

the works that she helped her father critique was that

called Almagest by Ptolemy. This was a thirteen page

treatise. This is the earliest of all of Ptolmey?s works.

It describes the mathematical theory of the motions of the

Sun, Moon, and the planets. Ptolmey was an interesting

man. He believed in the geocentric theory, that is the Sun

and other planets revolve around the Earth. It was

proposed by Aristotle. Another belief at the time was the

heliocentric theory in which the Earth and all of the other

planets revolve around the Sun. Along with this he also

figured out the seasons. He discovered that every day was

about 1/300 of a year. Later the exact number of days in a

year, 365 1/4, was determined by Hipparchus. Ptolmey also

started studying the motions of the moon. He discovered

using an inscribed 360-gon that pie was 3 17/120 which is

really close to pie?s true value. Also using this 360-gon

he discovered that a 60 degree chord with the length of

radical 3 is 1.73205.

Another important figure in the history of Algebra is

Pythagoras of Samos. He is often described as the first

pure mathematician. Pythagorus founded a philosophical and

religious school. It?s many members had no personal

belongings and they were vegetarians. He believes that at

it?s deepest level, reality is mathematical in nature. He

believes anything about nature relates to a mathematics

law. Pythagorus had a rather odd belief that each number

had it?s own individual personality and the number 10 was

the best number because it was the sum of the first 4

numbers. Pythagorus was best known for his famous geometry

theorem. It stated that the sum of the squares of the

lengths of the two sides of a right triangle is equal to

the square of the length of the hypotenuse. He also

discovered that the angles of a triangle add up to 2 right

angles. Pythagorus is also credited with the discovery of

irrational numbers. Irrational numbers are numbers that

are non-terminating non-repeating decimals. Pythagorus is

a very important figure when it come to developing algebra

and mathematics.

One of Pythagorus?s most prominent teachers was Thales

of Miletus. Born in 624 BC Thales seems to be known as the

first Greek philosopher, scientist, and mathematician. It

is quite difficult to determine what he discovered and what

his views were because much of his writing has been lost.

Thales is credited for discovering the Ursa Minor

constellation. There are claims that he wrote a book about

navigation. It was said that in this book he described how

to navigate using this constellation. Thales predicted an

eclipse of the Sun in the year 585 BC It was before said

that an eclipse of the sun would come every 19 years but

Thales used the Babylonian Saros, a cycle which lasts 18

years 10 days and 8 hours. Another one of Thales great

accomplishment is when he determined how to measure the

height of the pyramids. He did this by measuring the

length of the pyramid?s shadow at the time in which the

length of his shadow was equal to his height. Therefore he

concluded that the height of the pyramid would be the same

as the length of it?s shadow. Though he knew this he still

did not understand the basic facts of geometry such as

similar triangles. Thales is credited with five theorems

in which today we consider very simple, but back in his day

they were amazing discoveries. He said that a circle is

bisected by any diameter, the base angles of an isosceles

triangle are equal, the angles between two intersecting

straight lines are equal, two triangles are congruent if

they have two angles and one side congruent, and an angle

in a semicircle is a right angle. Later on about 900 years

down the road a philosopher named proclus described these

theorems and how they work. proclus was intended to be a

lawyer but while he was in his studies he decided that he

liked philosophy, and so he took to it. He mostly did

commentaries on other mathematicians works. Through this

he still made some pretty brilliant assumptions.

Another great mathematician in time was named Euclid.

He is known for his treatise on mathematics called The

Elements. This was a 13 book set. The first 6 books were

about plane geometry, such as the basic properties of

triangles, parallelograms, rectangles and squares. Books 7

through 9 deal with the number theory. Book 10 deals with

irrational numbers. Books 11 through 13 deal with 3

dimensional geometry. The long lasting nature of the

elements must make Euclid the leading mathematics teacher

of all time. In his treatise he arranged many of Exodus?s

theorems, and perfected many of Theaetetus?s. Euclid

discovered what eventually led to the discovery of the

transitive property of equality. He stated ?Things which

are equal to the same thing are equal to each other.?

Euclid was an interesting man and his work was studied up

until the nineteenth century when non-Euclidean geometry

was discovered.

Algebra?s long history is filled with many

philosophers and mathematicians. They all contributed

their part. If one of these important people would not

have existed chances are algebra would have not developed

the way that it did. Humans would not have as much in

depth knowledge about it as they do. The history of

Algebra is very complicated buy interesting.