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 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.