History of Algebra

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 as 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 athematics 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 he 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 is 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 traight 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.


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