History of Algebra Essays - Ancient Greek Mathematicians

History of Algebra Essays - Ancient Greek Mathematicians 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 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