Achievement By Diophantus In Arithmetica example essay topic
414 words
Diophantus is thought to be born around the year 200 AD. Very little is known about his life except for a puzzle from the Greek Anthology compiled by Metrodorus around 500 AD. The puzzle states that Diophantus married at the age of 26, had a son who died at the age of 42, and died himself four years later at the age of 84. These details may be totally fictitious, but they are all the information we know today about this great mathematician. Diophantus is best known for his work on the series of books, Arithmetica, which contains solutions to algebraic equations and theories on numbers. Only six of the original thirteen books have survived through the years. In Arithmetica, Diophantus outlines 130 problems giving numerical solutions of determinate and indeterminate equations. In these equations, he only considers positive rational solutions to be true. Diophantus believes that receiving a negative number as the solution to an equation absurd because it is meaningless to have negative of something.
Also in Arithmetica, he made small advances in the symbolism, yet still only used notation for a single unknown in his equations. When a problem called for more than one unknown, Diophantus simply wrote out "first unknown" and "second unknown" in words. He had to write out in words many of his equations because algebra had a long way to go before general problems could be solved concisely. Another achievement by Diophantus in Arithmetica is his introduction and work on three types of quadratic equations.
He had three types, while today we only have one, because he did not have any concept of zero and he avoided negative coefficients by considering the given numbers a, b, c to all be positive in each of them. Other works of Diophantus include a collection of lemmas called, The Porsims, and another book named, Preliminaries to the Geometric Elements. He refers to The Porsims, which is believed to be entirely lost, in Arithmetica. One lemma in this book is that "the difference of the cubes of two rational numbers is equal to the sum of the cubes of two other rational numbers".
Preliminaries to the Geometric Elements was once attributed to Heron, another Greek mathematician, but was found incorrect. Both of these works were very important to the mathematical society. Fortunately, Diophantus was given the renown that he deserved for them.
