Diophantus biography summary forms

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On the one hand Diophantus quotes the definition of a polygonal number from the work of Hypsicles so he must have written this later than 150 BC. On the other hand Theon of Alexandria, the father of Hypatia, quotes one of Diophantus's definitions so this means that Diophantus wrote no later than 350 AD. However this leaves a span of 500 years, so we have not narrowed down Diophantus's dates a great deal by these pieces of information.

Another extant work Preliminaries to the geometric elements, which has been attributed to Heron, has been studied recently in [16] where it is suggested that the attribution to Heron is incorrect and that the work is due to Diophantus. The work considers the solution of many problems concerning linear and quadratic equations, but considers only positive rational solutions to these problems.

Other works

Diophantus did not just write Arithmetica, but very few of his other works have survived.

There are no general comprehensive methods of solving used by Diophantus (that is found). He was perhaps the first to recognize fractions as numbers in their own right, allowing positive rational numbers for the coefficients and solutions of his equations.

Diophantus applied himself to some quite complex algebraic problems, particularly what has since become known as Diophantine Analysis, which deals with finding integer solutions to kinds of problems that lead to equations in several unknowns.

Diophantine equations

Diophantine equations can be defined as polynomial equations with integer coefficients to which only integer solutions are sought.

For example, he would explore problems such as: two integers such that the sum of their squares is a square (x² + y² = z², examples being x = 3 and y = 4 giving z = 5, or x = 5 and y =12 giving z = 13); or two integers such that the sum of their cubes is a square (x³ + y³ = z², a trivial example being x = 1 and y = 2, giving z = 3); or three integers such that their squares are in arithmetic progression (x² + z² = 2y², an example being x = 1, z = 7 and y = 5).

To give one specific example, he calls the equation 4=4x+20 'absurd' because it would lead to a meaningless answer. Bombelli did, however, borrow many of Diophantus's problems for his own book, Algebra. The editio princeps of Arithmetica was published in 1575, by Xylander. For example to find a square between 45​ and 2 he multiplies both by 64, spots the square 100 between 80 and 128, so obtaining the solution 1625​ to the original problem.

And the tomb tells scientifically the measure of his life. There is no evidence to suggest that Diophantus realised that a quadratic equation could have two solutions.
Consider y+z=10,yz=9. Put 2x=y−z so, adding y+z=10 and y−z=2x, we have y=5+x, then subtracting them gives z=5−x. Based on this information we have given him a life span of 84 years.

It is believed that Fermat did not actually have the proof he claimed to have.

in words. He writes:-

We conjecture the existence of a lost theoretical treatise of Diophantus, entitled "Teaching of the elements of arithmetic".

There is another piece of information which was accepted for many years as giving fairly accurate dates. Brown Publishers, 1991).

↑Wilbur Knorr, "Arithmêtike stoicheiôsis: On Diophantus and Hero of Alexandria," in Historia Matematica (New York, 1993).

↑Carl B.

Boyer, A History of Mathematics (Wiley, 1991), p. This letter was first published by Paul Tannery in [7] and in that work he comments that he believes that Psellus is quoting from a commentary on Diophantus which is now lost and was probably written by Hypatia. If indeed he did know this result it would be truly remarkable for even Fermat, who stated the result, failed to provide a proof of it and it was not settled until Lagrange proved it using results due to Euler.