The distinctive features of diophantus s problems appear in the later books. An example of these last two methods, is found in problem 9, book iv of the arithmetica, and. Diophantus of alexandria, arithmetica and diophantine equations. Book ii problem 8 to split a given square 16 in two squares. Problem to nd a number whose di erences from two given numbers 9,21 are both squares. He is sometimes called the father of algebra, and wrote an influential series of books called the arithmetica, a collection of algebraic problems which greatly influenced the subsequent development of number theory. Alexandrian algebra according to diophantus mathematics. In book 4, he finds rational powers between given numbers. As i was at the end of the chapter about equations linear, quadratic and radical i saw the well known riddle about diophantus s age. This book features a host of problems, the most significant of which have come to be called diophantine equations. For example, book ii, problem 8, seeks to express a given square number as the sum of two square numbers here read more. Gow describes diophantus as the engineer of two facets of algebra.
The eighth problem of the second book of diophantuss arithmetica is to divide a square into a sum of two squares. In book 3, diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes. Diophantus also appears to know that every number can be written as the sum of. At the close of the introduction, diophantus speaks of the thirteen books into.
Alternative solution for the diophantus age riddle. This problem became important when fermat, in his copy of diophantus arithmetica edited by bachet, noted that he had this wonderful proof that cubes cant. Diophantus was a hellenistic greek or possibly egyptian, jewish or even chaldean mathematician who lived in alexandria during the 3rd century ce. One of the most famous problems that diophantus treated was writing a square as the sum of two squares book ii, problem 8. Book iii problem 9 to nd three squares at equal intervals. Following is a sample of problems in the other books. As a 15 year old student in the netherlands who loves math, i was just casually going through some problems in my text book. To divide a given square into a sum of two squares. Book iv problem 21 to nd four numbers such that the product of any two added. Books were stored in the biblion place of books in the library.
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