Fibonacci's Method
Leonardo of Pisa (c. 1170 – c. 1250) described this method for generating primitive triples using the sequence of consecutive odd integers, and the fact that the sum of the first terms of this sequence is . If is the -th member of this sequence then .
Choose any odd square number from this sequence ( ) and let this square be the -th term of the sequence. Also, let be the sum of the previous terms, and let be the sum all terms . Then we have established that and we have generated the primitive triple . This method produces an infinite number of primitive triples, but not all of them.
EXAMPLE: Choose . This odd square number is the fifth term of the sequence, because . The sum of the previous 4 terms is and the sum of all terms is giving us and the primitive triple = .
Read more about this topic: Formulas For Generating Pythagorean Triples
Famous quotes containing the word method:
“The method of authority will always govern the mass of mankind; and those who wield the various forms of organized force in the state will never be convinced that dangerous reasoning ought not to be suppressed in some way.”
—Charles Sanders Peirce (1839–1914)