GENERATING PYTHAGOREAN TRIPLES
This study investigates which numbers can be part of triples such as (3, 4, 5) and (5, 12, 13) right-angled triangles with integer sides. It is limited in generating Pythagorean triples (a, b, c) with no common factor such that a right triangle exists with legs a, b and hypotenuse c and satisfies the equationa^2+ b^2= c^2. It sought to answer the questions: (1) what is a Pythagorean Triple? (2) Prove the general formula in generating Pythagorean triples. It made use of the exploratory approach through investigation and giving proof. The highlights of the study are as follows: (1) The Pythagorean triples was derived from the Pythagorean Theorem which states that “the square of the hypotenuse of a right triangle is equal to the sum of the squares on the two legs”, (2) The Pythagorean Triple is a triple of positive integers a, b, c such that a^2+ b^2= c^2. (3) For any choice of integers m and n where n < m, we can get a Pythagorean triple by setting values for a, b and c to show that (〖m^2+n^2)〗^2 = (〖m^2-n^2)〗^2+ (〖2mn)〗^2. (4) If restrictions on m and n that one of them must be even and the other is odd then, the values of (m^2+n^2), (m^2-n^2) and (2mn) have no common factor. It is recommended that teachers should possess the high level of mathematical intellect, integrity and always update themselves in the new trends to cope with the fast-changing world of mathematics.
Pythagorean Theorem, Pythagorean Triples