Integer Pythagorean Triples, Methods From the History of Math Part 1:

  Integer Pythagorean triples, methods from the history of math part 1:

The theorem of Pythagoras suggests that In any right triangle, the area of the square whose side is the Hypotenuse is equal to the sum of the areas of the Squares whose sides are the two legs.
it can be written as an equation: a² + b² = c²
A Pythagorean triple has three positive integers a, b, and c, such that a² + b² = c². In other words, a Pythagorean triple represents the Lengths of the sides of a right triangle where all three sides have integer Lengths
Through the History of mathematics many methods of finding Pythagorean triple were described, in this article I will introduce an easy method which based on simple Addition of fractions.
Description of algorithm:
Select two Consecutive odd numbers or two Consecutive even numbers. Let suppose: a and b
We calculate the sum (1/a + 1/b)
we express the result by simple rational fraction (c/d)
and we get the Pythagorean triple: c ; d ;√(c²+d²)
this method insures that value √(c²+d²) is an integer which means that it gives integer Pythagorean triple
try to figure out the reason for that…