Math

Pythagorean Triples

MAT126

Let m,n be two arbitrary integers and

Then if

Then:

So a, b, c are Pythagoras' triplets.

For a first triplet we can choose:

A second triplet:

Third triplet:

Fourth triplet:

Fifth triplet:

A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a, b, and hypotenuse c (Bluman, 2005). A Pythagorean triple is a triple of positive integers (a, b, c) where a2 + b2 = c2. A triple is simply a right triangle whose sides are positive integers. An easy way to generate Pythagorean triples is to multiply any known Pythagorean triple by an integer (any integer) (Vargas, 2008). In my research of the Pythagorean triple, I have found many different formulas that can generate an infinite number of Pythagorean triples. However, the one I chose to show in this paper is called the m, n formula for generating Pythagorean triples. The formulas for generating a Pythagorean triple are as follows:

1. a2+b2=c2

2. The m. n formula

3. The two-fraction formula, and the list just keeps going, like the numbers.

I learned that Pythagorean triples can be generated using so many different expressions with simple numbers and letters. It really takes more time figuring how to work your problem rather than writing it. I learned that the numeric system of numbers can take you too so many different levels of basic subtraction, multiplication, division, and addition when generating any Pythagorean triple.

In conclusion, we have heard about the different methods to use to generate Pythagorean triples. We have even demonstrated one of the equations for generating infinite numbers in Pythagorean triples. These types of methods will prove to be very useful in the future. In that, the will allow us to be able to see all the possible outcomes in number form.

REFERENCES

Bluman, 1st Ed, (2011). Math in our World, MAT126, VOL, 2, Chapter 10, page 620, Exercise 4.