THE GOLDEN TRIPLETS

Even though there exist infinitely many Pythagorean triplets, the most unique ones are those originating from 3, 4 and 5. 

It is known that:

3² +4² =5²

6²+8²=10²

9²+12²=15²

We can generalize these triplets in the form:

(3n) ²+ (4n) ²= (5n) ² 

Where ‘n’ is any whole number >0.

Let 3n=a  4n=b  5n=c 

It is observed that (c/a) = (5/3) = φ ≈ 1.66= Golden Ratio

Using the above formula, we can use various values of ‘n’ to find infinitely many such ‘golden triplets’

We have named them golden triplets because they follow the golden ratio.

For information about the golden ratio, please visit
http://en.wikipedia.org/wiki/Golden_ratio