Pythagorean Triple

Mathematics students study the Pythagorean Theorem named after Pythagoras .Pythagoras was a great philosopher and a mathematician. A triple is three sides of a right angle triangle. His name is famous in mathematics due to his theorem. The Pythagorean theorem relates the length of hypotenuse of aright angled triangle to the lengths of the other two sides.

 If you are given one number of a triple, you can construct two other numbers of the triple.

 

How to do this?

 

  

There are two situations, one is the number is odd and another is the number is even.

If the number is odd, follow the following steps.

1. Take an odd number greater than 1.This is the first number of the triple.
2. Square the odd number.
3. Subtract 1and divide by 2, from the step 2.This will be the second number of the triple.
4. Add 1 to the step 3.This will be the third number of the triple.

Example:-

 

Suppose the first number of the triple is 3.

Square of 3 is 9.

According to the step3, by subtracting 1, and dividing by 2 we get (9-1)/2=4.

This will be the second number of the triple.

By adding 1, we get 4+1=5.This is the third number of the triple.

Hence, 3, 4, 5 is a Pythagorean triple.

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If the number is even, follow the following steps.

1.  Take an even number greater than 2.This is the first triple number.
2.  Square the number.
3.  Divide by 4and subtract 1.This is the second number of the triple.
4.  Add 2 to the result of step 3.this will be the third number of the triple.

Example:-

 

Suppose the first number of the triple is 4.

Square of 4 is 16.

Divide it by4, and then subtract 1 we will get 3 .This is the second number of the triple.

Add 2 to the above result.3+2=5.This will be the third number of the triple.

Hence 4, 3, 5 is a Pythagorean triple.

 

 

 Take more examples and find out the triples.