# Beyond Pythagoras

Beyond Pythagoras

Pythagoras Theorem is a² + b² = c². 'a' being the shortest side, 'b' being the middle side and 'c' being the longest side (which is always the hypotenuse) of a right angled triangle.

The numbers 3, 4 and 5 satisfy this condition:

3² + 4² = 5²

because 3² = 3 x 3 = 9

4² = 4 x 4 = 16

5² = 5 x 5 = 25

and so 3² + 4² = 9 + 16 = 25 = 5²

We also checked to see if similar sets of numbers also satisfy this condition:

(smallest number)² + (middle number)² = (largest number)²

The numbers 5, 12 and 13 also satisfy this condition:

5² + 12² = 13²

because 5² = 5 x 5 = 25

12² = 12 x 12 = 144

13² = 13 x 13 = 169

and so 5² + 12² = 25 + 144 = 169 = 13²

The numbers 7, 24 and 25 also satisfy this condition:

7² + 24² = 25²

because 7² = 7 x 7 = 49

24² = 24 x 24 = 576

25² = 25 x 25 = 625

and so 7² + 24² = 49 + 576 = 625 = 25²

For the set of numbers 3, 4 and 5:

Perimeter = 3 + 4 + 5 = 12

Area = 1/2 x 3 x 4 = 6

For the set of numbers 5, 12 and 13:

Perimeter = 5 + 12 + 13 = 30

Area = 1/2 x 5 x 12 = 30

For the set of numbers 7, 24 and 25:

Perimeter = 7 + 24 + 25 = 56

Area = 1/2 x 7 x 24 = 84

From these sets of numbers I have noticed the following: -

* 'a' increases by +2 for ...