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

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Pythagoras Theorem is a2 + b2 = c2. ‘a’ being the shortest side, ‘b’ being the middle side and ‘c’ being the longest side (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

 

The numbers 5, 12, 13 and 7, 24, 25 also work for this theorem

                        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

 

                        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 

3 , 4, 5

Perimeter = 3 + 4 + 5 = 12

Area = ½ x 3 x 4 = 6

 

5, 12, 13

Perimeter = 5 + 12 + 13 = 30

Area = ½ x 5 x 12 = 30

 

7, 24, 25

Perimeter = 7 + 24 + 25 = 56

Area = ½ x 7 x 24 = 84

 

From the first three terms I have noticed the following: -

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  • ‘a’ increases by +2 each term
  • ‘a’ is equal to the term number times 2 then add 1
  • the last digit of ‘b’ is in a pattern 4, 2, 4
  • the last digit of ‘c’ is in a pattern 5, 3, 5
  • the square root of (‘b’ + ‘c’) = ‘a’
  • ‘c’ is always +1 to ‘b’
  • ‘b’ increases by +4 each term
  • (‘a’ x ‘n’) + n = ‘b’

From these observations I have worked out the next two terms.

I will now put the first five terms in ...

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