BEYOND PYTHAGORAS | |

The numbers 3, 4 and 5 satisfy the condition

3² + 4² = 5²

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

The numbers 3, 4 and 5 can be the lengths – in appropriate units – of the sides of a right-angled triangle.

By observation:

(3, 4, 5), (5, 12, 13) and (7, 24, 25) are all called Pythagorean triples because they satisfy the condition.

a² + b² = c² in a right angled triangle

With the family of right-angled triangles for which all the lengths are positive integers and the shortest is an odd number.

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Part 1

Investigate the family of Pythagorean triples linked to the triangles (3, 4, 5), (5, 12, 13) and (7, 24, 25) where the shortest side is an odd number, all 3 sides are positive integers and the two largest sides differ by one.

Part 2

Investigate other families of Pythagorean triples.

The Investigation should include three strands:

1. Making and monitoring decisions to solve problems

Find & explain patterns in the ‘triples’. Explain & set your own questioning agenda.

2. Communicating mathematically

Find formulae which ‘explain’ the above. Define your variables & be precise with your ‘mathematics’.

3. Developing skills of mathematical reasoning

‘Prove’ all/any formulae which you may have found.

This is to be written up & brought to the next G & T session on 19th Feb.
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4

3

5

12

5

13

24

7

25

The number 5, 12 and 13 can also be the length – in appropriate units – of a right-angled triangle

This is also true for the numbers 7, 24 and 25

c

b

a
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