# BEYOND PYTHAGORAS

Sohel Patel                                                                                Year 11

BEYOND PYTHAGORAS

In this report, I am going to investigate the Pythagorean Triple. The Pythagoras Theorem was invented by Pythagoras, a Greek mathematician and philosopher who lived in the 6th centaury BC.

The Pythagoras Theorem only works in right-angled triangles, where there are three different lengthed sides, one short, one medium, and the other long. A Pythagorean Triple is when a set of numbers satisfy the condition: Shortest side2 + Medium side2 =Longest side2. Also all the sides have to have positive integers.

Here is an example of a Pythagorean Triple:

The above triangle is a Pythagorean Triple because it satisfies the condition with all its sides being a positive integer. I will now work out the perimeter and area of the above Pythagorean Triple.

There are also other Pythagorean Triples. Here they are:

Both the triangles 2) and 3) are Pythagorean Triples because they satisfy the condition and all their sides have a positive integer.

Here is a table showing the results of the 3 Pythagorean Triples:

From the above table, I can see a few patterns emerging. Here they are:

1. The shortest side is always an odd number.
2. The medium side is always an even number.
3. The medium side plus one equals to the Longest side.
4. The Longest side is always odd.

To show that these patterns are correct and to see if there are any more patterns, I am going to extend this investigation and draw two more Pythagorean Triples. Here they are:

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