Beyond Pythagoras Investigation

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Beyond Pythagoras Investigation

In this investigation, I am trying to find the rules and patterns for

right-angled triangles. Each length of the right-angle triangle is

going to be a positive integer, and the shortest length is going to be

an odd number.

Below is a typical type of a Pythagoras triple equation:


Formula:a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

In this equation, the first step I took was to put the numbers instead

of the letters. Once I did that I squared all the numbers, and when I

add a² + b² it equaled to c². Incase one of the numbers was missing on

the triangle; I would replace that as x², and carry out the formula as

a normal algebraic expression. When you look at the numbers at first

they don't add up. If you do 3 + 4 it does not equal to 5, but once

the numbers are squared they add up.

This is the second type of a Pythagoras triple equation:


In this example the exact same procedure was done. I put all the

numbers instead of the formula and worked it out. The first step I

took was to square all the numbers. To check that my work was correct

I added a² + b² to get c². So far both example that were shown satisfy

the condition because when I added a² + b² I got c². One thing I found

in common between both of the right-angled triangle was that the

hypotenuse and the second biggest number had a one number difference.

This is the third type of Pythagoras triple:


On this third example, the Pythagoras triple worked because once 'a'

and b were squared, and when added then they equal to c². Just like

the other two examples, I used the same method to solve the equation

and also the check it. Also, in this example there are similar things

between the hypotenuse and the second biggest side, just like in the
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