Pythagoras Theorem


Introduction to Pythagoras

Most people have heard of Pythagoras and know that is something to do with geometry but not much else? Many of the things that we take for granted such as satellite navigation, mobile telephones and air travel all use the principles that Pythagoras proved over two thousand year ago.

Once you understand the principles of this simple theory then you can use it to calculate things such as measuring triangles, calculating distances and many other things that you haven’t even thought about yet?

What is Pythagoras?

Pythagoras was a mathematician who lived over 2000 years ago in Greece. His exact date of birth is not known but it’s thought that he was born around 580 BC and died around 500 BC.

He also founded a religious movement called Pythagoreanism which had many followers. Pythagoreans believed that many things in life could be explained by mathematics.

Pythagoras is best known for proving the Pythagorean Theorem, as it is known in the US, or Pythagoras Theorem in the UK, which has been used by scientists, students, mathematicians and engineers in their daily lives ever since. Many things which we take for granted nowadays would not be possible if it was not for Pythagoras Theorem.

What's Pythagoras Theorem?

Pythagoras' theorem states that in any right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Unless you understand the theory then this statement can seem a little baffling?
Like many things that are difficult to understand, it’s often easier to break the theory down into easily understandable pieces?

What’s a Right Angled triangle?

Right Angled TriangleA right angled triangle has a right angle of 90° as one of its interior angles. In the image here the right angle is marked with the white square.

Any triangle like this is a right angled triangle, it doesn't matter which side the right angle is on or what size the triangle is - the rule applies to all of them.

This is what makes the theory so useful as it can be applied to shapes as small as this one or those which are many miles wide.

What’s the Hypotenuse?

According to some sources the word hypotenuse derives from the Greek words for hypo (under) and teinein (stretch) or tenuse (side).

The hypotenuse is the longest side of a right angled triangle. As you can see, the hypotenuse is the side marked in purple on the image above.

What are the other two sides?

Now you know which side the hypotenuse is then this is easy, it's the two other sides marked in orange on the picture above.

OK, so now we know which side is which, what use is it?

Pythagoras TheoremWell, understanding the rule means that you can calculate lots of things without having to know the exact exact length of each side?

For example, if you knew that side x was 3 metres and side y was 4 metres long then you would be able to work out the length of the hypotenuse quite easily?

On the image here the hypotenuse is z and the other 2 sides are x and y .

Firstly you need to work out the sum of the squares of both x and y:

X² is 3 x 3 = 9

Y² is 4 x 4 =16

Z² = X² + Y² (25)

The sum of the other 2 sides squared is 25

The length of the hypotenuse therefore is the square root of 25

√25 = 5 ( 5 x 5 = 25)

So you have now calculated that the length of the hypotenuse is 5 metres

A Video Explanation of Pythagoras Theorem

Is that it then?

Not at all, no. There are many ways in which this simple rule can be used but unless you understand the basis of the rule then these can be difficult to comprehend.

The resources page lists lots of useful sites where you can learn more about Pythagoras Theorem and how you can apply this into your studies and future career.

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