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**envey_27****Member**- Registered: 2005-07-03
- Posts: 1

say it simple for a yr 8 person to understand

can you give me an example

what is da pythagoros theorem

*Last edited by envey_27 (2005-07-03 00:11:19)*

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

You have 3 sides of a right angled triangle.

The longest is the hypotenuse.

We'll call it C.

C is the only line not touching the right angle, where A and B do. A and B can be either of the remaining sides.

The theory goes; A squared + B squared = C squared.

Example; A = 3, B = 4 and C =5.

A squared = 9

B squared = 16

C squared = 25

9+16=25.

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,762

A right angled triangle is one in which one of the angles is 90 degrees.

Pythagoras theorem states that the sum of the square of the two sides is equal to the square of the longest side, i.e. the hypotenuse.

You can also think of it this way.

The total of the area of the squares formed by the two shorter sides of a right angled triangle would be equal to the area of the square formed by the longest side.

The first reply has given you one of the possibilities.

There are many more.

eg (5,12,13)

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Here's something weird that I found out whilst doing some coursework: if one of the sides is one unit less than the hypotenuse, the other side has a length equal to the square root of the other two sides' sum.

e.g. 3²+4²=5² --> 3²=4+5

Why did the vector cross the road?

It wanted to be normal.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

Well, ganesh's example (5,12,13) should qualify:

5² = 12+13 YES! ... how interesting. I wonder why.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

Zach and ganesh are right, of course, the Pythagoras Theorem is just:

For a Right-Angled Triangle, if you take the length of the longest side (the hypotenuse) and square it (multiply it by itself) then that will be the same value as adding up the squares of the other two sides:

|\

A | \ C

| \

|___\

B

A²+B²=C²

Try it with any size triangle, so long as there is a right angle in it!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,762

The three values of the sides of a right angled triangle are also called a Pythagorean Triple.

A Pythagorean triple is a set of three whole numbers , such that one number squared added to another number squared equals the third number squared. Euclid could prove that there are an infinite number of such Pythagorean triples.

Euclid's proof begins with the observation that the difference between successive square numbers is always an odd number.

4 - 1 = 3, 9 - 4 = 5, 16 - 9 = 7, 25 - 16 = 9, 36 - 25 = 11, 49 - 36 = 13 etc.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

Yes, because they are on the growing sides of a square:

The difference between 3² and 4² is the X's below:

OOOX

OOOX

OOOX

XXXX

So, how many X's do we need to add to grow the square from 3x3 to 4x4? Answer: 3+3+1

Likewise, to go from a 4x4 to 5x5 needs:

OOOOX

OOOOX

OOOOX

OOOOX

XXXXX

How many X's? 4+4+1

Hehe

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,762

Yes, 2(n)+1 and 2(2n+1)+1 are both odd numbers!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Polly****Member**- Registered: 2005-06-24
- Posts: 221

Hi my mate jaz1 is making her self sick i dont know what 2 do pleese help me im worried.

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**Polly****Member**- Registered: 2005-06-24
- Posts: 221

mathsyperson wrote:

Here's something weird that I found out whilst doing some coursework: if one of the sides is one unit less than the hypotenuse, the other side has a length equal to the square root of the other two sides' sum.

e.g. 3²+4²=5² --> 3²=4+5

hi

do u like reading my fav boo is harry potter

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**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

My favourite book is called 'The seer and the Sword' by Victoria Hanley.

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

My favourite book is called "Mort" by Terry Pratchett.

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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**im really bored****Member**- Registered: 2005-05-12
- Posts: 76

I like "False memorys" by Dean R. Kuntz

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

Wow. I Love "Mort" too.

AND SO DO I

Eeek!

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

Terry Pratchett'll take over the world!

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

Zach, you aren't banned!!!!!

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I concur. Very good for confusing people though. Well done!

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,762

My favorite book is

'The Man Who Loved Only numbers'

by Paul Hoffman

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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