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## #1 2007-05-24 18:22:36

Daniel123
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### Who discovered this?

I heard this on the radio a while ago, but i did not hear who discovered it - i would like to know who did discover it before applying it to anything.

The area of a right-angled triangle and a circle will be equal if:

i) the height of the triangle is equal to the radius of the circle

and

ii) the base of the triangle is equal to the circumference of the circle

I have looked on the internet but cant find anything on it.
A little explanation about it would be nice too:).. but im only 15 so it needs to be kept fairly simple.

Thanks.

## #2 2007-05-24 19:18:06

mathsyperson
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### Re: Who discovered this?

It's fairly easy to see why this is true if you think about their formulae.

The circumference of a circle is given by 2πr, where r is its radius.
So that means that your right-angled triangle has a base of 2πr and r.
The area of a right-angled triangle is given by 1/2 base x height.
So that means that the area is 1/2 x 2πr x r = πr², the area of a circle.

I'd never heard that theorem(?) before, but because it's a fairly easy proof, I wouldn't think that it was discovered by anyone very significant.

Why did the vector cross the road?
It wanted to be normal.

## #3 2007-05-24 19:24:47

Daniel123
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### Re: Who discovered this?

Oops i feel a bit stupid now...

Thank you.

Novice

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