Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

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.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

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.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Who discovered this?

Oops i feel a bit stupid now...

Thank you.

makada

Member

Registered: 2007-09-04

Posts: 6

Re: Who discovered this?

Dont feel bad.
Sometimes it is the simple questions in life which lead us to the great things

When I was your age, even I used to ask all sots of questions in class, sometimes I would get snubbed but then  other times I learnt a lot.

Never shy away from asking for if there were no questions we would never get the answers

Last edited by makada (2007-09-06 01:22:13)