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Tuesday, November 18, 2008

Infinite yet Finite

I've always been a bit of a math freak. Not in the sense 'exam-mathematics', but generally some crazy mathematics concepts always fascinated me.

Here's one.

Can there be a curve with infinite length, yet encloses only a finite area?

Sounds absurd? Trust me it is not. There are in fact such curves.
Who can find me one?

EDIT (The Answer) :

Here it is.

Hope you get the idea.
Simply you get an equilateral triangle, then to the middle 1/3 portion of each side of it you add another equilateral triangle, and so on. Keep doing this and as you can guess there is no end. Which ultimately results in a curve with infinite length.
Yet, the area it covers is less than the area of the circle which encircles the original triangle.

Not so absurd now, ha?

If you are interested, this is just a simple example of a vast and a wonderful theory called Chaos Theory.
Here is a place to get started.



  1. Not a maths person.. never was... and perhaps never will be... :( eventhough I come from a family of maths geniuses!!

  2. "Can there be a curve with infinite length, yet encloses only a finite area?"


    :D haha - sorry man - u know me and math. :D
    Let me know if u do manage to get the bottom of this mystery ;)

  3. I wish I was a Maths freak!!!

    What's that about curves...

  4. I'll put an edit... with the curve... :D