Possible Duplicate:
Is value of $\pi = 4$?

I know that you can take area out of a square without changing it's perimeter. Now, here's this problem:

Draw a circle with dia = 1;

Draw a square around with perimeter = 4, side = 1;

Remove the corners, still perimeter is same.

repeat this thing infinite times, you have to see the image below.


I know there is something missing, but what is it? I am not a mathematician, not even the worst one. Please be kind and answer in English as much as possible. Thanks

  • 3
    $\begingroup$ Hello Anubhav, it turns out your question has already been asked here before. You can find a link to the earlier question above. You didn't do anything wrong; it's just that we like to avoid duplicate questions. $\endgroup$ – Zev Chonoles Mar 23 '12 at 7:36
  • $\begingroup$ How kind of our mod! $\endgroup$ – user21436 Mar 23 '12 at 7:38
  • $\begingroup$ yes. you want to down vote? @KannappanSampath $\endgroup$ – Anubhav Mar 23 '12 at 7:40
  • 1
    $\begingroup$ @AnubhavSaini The corners don't become smoothed out, so you could imagine that it is like pressing a crinkled paper to the table. The area of the smoothed out paper would be more than the area of the table covered by the crinkled paper. (And yes, this comparison has some weaknesses, as there is no overlap in your example, a stretched/compressed rubber band is more accurate, but it might get you the idea.) $\endgroup$ – Phira Mar 23 '12 at 9:48
  • 1
    $\begingroup$ And I really don't see why this question has to be always asked with the ugly picture. $\endgroup$ – Phira Mar 23 '12 at 10:32

Browse other questions tagged or ask your own question.