Looking at the following image, which was posted on the internet:
Could someone tell me what is wrong? It seems true for the first 4 small images. But, when it comes to infinitesimal length, something must be wrong, i can feel it.
Asked
Active
Viewed 248 times
-2
-
For this reason some days back it was posted here that rather than $\pi$ symbol of $torque$ (dont know name exactly) is more precise whose value is almost $6.28=2\pi$ – Archis Welankar Feb 18 '16 at 13:57
-
How many debunkings of this are already available? Probably many more than pi... – Did Feb 18 '16 at 14:00
1 Answers
0
You're right that it's wrong. You can't approximate the length of a curve by stepping right and up and right and up ...
You can't even approximate the length of a line that way. Imagine a staircase built on a slide. The length of a carpet that covers the stairs is the sum of the change in height and in length. It's clearly greater than the length of the diagonal slide. Note that the length of the carpet is the same whether the steps are small or large, even though with small steps you stay closer to the slide.
I should put a picture here.
So you see that the paradox has nothing to do with the fact that a circle is curved. One thing studied in calculus is the length of a curve. Students there puzzle over the same paradox.
Note after reading comments. Yes, it's a duplicate. Perhaps this answer, less formal than those elsewhere, will help.
Ethan Bolker
- 95,224
- 7
- 108
- 199