Expert: Azeem Hussain - 3/31/2009

Question
March 31, 2009

Azeem,

If you pull a long steel measuring tape out to, say, 10 meters, and make a mark there, the mark will be, of course, at 10 meters.  But where will the mark be if the tape is twisted one revolution?  I can see it will be at less than 10 meters, but how does one calculate that distance short?

In case it's not clear, by "twisted one revolution" I mean that one end of the tape or the other has (mistakenly) been rotated 360 degrees.

In thinking about this problem I wonder about such variables as how wide the tape is and how tightly it can be twisted.  Also, I realize this might not be a question of geometry but rather topology or something.

Can you dream up a way to make such a calculation?

Thanks.

--Johnny

Answer
Hi Johnny,

There are undoubtedly the variables of tape width and how tightly it can be twisted.  From my own experimentation, there is no difference in the length measured after twisting.  Or if there is, it is truly negligible compared to the distance being measured.

I cannot provide you with any calculations, but even if I could, there would be several variables involved and I wouldn't know how to account for them.

Hope this was somewhat helpful,
Azeem