The Mobius Band - Oct. 10-14, 1994 Bernice and Boutros did a math project for the first science/math fair at school. They picked the Mobius band, after reading about it in another Martin Gardner book (they liked the polyiamonds problem a lot!) and seeing this really cool drawing by Escher of ants crawling around what turned out to be a Mobius band. They set up a small presentation, with an Escher poster, some samples, and a lot of rectangular pieces of paper for people to play with, provided a brief description of the Mobius band, and then asked their visitors two questions: Start with a longish rectangle of paper, give one end (A) a half-twist, and tape it to the opposite end (B). Voilà! You have created a Mobius band. ____________________________________________ | ^ | | | | A| <- length -> width |B | | | |__________________________v_______________| **************************** * * * * --->> * ****************** * * * * * * * * * * * * * * * * *** ** Assume that the width (height) of the rectangle is 1. If the rectangle is too short -- for example if it is a square of side 1 -- then you won't be able to follow the above instructions. What is the length of the SHORTEST rectangle of width = 1 that can be bent into a Mobius band as described above? We are assuming that the paper can be bent, but not stretched or torn (no fair using crepe paper!). Cut the Mobius strip into two by cutting down the middle lengthwise. What happens? Why do you think this is? (What if you cut it a bunch of times?) [Thanks to Dan Asimov for most of this problem.] Correct solutions to the problem were submitted by: Samantha Brenner, Julie Black, Mike Henry, and Justin Davies, Fairfield HS Michele Gibney, College Park High School Joe Fuston, College Park High School Dan Asimov, the problem's creator Next problem || Previous problem || Table of Contents || Forum Home Page