Both the torus and the Klein Bottle can be
obtained by rolling up a square into a tube and fastening the ends.
important: the arrows show how to glue the sides!
Pause and digest!
Now you just did this in reverse:
Note this is exactly the same as what we did at the top of this page,
except the centers of the squares have been removed. Thus: A torus:
And a Klein Bottle: We know how to physically make a torus and a Klein bottle with only one little square taken out!
Chaim Goodman-Strauss Dept. Mathematics Univ. Arkansas Fayetteville, AR 72701 firstname.lastname@example.org 501-575-6332
(c)1992-1994 Chaim Goodman-Strauss
Original paper masters available on request.