The material on non-Euclidean geometry and terms like Mobius band and Klein bottle
were introduced in a short period of time (2 hours) and it was too much information for background this audience had.
As Rosen suggests, the Klein bottle
offers a sign-vehicle for Kleinian (w)holeness, complexity, and dynamism.
Let M be a 3-manifold with a complete hyperbolic metric of finite volume with tori or Klein bottle
cusps and let T be a 1-efficient ideal triangulation of M.
I've designed a simple form and the characteristics of the Klein bottle
Thomassen, "Tilings of the torus and the Klein bottle
and vertex-transitive graphs on a fixed surface," Transactions of the American Mathematical Society, vol.
Returning to the Klein bottle
, Rosen proposes that it "...
The Klein bottle
has the same property of asymmetric one-sidedness as the two-dimensional Moebius surface, but embodies an added dimension (see Rosen 1994, 2004, 2006, 2008).
In addition to Taimina's hyperbolic planes and a Lorenz surface crocheted by Yackel, the exhibit featured Mobius strips, which are twisted rings that have only one side, and Klein bottles
, which are closed surfaces that have no inside.
The topological property of the Klein bottle
that is responsible for its peculiar nature is its one-sidedness.
Ferguson's dusty basement studio is filled with the results of his dialogues between materials and mathematical theorems -- sculpted geometrical forms that go by exotic names: Klein bottles
, trefoil knots, cross-caps, horned spheres and tori.
Because Idaszak was the first to see it, this one came to be called "Ida.' Like the Etruscan Venus, Ida is also the shadow of a four-dimensional Klein bottle