One Sided Shapes

Did you know that there are shapes that only have one side? It’s true! The shapes I am talking about are the Möbius Strips & Klein Bottles.

The Möbius strip is made by getting a strip, giving it a 180 degree turn on one of the sides then connecting it, it looks like this:

These shapes are defined by an ant, if it crosses an edge, it gets cut and a new one is placed on the edge it tried to get to, the number of edges is equal to the number of ants used.

The Möbius strip is special because it only takes one ant to go on every spot on the shape!

A Klein bottle is also special, because it too only uses one ant to traverse the whole shape, it looks like this:

This bottle is special because it (in 4d) has no edges, and it is made from two conjoined Möbius Strips. The bottle was discovered by a mathematician named Felix Klein, He said:

    If you glue the edges of two

    you will get a weird bottle like mine

    -- Felix Klein

The circle is also a possible one sided shape, the only problem is, that the circle is made of a constant arc, and you cannot cut and unravel it into a flat plane without making it hollow, and making it two sided (cutting a klein bottle will make a Möbius strip, cutting a mobius strip will make a square or rectangle).


Wikipedia: Möbius Strip, Klein Bottle