# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## Category Archives: topology

## 99: Non-Orientable Surfaces and the Möbius Strip

January 23, 2017

Posted by on The **Möbius strip** is a canonical and minimal example of a non-orientable surface, in the sense that

- a surface is non-orientable if and only if it has the Möbius strip as a topological subspace, and
- the Möbius strip is the
*only*surface with this property.

## 61: Coloring Problem on the Torus

December 11, 2016

Posted by on Given any division of a (2-)torus into regions, it is possible to color the regions with 7 distinct colors so that no two adjacent regions have the same color.

This contrasts with the more well-known fact that the plane is 4-colorable.

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