Choose Your Own Möbius Adventure — Part II

Geometry Level 2

Ugg lives on a strange space station, which has been constructed in the shape of a Möbius strip. The station has a central path on both the top and bottom surfaces of the ring. One day, Ugg decides to determine how large the space station is, and so, starting on the central path outside his room, he turns and walks 2 miles until he comes back to his room, where he began.

Therefore, Ugg concludes, the space station must have 4 total miles of central path, since he knows there's another path on the bottom surface of the ring.

What is Ugg's mistake?

Details and assumptions

This problem is part of the Choose Your Own Möbius Adventure series.


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