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, 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.

Then Ugg concludes that 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?

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

He's miscalculated; there's actually an infinite length of walkway No mistake; he's right He's miscalculated; there's actually 2 miles of walkway He's miscalculated; there's actually 1 mile of walkway

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Arron Kau by Arron Kau

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8 solutions

Paul Couch
Jan 27, 2014

He forgot that the band has only 1 side, and that he walked the whole of the walkway.

25 Helpful 0 Interesting 0 Brilliant 0 Confused
Atul Saswat
Jan 26, 2014

Being a mobius strip it ends where it begins...its all sort of a paradox and has only 1 path..probably Ugg was put in the station from the time he was born ....bcoz such says his childish theory of 2 paths. poor UGG !

3 Helpful 0 Interesting 0 Brilliant 0 Confused

its 2 mile ofcourse

Atul Saswat - 7 years, 4 months ago

2miles

Tamanna S Mohanty - 7 years, 2 months ago

Ugg is cool bro

Jean Lille - 7 years, 4 months ago
Boen Wang
Sep 11, 2019

there is one side

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Bruno Unna
Feb 17, 2017

"...he knows there's another path on the bottom surface of the ring".

No, there is no other path! There is one path: the one Ugg has walked through.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Ashtik Mahapatra
Mar 22, 2014

He forgot that the band has only 1 side, and that he walked the whole of the walkway

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Thushar Mn
Feb 28, 2014

in mobius, walking through it,we will reach same point as started.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Sofia Geet
Feb 3, 2014

As there is only one side of Möbius.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Meher Engineer
Jan 29, 2014

cut the strip along its breath anywhere. undo the twist, rejoin it to form an untwisted cylindrical space station. doing all that has not changed the length of the road., which is 2 miles long.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Mobius strip is made by twisting a strip and then joining it. If one starts from one end then to reach there he has to take all the route on the strip including the opposite side. ugg had travelled that lenghth already to reach his home. So he did the mistake of assuming it to be only of one side. He would have been right if after two miles he was just opposite to his room.

A Former Brilliant Member - 7 years, 4 months ago

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Ah, that explains my mistake. I'd say he's in his own room again in what is apparently called halfway. It's just that he's pointed in the opposite direction. I was already trying to imagine how one should furnish a room in such a weird case. But apparently we weren't suppose to see it that way, to think of it as a 'thickened' Möbius strip.

HS N - 7 years, 4 months ago

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