# Questions about mobiuses... mobii... those one things **URL:** \ **Category:** Factual Questions\ **Created:** [January 23, 2004, 7:50pm UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812 "2004-01-23T19:50:46Z")\ **Posts on this page:** 13\ **Page:** 1
**Author:** ![LittleYellowBus](https://avatars.discourse-cdn.com/v4/letter/l/7c8e57/32.png) [@LittleYellowBus](https://boards.straightdope.com/u/LittleYellowBus)\ **Post date:** [January 23, 2004, 7:50pm UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/1 "2004-01-23T19:50:46Z")
My little brother, who is ‘captain funny-sayings,’ said something absurd the other day. It made me laugh really hard, but then it got me to thinking, which is dangerous. He said, “I feel like a mobius with 3 sides.” Hmmm… A mobius by definition is one-sided right? A mobius strip is the symbol for infinity, right? So, I got to thinking, can you have a “mobius” with three sides? The answer I came up with is yes… sort of. I don’t know if you can still call it a mobius, though. If you take a hoola-hoop that has six distinct planes, cut it and twist it clockwise three sides, then you have a three sided “mobius,” right? If you twist it two sides, then you get a two sided “mobius.” I don’t know. What do you think? What would you call these things? AND if you have more than one mobius, do you have mobii? These are the questions that kept me out of the really good schools! ---
**Author:** ![sevenwood](https://avatars.discourse-cdn.com/v4/letter/s/6de8d8/32.png) [@sevenwood](https://boards.straightdope.com/u/sevenwood)\ **Post date:** [January 23, 2004, 8:29pm UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/2 "2004-01-23T20:29:45Z")
I’ll have an answer for you, but first I have to get some aspirin from my Klein bottle… ---
**Author:** ![NE\_Texan](https://avatars.discourse-cdn.com/v4/letter/n/e99b99/32.png) [@NE\_Texan](https://boards.straightdope.com/u/NE_Texan)\ **Post date:** [January 23, 2004, 8:42pm UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/3 "2004-01-23T20:42:38Z")
First, the grammar of this – you would not call the simplest version of the construct you are talking about “a mobius”, you would call it “A Mobius Strip” – Mobius is an adjective (the name of the mathematician that came up with the idea). And the o should have an umlaut over it, but I’m not that picky. Perhaps the next poster that comes along will be. Onwards. You can classify more complicated structures in several ways, but the ones that would interest you are:[ul][li]How many distinct sides does it have? (without crossing an edge), and What is the cross section?[/ul][/li] A standard Mobius strip (take a strip of paper, give it a half twist, and tape) has a line segment as a cross section, and one side. How about this for a “three-sided mobius”, or something like it: Take a triangular prism made out of clay, give it a twist of a third of a circle, and connect it. One side, one edge, triangular cross section. Your hula-hoop idea (hexagonal cross section) has some interesting possibilities. 60 degree twist – one side, one edge, you have to circle the opening 6 times to come back to where you start. Whee! But: a 120 degree twist gives you two distinct sides and two distinct edges, with the same cross section, and you circle the opening 3 times! Do 180 degree twist, and you have 3 sides and edges, circling twice. You can imagine more from there. ---
**Author:** ![NE\_Texan](https://avatars.discourse-cdn.com/v4/letter/n/e99b99/32.png) [@NE\_Texan](https://boards.straightdope.com/u/NE_Texan)\ **Post date:** [January 23, 2004, 8:53pm UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/4 "2004-01-23T20:53:32Z")
**sevenwood** : A mathematician named Klein Thought the Mobius strip was divine. Said he, “If you glue The edges of two You’ll get a weird bottle like mine!” ---
**Author:** ![LittleYellowBus](https://avatars.discourse-cdn.com/v4/letter/l/7c8e57/32.png) [@LittleYellowBus](https://boards.straightdope.com/u/LittleYellowBus)\ **Post date:** [January 23, 2004, 9:29pm UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/5 "2004-01-23T21:29:40Z")
Oh, cool. Well, I never miss a chance to show off my non-existent brain power! That’s why I chose this handle. So, tell me about this Klein bottle, please. I don’t get it. ---
**Author:** ![Colibri](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colibri/32/1841_2.png) [@Colibri](https://boards.straightdope.com/u/Colibri)\ **Post date:** [January 23, 2004, 9:58pm UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/6 "2004-01-23T21:58:07Z")
> [@LittleYellowBus](#): > > So, tell me about this Klein bottle, please. I don’t get it. A [Klein bottle](http://www.kleinbottle.com/) is the three-dimensional equivalent of a Moebius strip. It has a single surface with, topologically speaking, no inside or outside. ---
**Author:** ![LittleYellowBus](https://avatars.discourse-cdn.com/v4/letter/l/7c8e57/32.png) [@LittleYellowBus](https://boards.straightdope.com/u/LittleYellowBus)\ **Post date:** [January 23, 2004, 10:29pm UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/7 "2004-01-23T22:29:27Z")
> [@Colibri](#): > > A [Klein bottle](http://www.kleinbottle.com/) is the three-dimensional equivalent of a Moebius strip. It has a single surface with, topologically speaking, no inside or outside. That’s really amazing, **Colibri**. Thanks! ---
**Author:** ![jsc1953](https://avatars.discourse-cdn.com/v4/letter/j/5daacb/32.png) [@jsc1953](https://boards.straightdope.com/u/jsc1953)\ **Post date:** [January 24, 2004, 12:46am UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/8 "2004-01-24T00:46:02Z")
My high school math teacher used to like to read to us from a collection of math-related short stories called _Fantasia Mathematica_…two pertinent ones are _The No-Sided Professor_ by Martin Gardner, and _And He Built a Crooked House_ by Heinlein (or was it Bradbury…?) ---
**Author:** ![The\_Scrivener](https://avatars.discourse-cdn.com/v4/letter/t/eada6e/32.png) [@The\_Scrivener](https://boards.straightdope.com/u/The_Scrivener)\ **Post date:** [January 24, 2004, 2:07am UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/9 "2004-01-24T02:07:00Z")
Three improbably practical uses for the Moebius Strip: Linking them in chains for decorating X-Mas trees in M.C. Escher-land; Dangling overhead/tossing to Schroedinger’s Cat; Using as a bookmark when reading one of Douglas Hofstadter’s books (esp. the chapters on recursive writing and recursive fiction!). ---
**Author:** ![The\_Scrivener](https://avatars.discourse-cdn.com/v4/letter/t/eada6e/32.png) [@The\_Scrivener](https://boards.straightdope.com/u/The_Scrivener)\ **Post date:** [January 24, 2004, 2:09am UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/10 "2004-01-24T02:09:43Z")
Oh, and welcome to the boards, **LittleYellowBus**! _Hello, I must be going…_ ---
**Author:** ![Polycarp](https://avatars.discourse-cdn.com/v4/letter/p/82dd89/32.png) [@Polycarp](https://boards.straightdope.com/u/Polycarp)\ **Post date:** [January 24, 2004, 7:44pm UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/11 "2004-01-24T19:44:39Z")
> [@jsc1953](#): > > and _And He Built a Crooked House_ by Heinlein (or was it Bradbury…?) Heinlein. It’s in the collection 6XH, among other places. ---
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [January 24, 2004, 8:21pm UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/12 "2004-01-24T20:21:33Z")
Mobius strips are fun. After tracing a line down the strip to demonstrate to yourself it only has one side, cut down the line and see what happens. Make a new one, draw two lines, and cut it into thirds. (Neat!) Keep going… notice a pattern? 🙂 ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [January 24, 2004, 8:42pm UTC](https://boards.straightdope.com/t/questions-about-mobiuses-mobii-those-one-things/225812/13 "2004-01-24T20:42:41Z")
> [@LittleYellowBus](#): > > can you have a “mobius” with three sides? The answer I came up with is yes… sort of. I don’t know if you can still call it a mobius, though. > > If you take a hoola-hoop that has six distinct planes, cut it and twist it clockwise three sides, then you have a three sided “mobius,” right? If you twist it two sides, then you get a two sided “mobius.” I don’t know. What do you think? What would you call these things? The only resemblance your hula hoop bears to a Mobius strip is that you twist and connect. This is not what makes a Mobius strip special. So I would not call this a “three sided ‘mobius’”. In order to compare your hoop to a Mobius strip, you have to count both the outside and inside surfaces, of which there are six total. That is, you have to count _both_ sides of your ribbon-like surface. The cool thing about a Mobius strip is that when you do this, you get an odd number. If it’s solid, it’s an entirely different problem. All together. It’s trivial to make a solid with an odd number of “faces”. A sphere springs to mind, with one. What **NE Texan** describes is known as Umbilic Torus NC, and it also has one.