# Non-Euclidean Architecture **URL:** \ **Category:** Factual Questions\ **Created:** [January 9, 2018, 6:39pm UTC](https://boards.straightdope.com/t/non-euclidean-architecture/806257 "2018-01-09T18:39:43Z")\ **Posts on this page:** 6\ **Page:** 2
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 10, 2018, 2:32pm UTC](https://boards.straightdope.com/t/non-euclidean-architecture/806257/21 "2018-01-10T14:32:52Z")
> [@scr4](#): > > A curved surface _is_ a 2-dimensional curved space. Lines and patterns on a curved surface are non-Euclidean. I was tempted to say something last night upon reading comments like this from you and **Hari Seldon** , but I forebore, so it’s been interesting to me to see how this debate has deveoped. I’d say that statements like this are true in a sense, but potentially misleading. After all, people knew that the Earth’s surface was curved, and that therefore you could have “lines and patterns” on a curved surface, historically long before they accepted non-Euclidean geometry. Is it okay to say the following?: If you treat lines, etc. on a curved surface as if you were working in a flat plane, they follow the rules of a non-Euclidean geometry. (But, as **Apidastra** pointed out, they’re still part of Euclidean 3-space.) So, there are different ways to interpret the OP’s question. According to one interpretation, the answer is No, because any architecture that you actually build in the real world will have to follow the real world’s geometric structure, which is at least so close to Euclidean that you can’t tell the difference. And according to another interpretation, the answer is Yes, if you can somehow exploit the fact that plane geometry “looks” non-Euclidean on curved surfaces. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [January 10, 2018, 4:25pm UTC](https://boards.straightdope.com/t/non-euclidean-architecture/806257/22 "2018-01-10T16:25:10Z")
If Euclid is all Greek to you, try reading an English translation. What do you call the rendition of Euclid into English? Translation of axioms. ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [January 10, 2018, 4:41pm UTC](https://boards.straightdope.com/t/non-euclidean-architecture/806257/23 "2018-01-10T16:41:01Z")
I’ve got a pretty good background in Math, even took a grad course in Transformational Geometry\*. When someone mentioned “non-Euclidean” by itself it always meant planar geometry with an alternate parallel postulate. Taking “non-Euclidean” to mean something other than what Euclid ever wrote about is …, well, not exactly a common interpretation. - Which was surprisingly fun. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [January 10, 2018, 5:37pm UTC](https://boards.straightdope.com/t/non-euclidean-architecture/806257/24 "2018-01-10T17:37:54Z")
If you want “curved” lines (such as on a spherical or hyperbolic plane) to _look_ straight, you need the kind of space warping that is inadvisable in civil architecture. You can find on YouTube computer renderings of what flying about such spaces looks like. But you can go the other way and exploit the curvature mismatch for its own sake: [The Institute For Figuring // Online Exhibit: Hyperbolic Space](http://www.theiff.org/oexhibits/oe1e.html) I’m sure you could design a respectable Cthulhu-cult temple that could still be built on a real city street without sucking the entire block into a black hole. ---
**Author:** ![John\_Bredin](https://avatars.discourse-cdn.com/v4/letter/j/96bed5/32.png) [@John\_Bredin](https://boards.straightdope.com/u/John_Bredin)\ **Post date:** [January 10, 2018, 9:17pm UTC](https://boards.straightdope.com/t/non-euclidean-architecture/806257/25 "2018-01-10T21:17:53Z")
> [@B-Rad](#): > > Oh. Well that’s boring AF. So R’lyeh could have just been some onion domes or even that castle in The Little Mermaid? I picture the “what’s a straight line?” architecture of Frank Gehry and the like. I imagine something like [this](https://en.wikipedia.org/wiki/Ray_and_Maria_Stata_Center) or [this](https://www.google.com/search?q=Millennium+bandshell&rlz=1C1FLDB_enUS513US513&source=lnms&tbm=isch&sa=X&ved=0ahUKEwip6ZuSqM7YAhXGulMKHTE5ARoQ_AUICygC&biw=1280&bih=655#imgrc=zvZkWPf-QHscKM:) or [this](https://www.google.com/search?q=disney+concert+hall&rlz=1C1FLDB_enUS513US513&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiZqMqnqM7YAhXJoFMKHWSSDVQQ_AUICygC&biw=1280&bih=655) would look pretty damned trippy to someone of Lovecraft’s era, like the scenery in _Cabinet of Dr. Caligari_ brought to life. ---
**Author:** ![alphaboi867](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alphaboi867/32/3898_2.png) [@alphaboi867](https://boards.straightdope.com/u/alphaboi867)\ **Post date:** [January 11, 2018, 12:43am UTC](https://boards.straightdope.com/t/non-euclidean-architecture/806257/26 "2018-01-11T00:43:35Z")
Check out the [works](http://www.tdrinc.com/architecture.html) of Eugene Tsui. [Previous page](https://boards.straightdope.com/t/non-euclidean-architecture/806257.md?page=1)