[DF] Non-Euclidean Architecture in dungeons questions.

[robkelk]

In real life, non-Euclidean geometry refers to geometry that isn't on a flat surface. (Start at the North Pole, draw a line down the Prime Meridian to the Equator, make a 90-degree turn, draw a line to the 90th Meridian, make a 90-degree turn, and draw a line to the North Pole. You've just drawn a a really big triangle - the lines are as straight as the medium allows - with three 90-degree angles. If that triangle isn't non-Euclidean, I don't know what is.)

So, don't use flat surfaces... anywhere...

[sir_pudding]

Originally Posted by robkelk

In real life, non-Euclidean geometry refers to geometry that isn't on a flat surface. (Start at the North Pole, draw a line down the Prime Meridian to the Equator, make a 90-degree turn, draw a line to the 90th Meridian, make a 90-degree turn, and draw a line to the North Pole. You've just drawn a a really big triangle - the lines are as straight as the medium allows - with three 90-degree angles. If that triangle isn't non-Euclidean, I don't know what is.)

Yeah, I already pointed out the "triangle on a sphere" thing. He's not really talking about non-Euclidean geometry (even though he keeps saying it), he's talking about higher dimensions intersecting 3-space.

So, don't use flat surfaces... anywhere...

The surfaces will be Euclidean, but you can have all kinds of non-Euclidean geometries on them.

[b-dog]

Originally Posted by sir_pudding

Yeah, I already pointed out the "triangle on a sphere" thing. He's not really talking about non-Euclidean geometry (even though he keeps saying it), he's talking about higher dimensions intersecting 3-space.

That is because that is the term Lovecraft used to describe Mythos geometry. OK I will use extra-dimensional instead.

[sir_pudding]

Originally Posted by b-dog

That is because that is the term Lovecraft used to describe Mythos geometry.

He didn't use it to describe extra-dimensional geometry though (although it was often associated with extra-dimensional effects, like in " Dreams in the Witch House").

[b-dog]

Originally Posted by sir_pudding

To perceive a non-Euclidean door (like a triangular door in a sphere shaped wall) you'd need no such thing. Really there's nothing that spectacular about non-Euclidean geometry. It just refers to systems that don't use the fifth Euclidean postulate.

As far as n-dimensional features are concerned I'm not sure I'd allow a spell to allow someone to actually perceive the higher dimensions directly. Certainly no existing spell does this. If you do have a spell that does this, and since you are running cosmic horror, you might have it work something like Professor Tilinghast's device in "From Beyond".

It could (probably) should look really weird. A door through n-space, might look like a weird set of three dimensional objects just suspended immobile in the air until something opens it, in which case the shapes move and disappear, new shapes appear. If left open it stops in a new configuration. If closed it returns to the original configuration.

EDIT:
You could have a puzzle where an object rotates in n-space when certain things are done in 3-space. The 3-space parts of the object can actually be in completely different rooms of the dungeon and you need to move them for some reason.

As far as spells go I would imagine some Wizard discovering them in something like the Necronomicon of the DF world. The would most likely be secret spells though.

[Flyndaran]

Originally Posted by sir_pudding

He didn't use it to describe extra-dimensional geometry though (although it was often associated with extra-dimensional effects, like in " Dreams in the Witch House").

Why are you acting as if it's a definition he made up? It's the first and most widely used definition I've heard outside of higher math classes.
I love being pedantic too, but one post is enough.

[Flyndaran]

Run your fingers "straight" across the walls with closed eyes and friends watching. When they see you do something "impossible" or "wrong" you've found something.

[Bruno]

Originally Posted by Flyndaran

Why are you acting as if it's a definition he made up? It's the first and most widely used definition I've heard outside of higher math classes.
I love being pedantic too, but one post is enough.

Because otherwise it's about as free-form a word as "magic architecture", because it's a fantasy term.

One definition is easy to work with, the other is a puddle.

[Lamech]

Originally Posted by robkelk

In real life, non-Euclidean geometry refers to geometry that isn't on a flat surface. (Start at the North Pole, draw a line down the Prime Meridian to the Equator, make a 90-degree turn, draw a line to the 90th Meridian, make a 90-degree turn, and draw a line to the North Pole. You've just drawn a a really big triangle - the lines are as straight as the medium allows - with three 90-degree angles. If that triangle isn't non-Euclidean, I don't know what is.)

So, don't use flat surfaces... anywhere...

This is wrong. Non-euclidean geometry is any geometry that has different postulates from euclidean geometries (Or maybe changing the parallel postulate I'm not sure which). Second, you absolutely can model some non-euclidean geometries on a flat surface. Finally, you can totally expand a flat non-euclidean geometry to 3 dimensions similar to the way you expand euclidean geometry to 3 dimensions.

Originally Posted by sir_pudding

A triangle drawn on a sphere is non-euclidean for example.

Its an example of normal euclidean three space. I suppose you could argue that the surface of any finite three dimensional object in euclidean three space is non-euclidean. However you could also actually have non-euclidean three space for the adventures to play in.

Originally Posted by b-dog

There are also Non-Euclidean rooms and hallways that are difficult for 3-space beings to walk through and navigate. What kind of penalties would you assign to 3-space PCs who try to do so? There may be some secret spells that can help PCs to be able to navigate in extra-dimensional areas and PCs might be able to learn to navigate in them by reading texts as well although doing so might make them insane.

So what I would like is to have ideas to help to make my dungeon fair yet keep the Non-Euclidean architecture alien to 3-space delvers. Thanks.

Well you could have n-space buildings, that just use standard euclidean three space. (What has already been described to you by others.)

You could also use non-euclidean three space. I would probably go with hyperbolic space. This is fun. Lets say the PC's walk 100 yards down a hallway, and then they make a 90 degree right turn. They do this three more times. Normal geometry they are back at the starting point. But with hyperbolic geometry they aren't back yet.

Navigation would be extremely hard unless they knew what kind of geometry they were in. They might not even be able to do it, other than remembering where they've been. If you read a text on non-euclidean geometries and then applied it to navigating it might be possible, but I would argue it requires a whole new skill, or a hefty penalty.

[Bruno]

I made a maze in a MOO that was a hypercube - a 4 dimensional cube. You can walk in a "straight" line and end up in the same room you started in, only arriving by another wall. Requires relative gravity to "work".