Vector_Graphics wrote:A 3d object is flat in 4d, and a 3d space is analogous to a plane, but we also often talk about planes of rotation, and 2d surfaces as boundaries on the 3d surface of a 4d object (i.e. boundary lines on the ground). How do you guys talk about 2d objects in 4d space? Like, what analog to "line/length" (for 1d), "plane/area/surface" (for n-1 dimensions) is there?
gonegahgah wrote:@Vector,
The general thinking here is to call 4-Volume "bulk". My preference is to call it 4-Volume. All other objects are objectively flat.
We consider a line and a plane to be flat. However, it would need a new identifier for 3D objects or use the generic 3-Volume.
So I myself would also refer to 3-Volume as 4-Plane (as to their eyes a 3D object would be a plane flat object like a piece of paper).
To 4Der's a 2D object would be an edge so 4-Edge. So as a table:
Us / 4Der
3-dot / 4-dot
3-line / 4-line
3-plane / 4-edge
3-volume / 4-plane
3-hypervolume / 4-volume
That is how I like to think of it; but that is not the convention, I believe.
Vector_Graphics wrote:If anything, "surface" should be n-1 the same way "plane" is.
Vector_Graphics wrote:Most of the properties of 2d planes in 4d have to do with rotation, so I will probably end up deriving the terms for 2d stuff from words relating to rotating.
PatrickPowers wrote:But a line to partition a surface is 2D in the 4D world. So there are both 1D and 2D lines. In 4D a shoreline is 2D. Weird, eh?
gonegahgah wrote:I would be more inclined to call it a "shoreedge" than a shoreline (like water's edge) as it is more of a boundary than a line.
To my thinking a line always travels from and to somewhere whereas a 4-edge extends out in the full 360° of directions.
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