New user with some ideas

[Ryush806]

hi all. as you can tell from the subject i'm new so if i get things mixed up just correct me.

anyway, i was wondering...

when you take a line (1d) and bend it, the shape formed, such as a semi-circle, is a 2d object. similarly, when you bend a plane (2d), the shaped formed is like a archway(3d). doesn't it follow that bending a cube or other 3d object would somehow create a 4d object. i know that if you did this in "our" universe it would just create a crooked cube, but in a 4d universe would it be like bending the line or the plane for us?

just thinkin',
Ryan

[alkaline]

welcome to the forum!

you're exactly right, it would create a curved 4d shape, a shape that people from tetraspace would use for arches.

Good to see people using their brains :-)

[Keiji]

Wouldn't they use extruded spheres, rather like we use extruded circles?

[alkaline]

what do you mean by extruded circle/extrude sphere - are you talking about the shape of a dome = a hemisphere/hemiglome?

[Keiji]

By extruding a circle, a cylinder is formed. (2 -> 21)
So, by extruding a sphere, a spherinder is formed. (3 -> 31)

To create a sphere you lathe a circle. (2 -> 3)
To create a glome you lathe a sphere. (3 -> 4)

If you lathe a square, you get a cylinder (11 -> 12)
If you lathe a cube, you get a cubinder (111 -> 112)

If you lathe a cylinder one way, you get a spherinder... (12 -> 13)
... and if you lathe a cylinder the other way, you get a duocylinder (12 -> 22)

Understand?

[alkaline]

Yep i understand quite well as i've done a bit of thinking on these kinds of shapes - i just wasn't sure what you meant by "extrude". I have used the word "extend" throughout my pages for the same concept. The reason i didn't understand your comment about extruded spheres and circles is that we were talking about arches - the inverse of a solid shape, because it is a "hole" to walk through. In any case, what did you mean?

[Keiji]

A torus is a cylinder bent round into a circle. An arch is half of a torus. So, by extruding a circle and bending it, you get an arch.

By analogy, by extruding a sphere and bending it, you will get a 4d arch.

Then again, how many people build their arches out of rubber?

[alkaline]

i kind of see arch building in a different way - for a 3d arch, you would take a 3d wall, and subtract out a hemicylinder. for a 4d arch, you would take a 4d wall, and subtract out a hemi-spherinder. You could have something that was half-arch and half-square if you subtracted out a hemi-cubinder. To me, it seems like a more intuitive way to "construct" an arch.

[Polyhedron Dude]

If you want an arch that has an entrance and an exit, then it would be best to use the hemisphere arch. If you want an arch that allows people to come in and out from a circle of directions - use the bent cube style arch.

Polyhedron Dude

[alkaline]

so by this second style of arch - one that allows people to come in and out from a circle of directions - do you mean one that is more decorative than anything?

[Polyhedron Dude]

A bent cube arch would allow entry from a whole plane of directions - consider a cube that starts on the marp side and bends upwards and then curves back down on the garp side - you could enter this arch from the east, the west, the north, the south, and all directions in between! - to make it more decorative, maybe we could curve a gocco instead of a cube (gocco is the great cubicuboctahedron - it has 6 octagrams (8 pointed stars), 6 squares under the octagrams, and 8 triangles as faces).

Polyhedron Dude

[Aale de Winkel]

By extruding a circle, a cylinder is formed. (2 -> 21)
So, by extruding a sphere, a spherinder is formed. (3 -> 31)

To create a sphere you lathe a circle. (2 -> 3)
To create a glome you lathe a sphere. (3 -> 4)

If you lathe a square, you get a cylinder (11 -> 12)
If you lathe a cube, you get a cubinder (111 -> 112)

If you lathe a cylinder one way, you get a cubinder... (12 -> 112)
... and if you lathe a cylinder the other way, you get a duocylinder (12 -> 22)

Understand?

The extrusion process is clear to me.
Lathing at first sight:
I get confused by the process of lathing though, "lathing" the circle into a sphere, and the sphere into a glome, means that one further direction kicks in. Doing the same thing with a square I get the cubinder and not the cylinder, this corresponds with the formula for the cubinder. (In my view a line gets "lathed" into a cylinder!)

If you can "lathe" a cylinder into a duocylinder you must have quite another picture of the duocylinder then I have, which looks more like a duo-circle, then the penta-space duocylinder I can extract from the formula I have for the tetra-space "duocylinder".

Lathing at second sight:
If lathing means encircling one of the direction I indeed see the square turned into a cylinder, and the cube into something that might be a cubinder.
This way however I can also lathe a cylinder into a spherinder, forming the cubinder is more like extrusion of the cylinders linear part, and indeed lathing the cylinders lineair part does indeed gives something without lineair part and the picture might be of the duocylinder I know about.

A trionian getting tetronically confused

[alkaline]

If you lathe a cylinder one way, you get a cubinder... (12 -> 112)
... and if you lathe a cylinder the other way, you get a duocylinder (12 -> 22)

It looks like bobxp mispoke for the first cylinder lathing. Extrusion is basically adding a '1' to the code, and lathing is incrementing one of the numbers in the code. Thus, lathing a cylinder one way gives you a spherinder (12 -> 13), and lathing it the other way gives you a duocylinder (12 -> 22).

[Keiji]

Stupid me! ::goes to fix::