ATTN: PWrong

Higher-dimensional geometry (previously "Polyshapes").

ATTN: PWrong

Postby Keiji » Thu Aug 03, 2006 10:34 pm

There is >no< need for putting a "Forms" section on every shape page in the Wiki, and I have deleted them. :roll: Net spaces are explained on the Net space page, funnily enough. Determining your so-called "forms" of a shape is a task of obviousness.
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Postby PWrong » Fri Aug 04, 2006 8:14 am

I've never heard anyone call a form a "net space". What's your word for a cell? The forms and cells of an object are important, because they help find volumes and surface areas. They also have a nice Pascal's triangle structure to them. If we don't put this information on the shape pages, we should at least have a separate list of shapes with their form and cell info.

The next time you delete my work, it would be nice to tell me about it beforehand.
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Postby Keiji » Fri Aug 04, 2006 9:10 am

I've never heard anyone call a form a "net space".


No, forms are not called net spaces. But, each form of an object has the same bounding space with a different net space. If you say "a monoframe cylinder", for example, you know that you're talking about two circles making up a cylinder. If you say "two circles", you don't know where those circles came from.

What's your word for a cell?


Why would I have a word for a cell? I call cells cells. :roll:

The forms and cells of an object are important, because they help find volumes and surface areas. They also have a nice Pascal's triangle structure to them. If we don't put this information on the shape pages, we should at least have a separate list of shapes with their form and cell info.


Why? Like I said, determining the form of a shape with a certain net space, given the original shape, is a task of obviousness.

The next time you delete my work, it would be nice to tell me about it beforehand.


If it matters that much, you can just click "history"...
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Postby bo198214 » Fri Aug 04, 2006 9:52 am

Maybe this way it becomes different to fill the wiki ... of course everyone can delete the work of everyone ...

EDIT: oops, I mean "difficult" instead of "different"
Last edited by bo198214 on Fri Aug 04, 2006 11:30 am, edited 1 time in total.
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Postby PWrong » Fri Aug 04, 2006 10:56 am

Why? Like I said, determining the form of a shape with a certain net space, given the original shape, is a task of obviousness.

It's not obvious that the cells have a pascal's triangle structure. Not everyone knows how forms and cells work, so examples are helpful.
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Postby Keiji » Fri Aug 04, 2006 12:05 pm

What do they have to do with Pascal's triangle? And how is it helpful to know that?

If we really need this, it should be on a seperate page, entitled "Polytope forms"...
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Postby bo198214 » Fri Aug 04, 2006 12:49 pm

Seems as if Rob just turns into a hardliner...
Nobody asks for what we need 4d discussions, so why asking for what we need Pascals triangle oO
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Postby Nick » Fri Aug 04, 2006 12:56 pm

Rob wrote:What do they have to do with Pascal's triangle?


It's interesting knowledge, and increases your knowledge of 4d (even if by a little).

Rob wrote:And how is it helpful to know that?

How is it helpful to know anything about 4d? The entire purpose is to educate yourself in a topic that may become important in the future of theoretical physics. And if not for that, then to simply find it interesting.

Rob wrote:If we really need this, it should be on a seperate page, entitled "Polytope forms"...


Or you can leave it as it was before...
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Postby PWrong » Fri Aug 04, 2006 2:25 pm

What do they have to do with Pascal's triangle?


Ok, I'll put the list here to demonstrate. Note that a set of parallel objects counts as one cell. Also, I define two objects to be parallel if they differ only by a translation. This means any two points are always parallel.

Line:
0D form: 1 cell (a pair of points)
1D form: 1 cell

Circle:
1D form: 1 cell
2D form: 1 cell

Cylinder:
1D form: 1 cell
2D form: 2 cells
3D form: 1 cell

Duocylinder:
2D: 1 cell
3D: 2 cells
4D: 1 cell

Cubinder:
1D: 1 cell
2D: 3 cells
3D: 3 cells
4D: 1 cell

Cube:
0D: 1 cell (8 "parallel" points)
1D: 3 cells (3 sets of 4 parallel lines)
2D: 3 cells (3 sets of 2 parallel squares)
3D: 1 cell (1 solid cube)

Tetracube:
0D: 1 cell (16 "parallel" points)
1D: 4 cells (4 sets of 8 parallel lines)
2D: 6 cells (6 sets of 4 parallel squares)
3D: 4 cells (4 sets of 2 parallel cubes)
4D: 1 cell (1 solid tetracube)

See the pascal's triangle? If an object has n different forms, the number of cells in each give the nth row of pascals triangle. This applies for any rototope.
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Postby Keiji » Fri Aug 04, 2006 3:24 pm

PWrong wrote:Ok, I'll put the list here to demonstrate. Note that a set of parallel objects counts as one cell. Also, I define two objects to be parallel if they differ only by a translation. This means any two points are always parallel.


Well, that's certainly interesting but does it really have anything to do with anything? Especially given your parallelness rule? :|
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Postby PWrong » Fri Aug 04, 2006 3:34 pm

Well, that's certainly interesting but does it really have anything to do with anything? Especially given your parallelness rule?

I just think that in a page about a particular object, we should mention what that object is composed of. And if all objects have a similar structure, that's an important fact and we should mention that too.

My definition for "parallel" isn't just an arbitrary rule. It's consistent with the existing definition of parallel (which only works for lines and planes) and it generalises the concept to every possible shape.
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