Notations

[Nick]

I don't understand any of the notations that I am seeing in this forum. I would like to learn from what is being discussed here, but how can you learn something if you don't understand the language? Impossible.

Help? :?

[houserichichi]

I believe it's all in the wiki which is located here.

[Nick]

Someone should add tapering notation to RNS; I was going to do it, but I became afraid that I may be missing something and stopped.

[PWrong]

I don't understand any of the notations that I am seeing in this forum.

I think the best way to learn the notation would be to look at the list and try to work it out. If we try to explain it we'll just confuse ourselves.

Someone should add tapering notation to RNS; I was going to do it, but I became afraid that I may be missing something and stopped.

I think we're all being too reluctant to start new pages. Once it's up, someone will correct any mistakes you make. It's much easier to correct someone than to start a new page.

[Keiji]

I believe it's all in the wiki which is located here.

More specifically: http://tetraspace.alkaline.org/wiki/ind ... _notations

[Nick]

I don't understand any of the notations that I am seeing in this forum.

I think the best way to learn the notation would be to look at the list and try to work it out. If we try to explain it we'll just confuse ourselves.

I have tried, and I did get somewhat far, but something would always confuse me in the end.

[Keiji]

Which notation are you having trouble with, then?

[Nick]

The Wiki answered all of my questions. Problem solved

[Nick]

OK, here's something I am confused about that the wiki doesn't answer: what does the # represent? A#B=??

[Keiji]

# means torus product. But I won't say any more, because I still don't understand the damn thing properly.

[wendy]

There are many different products defined in higher dimensions, such as the torus product. The torus-product is a pondering product (ie if you multiply polygons together you get polyhedra).

If you take a sheet of squares, eg 5*6, you can make this into a cylinder either 5 high, or 6 high. You can then make a torus in two different ways: sock and hose construction.

In hose mode, you bend the thing around, so top joins bottom, and the interior of the cylinder becomes the interior of the torus.

In sock mode, it is as if you are taking off a sock. The hem is rolled down to meet the toe, and the interior of the cylinder becomes the exterior of the torus.

The symbol for the torus product is A##B, as the torus-product is a subclass of the general comb product.

We have then that A ## B is not B ## A. For a given figure, F, we could have,

if sock-torus is S ## F, then hose-torus is F ## S.

You can then make A ## B ## C by series of sock and hose torus, as long as sock-modes prefix and hose suffix it.

eg A hose B hose C = C sock B sock A = B hose C sock A = B sock A hose C.

Note that A ## B is not the same as B ## A, except that the surfaces are identical. For example, one can have a 6*5 grid of squares, that forms a hose of length 6 units, or a hose of length 5 units.

In four dimensions, one can get a product of a polygon ## polyhedron, polyhedron ## polygon, or polygon ## polygon ## polygon. For the last, imagine you have a choric (3d) sheet. You join top to bottom, and you have in wx a square, and yz a circle-outline, in wxz or wyz the cylinder. You now bend this cylinder into a torus, either by sock or hose method, to get something that in xyz is a torus, but extended for some length in w.

You can now bend this, in w space, by either sock or hose method, to get a tri-polygonal torus.

[Nick]

Thanks, that clears ALOT up