PWrong wrote:We used to use square brackets for RNS. They turned out to be redundant.
Otherwise the notation is ambigous.
We can directly convert RNS to cartesian equations, so it's definately not ambiguous.
bo198214 wrote:PWrong wrote:We used to use square brackets for RNS. They turned out to be redundant.
Its definitely not redundant. So how do you then write ([11][11]) in normal RNS notation? (This should be topologically equivalent to the duocylinder.)
Rob wrote:Maybe you could give some examples?
What do you mean? Of course 111 is a rotope, it's a cube. Your square torus has never been suggested as a rotope, and for good reason.Yes 111 isnt a rotope either.
This was already misleading to Rob, that the shape between the parentheses has to do with the shape including the parenthesis. So we see this notation is quite misleading.
We can call them simply rectangular or lozenge xyz.
Sorry PWrong but I have the impression that you generally have something against my suggestion here.
a) we allow rotopes only to be things with parentheses around
b) when we allow rectangular shapes (for example square, cube and tesseract - what have these todo with rotations?) for rotopes too, then we should use bracket notation.
And if you would look independently and the RNS notation you would notice that exactly 111 or 1(11) does not convert to parametric equation.
This is another reason to use brackets, then we have an easy way to convert [111] and [1(11)] to convert to parametric equations.
PWrong wrote:Rotopes is short for rotatopes, and it's the general name for anything formed by x and # products of k-spheres. I don't know why Marek chose that name.
You'll have to use better examples to show that there's a difference.
With parametric equation I meant the usual one derived by the parenthesis expression. I.e. (A1...An) is the parametric equation sqrt(A12+...+An2) - R = 0.
(If we dont, we need at least an additional rule for 111 which is then though nothing more than the rule for [111].)
PWrong wrote:That's a cartesian equation or an implicit equation. Parametric equations have parameters.
We already have that rule. The rule for [111] is nothing more than the rule for 111.
PWrong wrote:Sorry PWrong but I have the impression that you generally have something against my suggestion here.
Well I don't fully understand it yet, but I happen to like our current notation (admittedly because Marek and I invented it).a) we allow rotopes only to be things with parentheses around
b) when we allow rectangular shapes (for example square, cube and tesseract - what have these todo with rotations?) for rotopes too, then we should use bracket notation.
Rotopes is short for rotatopes, and it's the general name for anything formed by x and # products of k-spheres. I don't know why Marek chose that name.
Too bad that my other idea to expand on rotatopes - the "graphotopes" disappeared in history
I'm only absolutely sure that it was me who invented the term "tiger", which I am glad to see universally accepted here
PWrong wrote:Too bad that my other idea to expand on rotatopes - the "graphotopes" disappeared in history
Yes, although the crind is still on the wiki. And that first extension of the notation may have inspired everything else we've achieved.
PWrong wrote:Rotopes is short for rotatopes, and it's the general name for anything formed by x and # products of k-spheres. I don't know why Marek chose that name.
bo198214 wrote:PWrong wrote:Rotopes is short for rotatopes, and it's the general name for anything formed by x and # products of k-spheres. I don't know why Marek chose that name.
If we take only take x and # products of k-spheres then we never get square, cube and tesseract. The only edgy thing we get is the 0-sphere which are 2 points and its cross products. So even this definition shows that they dont fit into rotatopes.
So I think that this is the basic discrepancy - if you only use "hollow" spheres, it's of course correct to exclude cube, but then you have to exclude cylinder, too
I propose to use "filled" spheres as a default mode, with spheration meaning spherating the "skin" or parent shape.
bo198214 wrote:The implicit description of the cylinder is quite mixed what regards F=0 and F<=0:
(sqrt(x^2+y^2)=r and |z|<=r) or (sqrt(x^2+y^2)<=r and |z|=r)
I wonder whether we can make a new (another one!) product of it.
bo198214 wrote:perhaps then you should take second try to roll out your graphotopes - never heard of them.
bo198214 wrote:(sqrt(x^2+y^2)=r and |z|<=r) or (sqrt(x^2+y^2)<=r and |z|=r)
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