Re: Third dimension...

On 4 Lis, 07:03, Proginoskes <CCHeck...@xxxxxxxxx> wrote:
On Nov 3, 5:23 am, kunzmilan <kunzmi...@xxxxxxxx> wrote:



On 3 Lis, 12:43, Clifford Nelson <cjnels...@xxxxxxxxxxx> wrote:

In article <1194079190.519857.138...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,

kunzmilan <kunzmi...@xxxxxxxx> wrote:
On 31 ?j, 18:52, "jay1b...@xxxxxxx" <jay1b...@xxxxxxx> wrote:
On Oct 31, 10:28 am, David W. Cantrell <DWCantr...@xxxxxxxxxxx> wrote:

What is to the third dimension as a point is to the first dimension and as
a line is to the second dimension?

As I noted in my original response, the answer should be "plain" to see.

David

Well put. Now ... borrowing that...

What is to the fourth dimension
as a point is to the first dimension,
as a line is to the second dimension and
as a plain is to the third dimension?

Regards,
Jay Bala.

When you have a line, you need 2 points to make from it an abscissa.
When you have two lines (parallel), you need 2 lines to make from it
a square or a rectangle.
When you have a tube with a square profile, you need 2 squares to make
from it a cube.
When you have a tube with a cubical profile, you need 2 cubes to make
from it a 4-dimensional cube. Two free ends in the new dimension must
be closed, always. Plugs in (n + 1) dimensions have n-dimensions.
Write all vertices of 4-dimensional cube as (0,0,0,0) till (1,1,1,1).
You get 16 vectors giving position of vertices. 8 from them have on
the last place 0. They form 3 dimensional cube, the first side of the
higher dimensional cube.
kunzmilan

http://en.wikipedia.org/wiki/Gimbal_lockhttp://www.hq.nasa.gov/alsj/g...

From Synergetics: "The specialists brief on brevity is dubious".

Is gimbal lock a hint that the definition of physical space as three
dimensional instead of four dimensional is just a case of too much
brevity by mathematicians?

The reason I ask is that you can define physical space as four
dimensional like the Synergetics coordinate system, which is from the
tetrahedron, described at:http://bfi.org/node/574
and a method to overcome gimbal lock uses four dimensional unit
quaternions.

And the Pythagoreons might have had the right idea at:

http://kmr.nada.kth.se/files/gok/firstproto/index.php?gallery=Fenomen...
_Begrepp/Pythagoras/Misc&image=Number_related_to_form.jpg

Cliff Nelson

Dry your tears, there's more fun for your ears,
"Forward Into The Past" 2 PM to 5 PM, Sundays,
California time,http://www.geocities.com/forwardintothepast/
Don't be a square or a blockhead; see:http://bfi.org/node/574http://library.wolfram.com/infocenter/search/?......
son_id=607

I am not sure, what you want. Your publications on internet are not
more than 30 years old. I already published my first results in
scientific journals before this time. Thus you can not claim priority.
Tetrahedrons are only four dimensional planes,

No, they aren't; they are three-dimensional solids. If you take the
convex hull of the points (0,0,0), (0,0,1), (0,1,0), and (1,0,0), you
get a tetrahedron.

--- Christopher Heckman

only ones from
different n possibilities of multidimensional planes. These planes
form comlexes. You limited yourself only on one posibility.
I was chemist, and I tried to solve some chemical problems. Physical
properties of molecules, as boiling points of alkanes can be explained
using my results, some, and even more important were known even before
I was born. Similarly, most of mathematics I use is older than I am.
The couting of products n^m as sums of products of two polynomial
coefficient was described in textbooks before I rediscovered it and
realized its importance.
kunzmilan

I am sorry, I misread you note yesterday. This tetrahedron is not
regular, it can be interpreted just as a sum of two triangles in 3-
dimensional space. To it can be added the second triangle with vertice
coordinates (2,0,0), (0,2,0), (0,0,2), the third triangle with
vertice coordinates (3,0,0), (0,3,0), (0,0,3). In the second, points
with coordinates (1,1,0), etc. appear.
kunzmilan

.

Relevant Pages

  • Re: Analysis Manager Operations extremely slow
    ... both RDBMS SMO and Analysis Services ... testing domain authentication. ... cube editor slowness if connecting to Oracle. ... Gender dimension to "M" and still browse the Sales cube. ...
    (microsoft.public.sqlserver.olap)
  • Re: Automatic MOLAP questions
    ... there is a lock when the polling query is evaluated. ... when you execute a polling query, the result of the query and the previous datetime can be used to do an incremental processing. ... so an incremental process only add content in a cube and can't update the cube. ... SSAS will not try to process the dimension. ...
    (microsoft.public.sqlserver.olap)
  • Re: SSAS2005 - When do partitions need to be processed?
    ... InsertCubeProcessingLog("Process Dimension All End", 1, 1, BeginTime, Now, ... The actual processing of partitions doesn't appear to be significant here ... Processing Cube 'Sales Current' completed successfully. ... With AS2005 there is a proactive caching option at the dimension level, ...
    (microsoft.public.sqlserver.olap)
  • Re: The attribute key cannot be found (a new twist in the story)
    ... Here is another story and NeilW unless I don't get better control of 2005 I ... In AS2000 we have only one place in cube to fix data integrity issues. ... I have actually solved my problem by deleting the dimension and creating it ... I'd run a trace (if you're using SQL Server RDBMS) to ...
    (microsoft.public.sqlserver.olap)
  • Re: Filtering a dimension based on value from another cube?
    ... creating a new dimension called "Targeted population". ... Employees with more then XX absences in the month ... calculated cells formula can apply the MDX formula in the cube. ... then the standard calculation is applied. ...
    (microsoft.public.sqlserver.olap)