Re: Third dimension...

On Nov 6, 2:25 am, kunzmilan <kunzmi...@xxxxxxxx> wrote:
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.

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),

Okay, but you'll still have a 3-dimensional solid.

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.

Yes, when you take the convex hull: (1,1,0) = 1/2 * (2,0,0) + 1/2 *
(0,2,0) is a convex combination of (2,0,0) and (0,2,0).

--- Christopher Heckman

.

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