Re: Third dimension...

In article <1194079190.519857.138480@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
kunzmilan <kunzmilan@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_lock
http://www.hq.nasa.gov/alsj/gimbals.html
http://en.wikipedia.org/wiki/Image:Gyroscope_operation.gif

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_och
_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/574
http://library.wolfram.com/infocenter/search/?search_results=1;search_per
son_id=607
.

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