 |
|
|
|
|
|
| |
| |
|
|
|
|
| |
| |
|
|
I just thought of an interesting shape: a 4D torus, equivalent to a 3D torus,
but if you exit the torus you reenter it at the opposite side, that being the
point on the opposite side of the cross-section halfway around the torus.
Is that possible in 4d?
--
David Fontaine <dav### [at] faricy net> ICQ 55354965
Please visit my website: http://www.faricy.net/~davidf/
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Some images just scream for an animated fly-by.
--
Ian
Inkwell: Ian's Homepage
http://www.topcities.com/cartoon/inkwell/index.htm
"Ken" <tyl### [at] pacbellnet> wrote in message
news:39885669.1EAF1E05@pacbell.net...
>
> My version of the un-twisted, un-rolled, un-torus.
>
> You think I am on to something ?
>
> --
> Ken Tyler - 1400+ POV-Ray, Graphics, 3D Rendering, and Raytracing Links:
> http://home.pacbell.net/tylereng/index.html http://www.povray.org/links/
----------------------------------------------------------------------------
----
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Sure, if both of the ends intersect the mouth of a wormhole that connects
the two points in space time.
Mike wrote:
> But can you make an un-twisted, un-rolled, un-torus while keeping the
> two ends together? Wrap your mind around that one!
>
> -Mike
--
Come visit my web site:-) : http://www.geocities.com/~thomaslake/
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Dounds like the shape of the universe.
David Fontaine wrote:
> I just thought of an interesting shape: a 4D torus, equivalent to a 3D torus,
> but if you exit the torus you reenter it at the opposite side, that being the
> point on the opposite side of the cross-section halfway around the torus.
> Is that possible in 4d?
>
> --
> David Fontaine <dav### [at] faricynet> ICQ 55354965
> Please visit my website: http://www.faricy.net/~davidf/
--
Come visit my web site:-) : http://www.geocities.com/~thomaslake/
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Mike wrote:
> But can you make an un-twisted, un-rolled, un-torus while
> keeping the two ends together? Wrap your mind around that one!
Sure, just do it in a periodic universe.
--
Anton Sherwood -- br0### [at] p0b0xcom -- http://ogre.nu/
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
David Fontaine wrote:
> I just thought of an interesting shape: a 4D torus, equivalent to a 3D torus,
> but if you exit the torus you reenter it at the opposite side, that being the
> point on the opposite side of the cross-section halfway around the torus.
> Is that possible in 4d?
Dammit, Jim, I'm a ray-tracer, not a topologist!
--
Anton Sherwood -- br0### [at] p0b0xcom -- http://ogre.nu/
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
On Wed, 02 Aug 2000 18:59:59 -0500, Mike wrote:
>But can you make an un-twisted, un-rolled, un-torus while keeping the
>two ends together? Wrap your mind around that one!
If it was an infinite length then due to some law of physics I think
the ends would meet weather you wanted them to or not.
--
Cheers
Steve email mailto:ste### [at] zeroppsuklinuxnet
%HAV-A-NICEDAY Error not enough coffee 0 pps.
web http://www.zeropps.uklinux.net/
or http://start.at/zero-pps
3:48am up 19 days, 2:15, 2 users, load average: 2.03, 1.91, 1.62
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
"Steve" <ste### [at] zeroppsuklinuxnet> wrote in message
news:slr### [at] zero-ppslocaldomain...
> On Wed, 02 Aug 2000 18:59:59 -0500, Mike wrote:
> >But can you make an un-twisted, un-rolled, un-torus while keeping the
> >two ends together? Wrap your mind around that one!
>
> If it was an infinite length then due to some law of physics I think
> the ends would meet weather you wanted them to or not.
That would be obtuse non-Euclidean geometry, where space is boundless yet
finite, the 3d equivalent of a 2d system drawn on the surface of a sphere.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
On Wed, 02 Aug 2000 10:12:09 -0700, Ken <tyl### [at] pacbellnet> wrote:
>
>My version of the un-twisted, un-rolled, un-torus.
>
>You think I am on to something ?
For one thing you're wrong. This *is* a torus (with caps added), it's
just not a circular nor a closed one. But it is a torus.
Well, some topologists might argue that a torus has to be closed but I
would stick to the more general definition, thank you.
As of twisted... how do you know? I mean, sure, it looks smooth, but
this doesn't mean it's untwisted. Besides, it's the product of a
twisted mind (i's, not y's :) ) <grin>
Peter Popov ICQ : 15002700
Personal e-mail : pet### [at] usanet
TAG e-mail : pet### [at] tagpovrayorg
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
On Wed, 02 Aug 2000 22:26:51 -0500, David Fontaine <dav### [at] faricynet>
wrote:
>I just thought of an interesting shape: a 4D torus, equivalent to a 3D torus,
>but if you exit the torus you reenter it at the opposite side, that being the
>point on the opposite side of the cross-section halfway around the torus.
>Is that possible in 4d?
Hey, usind 4D to tie and untie tori is *cheating*!!! Do it in 3D if
you dare!
:)
Peter Popov ICQ : 15002700
Personal e-mail : pet### [at] usanet
TAG e-mail : pet### [at] tagpovrayorg
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
