On 10/24/07, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote:

> *wow*
>
> Croquet is really really neat.  I think we're at least another decade away 
> from this sort
> of interface being workable, but I'd love it if somebody could prove me 
> wrong.  <snip>

A possibility that comes to mind is to enable the creation of SAGE
cell windows in the 3D environment that can be placed and organized by
the user to suit their needs.  The user enters SAGE code as usual into
the cells, evaluates it, and the result can simply be displayed in 2D
windows in the 3D environment.  Even at this mundane level, the
organizational possibilities may prove to be useful.  For example, all
of one's calculus work can be placed on one island while other work
can be placed on other islands, inside buildings, etc.  One can
navigate to these places by flying, or teleport windows can be used to
move between locations.

Beyond this, another thing that interests me is to have the 3D
environment render mathematics objects instead of having SAGE render
them.  An example would be the 2D graph of a function rendered as
large a house that the user can fly around and interact with.  The
user can measure slopes by placing a slope tool at various points on
the plot and they can estimate the area under a curve by getting
underneath the curve and taking measurements.  3D plots should even be
more exciting to interact with.

The ability to bring a number of people into a SAGE-enabled 3D world
to demonstrate topics in mathematics and physics also seems useful.
For example, imagine a class of students flying to the top of a 10
story building with their teacher.  The teacher has a special
sensor-enabled ball that is able to record its height every 50
milliseconds and then the ball can be dropped from the top of the
building.  The ball can then be retrieved from the ground and a button
can be pressed on it which will automatically send the data to SAGE
for analysis.

Anyway, it seems to me that it should not be too difficult to enable
Croquet to communicate with SAGE for simpler scenarios like these.
Perhaps I am missing something?

Ted

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