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It's a bit challenging to teach some of the counter-intuitive
notions of geometry in curved spaces. Most lecturers resort
(physical) hand-waving, or some very bad diagrams.
A curved whiteboard would solve this problem. The base
would sit horizontally, but the surface would have concave
and convex areas, so that it can be shown directly that the
angles of a triangle don't always add up to 180 degrees.
(It would be even better if it were flexible, but that's
beyond me right now.)
And where would the teachers go after a hard day of work?
[theircompetitor, Oct 04 2004, last modified Oct 05 2004]
Memerase flexible whiteboard
Doesn't do convex/concaves though, only bends. [booleanfool, Oct 04 2004, last modified Oct 05 2004]
||With my luck I'd inadvertantly dig into an asymptote and generate a rip.
||I think this is completely doable and not a half bad idea. I'll give it a [+]
||Professor Frink: "Oh dear, I've torn the space-time
continuum again, class..."
||This idea is totally bent. (+)
||The globe's good for convex surfaces, but not concave, or
||For the flexible sheet, I thought maybe a chain-mail like
structure (like those horrible purses from the 80's),
covered in some acrylic sheet. I couldn't figure out how
to hold it in place when it was changed, though - I like
||Mr. Hand: Yes?
Spicoli: I'm registered in this class.
Mr Hand: What class?
Spicoli: This is US history, I see the globe right there.
Mr. Hand: Really?
Spicoli: Really, can I come in?
Mr. Hand: Oh please, I get so lonely when that third attendance bell rings and all of my kids are not here.
||..so you see, in 156 dimensions
A hand shoots up. Ah, professor...
156 dimensions! I cant visualize that.
Well, its very simple. Grinning broadly, the professor deftly pulls and pushes at the Riemann whiteboard. Portions of it seem to glitter with a holographic iridescence as they slip into heretofore unsuspected dimensions. Finally, the Professor stands back, sweating, but pleased with the result.
Yes yes, surely you see them?
Well, I see 155.
But not 156?
Cant visualize one more dimension?
Good Lord no!
The professor appears to think for a moment, then looks up. There...there it is--its right behind you!
Professor kicks students ass.
||When I was learning spherical geometry for navigation, we had a globe painted with blackboard paint for this purpose.
||I dread to think what the Equipartition Theorem would have to say about [ldischler]'s scenario.
||I think what you're after is a whiteboard
made from a flexible, rubber-like
material. Normally this whiteboard
would be boringly flat and Cartesian,
but when you want to illustrate curved
space geometry, just whip out your
bicycle pump and pump air into the
screen. This inflates the space between
the screen and the wall behind, so that
the screen bulges away from the wall.
You would then be able to draw a
triangle on the flat whiteboard and
show how the sum of its internal angles
changes as you inflate the whiteboard.
||Would that work for concave?
||so Zanzibar Concave is standard in the US