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Matabiri
5th July 2005, 03:28 AM
"While the circle cannot be squared in Euclidean space, it can in Gauss-Bolyai-Lobachevsky Space."

- Mathworld (http://mathworld.wolfram.com/CircleSquaring.html)

I did not know that.
Ashles
5th July 2005, 05:45 AM
Well duh.
Paul C. Anagnostopoulos
5th July 2005, 07:40 AM
Well sure, if you use some whacky value for pi instead of 3.

~~ Paul
Matabiri
5th July 2005, 07:45 AM
Originally posted by Ashles
Well duh.

I know. I've been so blind.
pgwenthold
5th July 2005, 08:05 AM
Originally posted by Matabiri
"While the circle cannot be squared in Euclidean space, it can in Gauss-Bolyai-Lobachevsky Space."

- Mathworld (http://mathworld.wolfram.com/CircleSquaring.html)

I did not know that.

Well, if GBL space is spherical, then I'm not surprised that the circle can be squared. It is the fundamental unit of the geometry.
Matabiri
5th July 2005, 09:25 AM
Originally posted by pgwenthold
Well, if GBL space is spherical, then I'm not surprised that the circle can be squared. It is the fundamental unit of the geometry.

GBL space has a negative curvature (e.g. saddle-shaped). A sphere has positive curvature.

I think your point still applies, though.
pgwenthold
5th July 2005, 10:12 AM
Originally posted by Matabiri
GBL space has a negative curvature (e.g. saddle-shaped). A sphere has positive curvature.

I think your point still applies, though.

Not really. Under my argument made above, the fundamental unit of GBL space is actually a hyperbola, not a circle. Mathematically very different.

OK, then, so is the circle squarable in Reimann geometry?
Matabiri
6th July 2005, 03:46 AM
Originally posted by pgwenthold
Not really. Under my argument made above, the fundamental unit of GBL space is actually a hyperbola, not a circle. Mathematically very different.

I know that, just that the change of basic unit was what allowed the squaring. I think in spherical space, unless your square was sufficiently large, you still wouldn't be able to do it.

I don't know what construction was used in GBL space, though. I'm mainly just guessing. Someone linked to this (http://encyclopedia.jrank.org/CRE_DAH/CRP.html) which seems to talk about it, but it's quite hard to follow.