I know what he was talking about, but since the curvature of space time is of similar geometry to any curvature, at least at face value, it's another answer. Obviously the answer you were looking for had already been given, so there was no point reiterating that.
Cumulative General Science/Technology Quiz
- Thread starter Catharsis
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Perfection
The Great Head.
Well, the issue here is that this sort of relationship can be explained with Euclidian geometry. In doing so we deny that the region of the shpere's surface constructed by the three arcs is in fact a triangle, but we can explain all the angles and can calculate new angles and ac lenghts given sufficient knwoledge about other arc lengths and angle lengths. Certainly using noneuclidian geometry can be better at framing the problem, but the problem can be completely solved using Euclidian geometry.
It's only when we get into relativity does noneuclidian geometry truely stick out as being neccesary to phyisically understand the nature of space and time.
Catharsis
catch u on the flip scythe
LAnkou
Breizh A Tao
well, it all depend on how you define triangle in euclidian geometry.
Here in France, euclidian geometry is taught in a way that:
A surface defined by 3 angles is a triangle.
and the sum of a triangle's angle is 180°
the trouble comes from euclidian geometry is geometry of plan and the triangle i defined can't be comprised on an euclidian plan.
Of course you can define the same physical object in euclidian geometry, but it won't be recognize as a triangle.
IIRC, in euclidian geometry, a sphere is just the assembling object of circles in all possible plans. By cutting it with 3 plans, you get the same object, but it's a sum of arcs, not a triangle...and everybody here can see it's a triangle!!!
To Catharsis: a used the term simpler where i should have used easier, because it's easier to cut and unskin an orange than to get to the pole !!!
Perfection
The Great Head.
Soidhe, IIRC it basicly has to do with the Inertial reference frame supplying a common frame )general relativity) to the two twins, so that it is the traveling one that experiences time dilation.
Perfection
The Great Head.
Well that just becomes a semantic issue (what you call a triangle), Euclidean geometry can fully explain everything in this situation just as much as noneuclidean can, only the wording and perspective are different. I don't see how not calling something a triangle constitutes a failure of descriptive system.
Indeed. It therefore follows that one twin ageing more slowly than another is not a paradox, it's a prerequisite of time dilation in special relativity between frames of reference.
As for the maths question it sounds like me to be the difference between the sort of maths you learn at a college/pre-university level and that which you learn as a University student. In other words there are few things that cannot be described by Euclidian geometry in a pure form, but since the Greeks derived a sort of integral for describing a sphere in terms of 4/3*pi*r^3 long before Newton's calculus I'm sure they were well aware of how to infer distance on global objects, and a triangular path, using as noted arc lengths and radius, since quite patently the circular relationship obviously can be applied to a sphere with some adjustment, which notably is an integral of the surface area of a sphere which in turn is related by some maths to the area of a circle. I forget how the Greeks did it but essentially it was by dividing it up into sections and then deriving the whole from that, which is integration without the formalism.
LAnkou
Breizh A Tao
so again, it's a semantic issue...
By using "can't describe the universe", i was refering to the fact that euclidian geometry can't recognize an object as it is (here the triangle).
As I said, here in France, and that's something that can have a lot of impact, a triangle is: the surface defined by 3 angles.
The object i describe is a surface defined by 3 angles, so it's a triangle, but not in euclidian geometry...
You can continue nosepicking, but this little "fight over Euclide" just prove the importance of hypothesis and axioms. the ones from Euclide are good for everyday, but are limited.
Perfection
The Great Head.
But it can describe the entire situation, it just doesn't use your definition.
Also open floor.
I think there's a sort of strange justice here, since the real "non-Euclidian" answers have gained the right to post the questions. Perfection is next.
Even in Euclid's time it was no doubt possible to derive the angles on a sphere from Euclidean geometry but since you asked only about it in terms of triangles, not circles then the first answer was correct, even if such things are easily derivable from basic geometric principles. With the advent of imaginary numbers and spherical polar co-ordinates, it's simple to work out any position and derive any angle from any formula, that is all a part of Euclidean geometry. Still I think we've nitpicked enough.
EDIT: anyone is next.
Even in Euclid's time it was no doubt possible to derive the angles on a sphere from Euclidean geometry but since you asked only about it in terms of triangles, not circles then the first answer was correct, even if such things are easily derivable from basic geometric principles. With the advent of imaginary numbers and spherical polar co-ordinates, it's simple to work out any position and derive any angle from any formula, that is all a part of Euclidean geometry. Still I think we've nitpicked enough.
EDIT: anyone is next.
ok: current events then 
how large is the largest eye of any species ever found - and what species does it belong to
how large is the largest eye of any species ever found - and what species does it belong to
The giant squid recently thawed out in NZ? Size of a dinner plate IIRC.
Perfection
The Great Head.
Giant Squid, a foot, open floor.
edit: frick
edit: frick
Ozbenno is up (actually a [wiki=Colossal_Squid]Colossal Squid[/wiki] which apparently is something else than a [wiki=Giant_squid]Giant Squid[/wiki]
and the eye is 27 cm)
Why don't we OPEN FLOOR it again.
LAnkou
Breizh A Tao
well, can you give the meaning of TB for non-natural english speaker, please?
Catharsis
catch u on the flip scythe
TB = Tuberculosis.
Does the answer involve chucking them on a pyre?
Does the answer involve chucking them on a pyre?
Any answer involves chucking them into a pyre, according to the government.
But we're talking science and technology in this thread, not stupidity.
Maybe I'll go with just one of the tests, if it's explained thoroughly. Best to give it some time though.
But we're talking science and technology in this thread, not stupidity.
Maybe I'll go with just one of the tests, if it's explained thoroughly. Best to give it some time though.
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