Mathematical Numbers are Theoretical; Not Proven

UM but you don't. Einstein general relativity is based on non-Euclidean geometry which you don't agree with.

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Originally Posted by wendylove

UM but you don't. Einstein general relativity is based on non-Euclidean geometry which you don't agree with.

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Please quote where Einstein said parallel lines look like the ones in 2 and 3...

http://upload.wikimedia.org/wikipedi...n_geometry.png

Did Einstein ever claim that alternate interior angles created by parallel lines are not congruent? Did he ever say that there are not 360 degrees in a circle? Did he ever say a central angle of a circle does not intercept an arc of the same degree measure? Did he ever say that if two sides of a triangle are congruent, the angles opposite those sides are not congruent? Can you quote Einstein saying that the diagonals of a rhombus do not bisect each other?

Actually I think I did read in something about relativity once that a triangle drawn around the sun would not have 180° in it...

But anyway I thought the whole basis of general relativity was that the force of gravity is not a force, but just a result of movement in a straight line through space curved by a mass. So it follows directly from relativity that if gravity can bend light so parallel rays intersect, space is not euclidean.

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Originally Posted by RedfishBluefish

Actually I think I did read in something about relativity once that a triangle drawn around the sun would not have 180° in it...

But anyway I thought the whole basis of general relativity was that the force of gravity is not a force, but just a result of movement in a straight line through space curved by a mass. So it follows directly from relativity that if gravity can bend light so parallel rays intersect, space is not euclidean.

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Wouldn't that mean the triangle ceases to be a triangle and the rays cease to be parallel?

The sides of the triangle are straight in the same way lines from the north pole to the equator along the earth's surface are straight. If you could step "outside" the universe and look at space-time itself from the 5th (or whatever high enough) dimension, sure, you would probably see that the lines aren't straight, they are bent by being drawn on a curved surface.

But in our 3 dimensions they are straight line segments connecting three vertices - ie. a triangle.

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Originally Posted by RedfishBluefish

The sides of the triangle are straight in the same way lines from the north pole to the equator along the earth's surface are straight. If you could step "outside" the universe and look at space-time itself from the 5th (or whatever high enough) dimension, sure, you would probably see that the lines aren't straight, they are bent by being drawn on a curved surface.

But in our 3 dimensions they are straight line segments connecting three vertices - ie. a triangle.

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Maybe there is something to what you are saying, but the figure can no longer be classified as a triangle once the sides are bent.

They aren't bent as far as I am aware; they are straight within the geometry of general relativity.

I searched for the triangle thing and found this nice page on Wikibooks:

http://en.wikibooks.org/wiki/General...vity/Curvature

And this one's good too:

http://members.tripod.com/~noneuclid...lications.html