Can two skew lines in parallel planes ever intersect?

[samoth]

Unless you were breaking the speed of light at the time there by warping the planes.

Actually, mapping euclidean space to a moving frame near c would not make any difference here (see special relativity and Lorentz contraction).

However, near a gravitational field it would, which is the whole idea behind differential geometry and general relativity -- incorporating spacetime geometry into everything.

The thing is, since gravity goes as the inverse square of the distance, it never technically goes to zero, and thus the familiar geometries we're used to are actually only a special case of something much more complicated.

 

[Smurfy]

Actually, mapping euclidean space to a moving frame near c would not make any difference here (see special relativity and Lorentz contraction).

However, near a gravitational field it would, which is the whole idea behind differential geometry and general relativity -- incorporating spacetime geometry into everything.

The thing is, since gravity goes as the inverse square of the distance, it never technically goes to zero, and thus the familiar geometries we're used to are actually only a special case of something much more complicated.

 

[samoth]

also is it at positive infinity or negative infinity?

The symmetry of the problem in question would not make such a thing matter.

By definition, the derivative of a straight line is zero, so the only way they could intersect would be for the geometry of the system to change from the everywhere-smooth and infinitely flat orthogonal planes that was implied.

 

[the_alcatraz]

The symmetry of the problem in question would not make such a thing matter.

By definition, the derivative of a straight line is zero, so the only way they could intersect would be for the geometry of the system to change from the everywhere-smooth and infinitely flat orthogonal planes that was implied.

I'm impressed. Really.

 

[samoth]

I'm impressed. Really.

I'm curious why you started this thread. Is this something you were just pondering one night?

 

[the_alcatraz]

I'm curious why you started this thread. Is this something you were just pondering one night?

I love math. I always read theories. Geometry, trig, calculus. was a math wiz as a kid, sucked at everything else in school...but math came to me naturally...I loved it. It must be cause I play chess.

 

[the_alcatraz]

waiting for Samoth's update on this.

 

[samoth]

waiting for Samoth's update on this.

Euclid's parallelism postulate must hold for all Euclidean space. Since that is what we approximate ourselfs to exist in, then I take the original post to imply that, and thus the answer is no, they cannot.

Interstingly enough, if you take away this fifth axiom of "normal" euclidean space, you get non-euclidean, or curved space. In four dimensions, this is spacetime.

 

[the_alcatraz]

Euclid's parallelism postulate must hold for all Euclidean space. Since that is what we approximate ourselfs to exist in, then I take the original post to imply that, and thus the answer is no, they cannot.

Interstingly enough, if you take away this fifth axiom of "normal" euclidean space, you get non-euclidean, or curved space. In four dimensions, this is spacetime.

if we were to talk about curved space, can the rules of normal euclidean space be bent?

 

[chris302001]

How bout we drop dead cats outta airplanes and see make calculations as to how far away they fall from the point at which they dropped? Or we can show how the refridgerator in your house has more gravitational pull (and thereby more of an "astrological effect") than the nearest star outside our solar system (alpha centauri), or play with something like time dilation and the twin paradox..... That all involves math......


LOL, I havent the slightest idea about this geometry though........