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Can two skew lines in parallel planes ever intersect?

It all depends on the geometry. If you're talking about a differentiable manifold or something, then the geometry is intrinsic and locally defined by a metric. Curvature and topology are some of the most weird and difficult areas in mathematics.

If you're assuming a well-behaved system with infinitely long planes in euclidean 2-space, then I believe it's true. (I think it might always be true if you reduce the system enough.)

The biggest thing in pure mathematics is defining the system. I would think it would be relatively straightforward to formulate a layman's "proof" in E2 using a few postulates from high school geometry. You could probably extend the proof to higher dimensions, too, since they're all orthogonal.



:cow:


Samoth, I'm dealing with solid geometry and Desargues' theorem. Trying to uderstand how rules of geometry change in projective space.

Care to elaborate?
 
no because the planes are parallel, and a line is constrained to each plane, and the planes will never intersect

TITCR! Skewness of lines is incidental. It's all about "da planes" as they might have said on "Fantasy Island" and the fact that they are parallel.
 
It all depends on the geometry. If you're talking about a differentiable manifold or something, then the geometry is intrinsic and locally defined by a metric. Curvature and topology are some of the most weird and difficult areas in mathematics.

If you're assuming a well-behaved system with infinitely long planes in euclidean 2-space, then I believe it's true. (I think it might always be true if you reduce the system enough.)

The biggest thing in pure mathematics is defining the system. I would think it would be relatively straightforward to formulate a layman's "proof" in E2 using a few postulates from high school geometry. You could probably extend the proof to higher dimensions, too, since they're all orthogonal.



:cow:

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