Why are all horizontal planes necessarily parallel, whereas all vertical planes are not? (vertical planes being possibly parallel, but not necessarily parallel) In different words: how is it possible for vertical planes to intersect while it is impossible for horizontal planes to intersect?
asked Oct 7, 2014 at 19:06 11 2 2 bronze badges $\begingroup$ Hi! Can you please add any reference to your question? Thank you. $\endgroup$ Commented Oct 7, 2014 at 19:16 $\begingroup$ No reference really, just a thought experiment . $\endgroup$ Commented Oct 7, 2014 at 20:03This is just matter of definition. We have only 1 vertical dimension and defined horizontal planes as all planes orthogonal to this vertical line. But we have 2 horizontal dimensions so vertical planes are those who orthogonal to horizontal PLANE not a line. This is why our vertical planes are not defined in the same way and then can intersect. It is about how we formalize 3D space.
answered Oct 7, 2014 at 19:19 Alexander Vigodner Alexander Vigodner 2,277 1 1 gold badge 13 13 silver badges 14 14 bronze badges$\begingroup$ Ah yes, a matter of definition. I suppose the roots of this question then dig into why there are two horizontal dimensions while only one vertical dimension. But then again, just a way to formalize 3D space. Thanks. $\endgroup$