What is the difference between superposition and intersection?

Thread starter phya
Start date Oct 9, 2010
Tags

Geometry Mistake Spherical Spherical geometry

AI Thread Summary

The discussion centers on the concepts of superposition and intersection in geometry, particularly in spherical geometry. It argues against the notion that there are no parallel lines on a spherical surface, asserting that curves can be parallel if their distances remain constant. The dialogue also highlights confusion over the definition of parallelism, with participants debating whether a line can be parallel to itself and the implications of equidistance in defining parallel lines. Additionally, there is a focus on the distinction between great circles as straight lines in spherical geometry and the nature of lines on different surfaces, such as conical surfaces. The conversation reflects a mix of mathematical concepts and misunderstandings, emphasizing the complexity of geometric definitions.

Oct 12, 2010

phya

HallsofIvy said:

You seem to be saying that a straight line "superposes" on itself rather than "intersecting" and only "intersecting" lines are not parallel. It is your distinction between "superposing" and "intersecting" that is incorrect. "Superposing" is "intersecting". A straight line is not, in the usual definition of the word, "parallel" to itself. It "lies in the same direction" as itself but that is not the same as "parallel".

Superposes a straight line, with two straight line intersections, this is obviously different, the intersection is two straight line directions is different, but superposes is two straight line directions is the same. The superposition is the parallel special situation, but intersects is not parallel. This obvious different.