Spread is...
Geometry
Level
2
Spread is supposed to replace angle as a concept to make things more purely mathematical. Why? Because it measures the separation between...
Lines
Line Segments
Rays
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1 solution
The inherent problem with measuring "angles" between lines is knowing which "angle" we are referring to. Given two intersecting, non-parallel lines in affine n -space, there could be EIGHT different representations of an "angle" between them (the four various separations between any two "rays" emanating from the point of intersection, times the number of possible orientations of the "angle", i.e. two, as a result of the "arclength" used as the definition of this "angle"). Noting that the "arclength" is very difficult to compute, even with respect to Euclidean geometry, we must find a way of correcting our definitions to remove any reference to "angles".
The spread is an inherent property between two intersecting, non-parallel lines in affine n -space which depends ONLY on the direction of the two lines; not only do we replace a "calculus"-based definition with a linear-algebraic one, we also remove any notion of "orientation" that we must account for when we talk about "lengths".