
Re: What does one call vector geometry without a coordinate system?
Posted:
Aug 31, 2013 2:57 PM


On Saturday, August 31, 2013 7:46:12 AM UTC7, fom wrote: > > In the kind of geometric situation described here > it is more than a vector space. > > Vectors in this situation are equivalence classes > of directed line segments (magnitude and direction). > The original poster is discussing specific, labeled > directed line segments. > > It would be called a Euclidean point space. The > point difference (the additional algebraic structure) > then becomes a ground for a distance function.
I could be mistaken, but I believe that what you (and Professor Bowen) call a Euclidean point space is referred to by many others as a real affine space.
Another reference: http://math.sjtu.edu.cn/course/gdds/%E6%95%99%E5%AD%A6%E8%AF%BE%E4%BB%B6/affinegeometry.pdf
Note the fourth paragraph: "Use coordinate systems only when needed!"

