Affine space
In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments. Affine space is the setting for affine geometry.
Affine space - Wikipedia Jump to content From Wikipedia, the free encyclopedia Euclidean space without distance and angles Not to be confused with Affinity space . In R 3 {\displaystyle \mathbb {R} ^{3}} , the upper plane (in blue) P 2 {\displaystyle P_{2}} is not a vector subspace, since 0 ∉ P 2 {\displaystyle \mathbf {0} \notin P_{2}} and a + b ∉ P 2 {\displaystyle \mathbf {a} +\mathbf {b} \notin P_{2}} ; it is an affine subspace . Its direction (the linear subspace associated with this affine subspace) is the lower (green) plane P 1 {\displaystyle P_{1}} , which is a vector subs
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