Thus it makes sense to subtract two points of the space, giving a translation vector, but it does not make sense to add two points of the space. In an affine space, there are instead displacement vectors, also called translation vectors or simply translations, between two points of the space. Hence, no vector has a fixed origin and no vector can be uniquely associated to a point. In an affine space, there is no distinguished point that serves as an origin. 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.Jedná se o zobecnění eukleidovského prostoru. Afinní prostor je v geometrii prostor, na kterém je definováno sčítání bodů a vektorů.
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