posted Tue 28 Feb 2012 12:12 AM                     

The following characterization may be easier to understand than the usual formal definition: an affine space is what is left of a vector space after you've forgotten which point is the origin (or, in the words of the French mathematician Marcel Berger, "An affine space is nothing more than a vector space whose origin we try to forget about, by adding translations to the linear maps").[1] Imagine that Alice knows that a certain point is the true origin, and Bob believes that another point — call it p — is the origin. Two vectors, a and b, are to be added. Bob draws an arrow from p to a and another arrow from p to b, and completes the parall

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