## Related pagesThe projective plane over a vector spaceDesarguesian planes Fundamental theorem of affine geometry |

An affine plane is isomorphic to some AG(V) if and only if the projective closure of is desarguesian. Moreover, given two vector space V, V' of dimension two over skewfields K and K', respectively, then the affine planes AG(V) and AG(V') are isomorphic if and only if the skewfields K and K' are isomorphic.

Given a vector space V of dimension 2 over a skewfield K, then

via the isomorphism

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