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Fundamental theorem of projective geometry
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Fundamental theorem of projective geometry

In mathematics, the fundamental theorem of projective geometry states that if Pn is a projective space and F and F′ are framess of Pn, then there exists a unique projective transformation sending F to F′.

In case n = 1 this comes down to saying that given two ordered triples of distinct points, there is a projective transformation of the projective line taking the first triple to the second. This is a basic result on Möbius transformations, saying that the group they form is "triply" transitive.