My Math Forum Mapping beetween affine coordinate functions
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 April 9th, 2018, 10:00 PM #1 Newbie   Joined: Apr 2018 From: Italy Posts: 2 Thanks: 0 Mapping beetween affine coordinate functions As the book says , an affine function of a line is A→R and represent the real number that, multiplied for a basis and starting from an origin of the line gives a certain point of the line, so a origin of the line and a basis is implicitly taken when defining the affine coordinate function. Suppose we have 2 affine lines (NOT paralells), for each line we set an arbitrary origin and an arbitrary basis. I choose a point P in the first line and i get x(P) = 3. Then, I choose an arbitrary point P' in the second line , and i get y(P') = 1 . So, the mapping beetween the first line and the second line is F(α)=α/3. Why it's wrong and F(α) should be F(α)=rα+s, and not just F(α)=rα as my result ?

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