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This article should not rely on linear algebra for its description. Today a new section on "Projective view" was added to indicate the context of affine geometry. The lede will have to be reworked to make the article accurately reflect the place of affine geometry in mathematics.[[User:Rgdboer|Rgdboer]] ([[User talk:Rgdboer|talk]]) 20:23, 18 October 2011 (UTC)
:Please be more specific. The current lead says "Affine geometry can be developed on the basis of linear algebra" which is perfectly accurate. It does not have to be developed like that: there are axiomatic descriptions of affine geometry that never mention a field. Yet the translations in an affine space turn out to always be a vector space over some field, so in the end one arrives at the same resulting theory. The axiomatic approach can be considered more "purely geometric", but whether that is important is a matter of taste and pedagogical preferences. From a pragmatic point of view, since students are likely to know linear algebra anyway, the approach saying from the start that an affine space has a vector space attached to it can save a lot of time, and in fact manifests strong parallels between linear algebra an affine geometry. What should not be done, and it ''is'' done in various geometry related articles, is to assume implicitly that every affine space is coordinatized, and particular that there is an origin. In the current lead the phrase "affine transformations, i.e. non-singular linear transformations and translations" does that, and I fully agree that it should be changed (there is no such thing as a linear transformation of an affine space, and by the way for an affine transformation there is no requirement of non-singularity). But please don't start transforming the whole article/lead according to one particular approach; we should present a balanced view. [[User:Marc van Leeuwen|Marc van Leeuwen]] ([[User talk:Marc van Leeuwen|talk]]) 08:20, 19 October 2011 (UTC)
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