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The Klein View of Geometry |
In the projective geometry pages, we introduced
Definitions
We shall see that E(2) is a subgroup of P(2), so this geometry is related to euclidean geometry.
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For the moment, we will concentrate on the fundamental theorem, developing only such results as are required for this purpose.
Notation
Recall that a p-line is a plane through O, with the point O deleted.
Theorem P0
Proof
Thus, collinearity is an projective property. It follows that a list without collinear points
The Fundamental Theorem of Projective Geometry
Much as in affine geometry, this follows easily from a special case with the four
The (X,Y,Z,U) Theorem
You can find out more about the projective group, including its
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