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# Projective geometry

Projective Geometry

Problem 1
i. Prove that a set of four points in a projective plane P (i.e. dim P = 2) form a projective frame if and only if no three of the points are collinear, i.e. no three lie on the same projective line.
ii. Find a necessary and sufficient condition for five points to form a projective frame in a three dimensional projective space P.

#### Solution Preview

Projective Geometry
Problem 1
i. Prove that a set of four points in a projective plane P (i.e. dim P = 2) form a projective frame if and only if no three of the points are collinear, i.e. no three lie on the same projective line.
ii. Find a necessary and sufficient condition for five points to form a projective frame in a three dimensional projective space P.

(i) Recall
Definition An (n+2)-tuple of points in is a projective frame
iff there exists a basis of such that for
and .
We are dealing with case n = 2.
Note that the condition
are collinear.
 ...

#### Solution Summary

This is a proof regarding a projective frame and explains necessary and sufficient conditions for points to form a frame. A necessary and sufficient conditions for five points to form a projective from in a three dimensional projective space is determined.

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