FPG6 Fundamental Theorem of Projective Geometry Proof

In this lecture we prove the fundamental theorem of projective geometry -that a projectivity is uniquely determined by specifying how to sends 3 distinct collinear points to three collinear points. We also show how this means each such projection can be associated with a unique line called the axis of projectivity.

Projective geometry is more basic and important than Euclidean geometry, because it uses less assumptions, and in concerned with statements which remain true for a much wider range of different geometric setups. In fact, with this algebraic approach, we do not even define a metric. We shall see how such ideas, as well as those of polarity, harmony and conic curves arise as natural consequences of our small set of initial axioms.

Видео FPG6 Fundamental Theorem of Projective Geometry Proof канала Richard Southwell