# A First Glimpse on Projective Techniques

## Abstract

This chapter presents the fundamentals of inversion and some techniques emanated from Projective Geometry, along with a number of applications. Instead of trying to convey a comprehensive (and axiomatic) account of Projective Geometry, we center attention on the concepts of cross ratio and polarity, for this leads us more quickly to applications. In doing so, we take the somewhat unusual route of first discussing harmonic conjugation and harmonic pencils, which is all we need for studying polarity, thus postponing the introduction of the more general notions of cross ratio, projective pencils and perspectivity. Although such an approach contains some repetition, we believe it is pedagogically more adequate for the novices. In particular, points at infinity are avoided throughout.

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