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Projective geometry is developed analytically. Affine and projective planes are defined over fields, followed by an exposition of duality. We then investigate automorphisms of the projective plane over a field and determine the structure of the automorphism group. Some of these properties are then used to prove Desargues’ and Pappus’ Theorems. Projectivities and harmonic points are also covered.

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The Analytic Approach: Projective Planes over a Field

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  • 发表日期：

    2025年

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  • Emre Coşkun

摘要

Projective geometry is developed analytically. Affine and projective planes are defined over fields, followed by an exposition of duality. We then investigate automorphisms of the projective plane over a field and determine the structure of the automorphism group. Some of these properties are then used to prove Desargues’ and Pappus’ Theorems. Projectivities and harmonic points are also covered.