2019•arXiv (Cornell University)Open access

On Constructive-Deductive Method For Plane Euclidean Geometry

Evgeny V. Ivashkevich

Abstract

Constructive-deductive method for plane Euclidean geometry is proposed and formalized within Coq Proof Assistant. This method includes both postulates that describe elementary constructions by idealized geometric tools (pencil, straightedge and compass), and axioms that describes properties of basic geometric figures (points, lines, circles and triangles). The proposed system of postulates and axioms can be considered as a constructive version of the Hilbert's formalization of plane Euclidean geometry.

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Key concepts: Euclidean geometry, Constructive, Non-Euclidean geometry, Axiom, Foundations of geometry, Analytic geometry, Plane (geometry), Pencil (optics)