Canonical Closure of Classical Geometric Constructivism over ℝ²
Year: 2025
Type: article
Abstract: This work presents the first complete and irreducible enumeration of compass-and-straightedge geometric constructions over the Euclidean plane ℝ². A total of 500 distinct constructions are rigorously defined, categorized, and formally derived under strict classical constraints. Of these, 413 are historically documented constructions, 79 are novel but provably constructible, and 8 are formally impossible but included to define the theoretical boundary of classical constructivism. Each construction terminates in a finite number of steps and adheres strictly to Euclidean geometric logic without coordinates, approximations, or analytic methods. The result defines the canonical closure of geometric constructibility in classical mathematics.
Author: Daniels, Justin
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6949638726
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