The Area Method in the Wolfram Language
Jack Heimrath (Wolfram|Alpha, 100 Trade Centre Drive, Champaign, IL, 61820, US)
TL;DR
This paper presents a Mathematica package implementing the area method, a decision procedure for Euclidean geometry that reduces geometric hypotheses to algebraically verifiable forms.
Contribution
It introduces a new software implementation of the area method for Euclidean geometry within the Wolfram Language, facilitating automated geometric reasoning.
Findings
Successfully implemented the area method as a Mathematica package
Enables algebraic verification of geometric conjectures
Improves automation in Euclidean geometry problem solving
Abstract
The area method is a decision procedure for geometry developed by Chou et al. in the 1990's. The method aims to reduce the specified hypothesis to an algebraically verifiable form by applying elimination lemmas. The order in which the lemmas are applied is determined by the stated conjecture and the underlying geometric construction. In this paper we present our implementation of the area method for Euclidean geometry as a stand-alone Mathematica package.
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