NDLI: An Application of CLP: Checking the Correctness of Theorems in Geometry

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An Application of CLP: Checking the Correctness of Theorems in Geometry

Content Provider	Springer Nature Link
Author	Bouhineau, Denis Trilling, Laurent Cohen, Jacques
Copyright Year	1999
Abstract	Constraint Logic Programming can be advantageously used to deal with quadratic constraints stemming from the verification of planar geometry theorems. A hybrid symbolic-numeric representation involving radicals and multiple precision rationals is used to denote the results of quadratic equations. A unification-like algorithm tests for the equality of two expressions using that representation. The proposed approach also utilizes geometric transformations to reduce the number of quadratic equations defining geometric constructions involving circles and straight lines. A large number (512) of geometry theorems has been verified using the proposed approach. Those theorems had been proven correct using a significant more complex (exponential) approach in a treatise authored by Chou in 1988. Even though the proposed approach is based on verification—rather than strict correctness utilized by Chou—the efficiency attained is polynomial thus making the approach useful in classroom situations where a construction attempted by student has to be quickly validated or refuted.
Starting Page	383
Ending Page	405
Page Count	23
File Format	PDF
ISSN	13837133
Journal	Constraints
Volume Number	4
Issue Number	4
e-ISSN	15729354
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1999-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Artificial Intelligence (incl. Robotics) Optimization Operation Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Artificial Intelligence Computational Theory and Mathematics Software

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