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Automated production of traditional proofs for theorems in Euclidean geometry I. The Hilbert intersection point theorems

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/3-540-55602-8_153openalex-snapshot

Proving geometry statements of constructive type

inferredcites →https://doi.org/10.1007/978-3-642-81952-0_10openalex-snapshot

Empirical Explorations of the Geometry-Theorem Proving Machine

inferredcites →https://doi.org/10.1007/978-3-7091-9459-1_3openalex-snapshot

A Decision Method for Elementary Algebra and Geometry

inferredcites →https://doi.org/10.1007/978-94-009-4037-6openalex-snapshot

Mechanical Geometry Theorem Proving

inferredcites →https://doi.org/10.1007/bf00248249openalex-snapshot

Automated reasoning in geometry theorem proving with Prolog

inferredcites →https://doi.org/10.1007/bf02328447openalex-snapshot

Basic principles of mechanical theorem proving in elementary geometries

inferredcites →https://doi.org/10.1007/bf02328448openalex-snapshot

Proving geometry theorems with rewrite rules

inferredcites →https://doi.org/10.1016/0004-3702(75)90013-2openalex-snapshot

Plane geometry theorem proving using forward chaining

inferredcites →https://doi.org/10.1016/0304-3975(90)90077-uopenalex-snapshot

The parallel numerical method of mechanical theorem proving

inferredcites →https://doi.org/10.1016/0364-0213(90)90008-kopenalex-snapshot

Abstract Planning and Perceptual Chunks: Elements of Expertise in Geometry

inferredcites →https://doi.org/10.1016/s0252-9602(18)30628-3openalex-snapshot

TOWARD MECHANIZATION OF GEOMETRY — SOME COMMENTS ON HILBERT'S GRUNDLAGEN DER GEOMETRIE”

inferredcites →https://doi.org/10.1090/conm/029/14openalex-snapshot

Proving Elementary Geometry Theorems Using Wu’s Algorithm

inferredcites →https://doi.org/10.1109/lics.1993.287601openalex-snapshot

Automated production of traditional proofs for constructive geometry theorems

inferredcites →https://doi.org/10.1109/tc.1976.1674696openalex-snapshot

Problems and Experiments for and with Automated Theorem-Proving Programs

inferredcites →https://doi.org/10.1145/1460361.1460381openalex-snapshot

Empirical explorations of the geometry theorem machine

inferredcites →https://doi.org/10.1145/32439.32479openalex-snapshot

Geometry theorem proving using Hilbert's Nullstellensatz

inferredcites →https://doi.org/10.1145/32439.32480openalex-snapshot

Automated geometry theorem proving using Buchberger's algorithm

inferredcites →https://doi.org/10.1145/96877.96946openalex-snapshot

Methods for mechanical geometry formula deriving

inferredcites →https://doi.org/10.2307/3605120openalex-snapshot

Foundations of Geometry

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/3-540-47997-x_5openalex-snapshot

Readable Machine Solving in Geometry and ICAI Software MSG

inferred← citeshttps://doi.org/10.1007/3-540-61732-9_60openalex-snapshot

Geometry machines: From AI to SMC

inferred← citeshttps://doi.org/10.1007/978-1-4612-4088-4_5openalex-snapshot

A Survey of Geometric Reasoning Using Algebraic Methods

inferred← citeshttps://doi.org/10.1007/978-3-030-86909-0_1openalex-snapshot

Evolution of Automated Deduction and Dynamic Constructions in Geometry

inferred← citeshttps://doi.org/10.1007/978-3-030-86909-0_8openalex-snapshot

Combining Pencil/Paper Proofs and Formal Proofs, A Challenge for Artificial Intelligence and Mathematics Education

inferred← citeshttps://doi.org/10.1007/978-3-319-92753-4_9openalex-snapshot

Machine Solving on Hypergeometric Distribution Problems

inferred← citeshttps://doi.org/10.1007/bf00283133openalex-snapshot

Automated generation of readable proofs with geometric invariants

inferred← citeshttps://doi.org/10.1007/bf00881858openalex-snapshot

Automated production of traditional proofs in solid geometry

inferred← citeshttps://doi.org/10.1007/bfb0022716openalex-snapshot

Automated geometric reasoning: Dixon resultants, Gröbner bases, and characteristic sets

inferred← citeshttps://doi.org/10.1007/s10817-010-9209-7openalex-snapshot

The Area Method

inferred← citeshttps://doi.org/10.1007/s11424-012-2048-3openalex-snapshot

A review and prospect of readable machine proofs for geometry theorems

inferred← citeshttps://doi.org/10.1016/b978-012734760-8/50022-3openalex-snapshot

References

inferred← citeshttps://doi.org/10.1016/b978-044450813-3/50013-8openalex-snapshot

Automated Reasoning in Geometry

inferred← citeshttps://doi.org/10.1016/j.jsc.2018.12.004openalex-snapshot

Taxonomies of geometric problems

inferred← citeshttps://doi.org/10.1016/s0747-7171(03)00066-xopenalex-snapshot

Automated short proof generation for projective geometric theorems with Cayley and bracket algebras

inferred← citeshttps://doi.org/10.1109/lics.1993.287601openalex-snapshot

Automated production of traditional proofs for constructive geometry theorems

inferred← citeshttps://doi.org/10.1142/2196#t=tocopenalex-snapshot

Machine Proofs in Geometry: Automated Production of Readable Proofs for Geometry Theorems

inferred← citeshttps://doi.org/10.1145/3783996openalex-snapshot

A Brief History of Formal Methods in China

inferred← citeshttps://doi.org/10.12677/aam.2018.712173openalex-snapshot

Research Progress of Automated Particle Geometry Theorems Proving

inferred← citeshttps://doi.org/10.23919/chicc.2018.8483929openalex-snapshot

A Mechanical Proof for Mordell Inequality Conjecture

inferred← citeshttps://doi.org/10.3390/sym16040404openalex-snapshot

FGeo-SSS: A Search-Based Symbolic Solver for Human-like Automated Geometric Reasoning

inferred← citeshttps://doi.org/10.3390/sym16040421openalex-snapshot

FGeo-TP: A Language Model-Enhanced Solver for Euclidean Geometry Problems

inferred← citeshttps://doi.org/10.3390/sym17010008openalex-snapshot

FGeo-Parser: Autoformalization and Solution of Plane Geometric Problems

inferred← citeshttps://doi.org/10.3390/sym17060902openalex-snapshot

FGeo-Eval: Evaluation System for Plane Geometry Problem Solving

inferred← citeshttps://doi.org/10.3724/sp.j.1087.2008.02984openalex-snapshot

Realization of automatic reasoning system of geometry based on point-eliminating method

inferred← citeshttps://doi.org/10.3724/sp.j.1087.2010.01899openalex-snapshot

Readable machine proofs for mass point geometry

inferred← citeshttps://doi.org/10.4204/eptcs.290.3openalex-snapshot

Towards Ranking Geometric Automated Theorem Provers

inferred← citeshttps://doi.org/10.4236/apm.2021.118045openalex-snapshot

A Study on Computer Consciousness on Intuitive Geometry Based on Mathematics Experiments and Statistical Analysis

inferred← citeshttps://doi.org/10.5772/164openalex-snapshot

Advances in Learning Processes

inferred← citeshttps://doi.org/10.5772/7941openalex-snapshot

Adaptative Learning Environment for Geometry

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