Machine proofs in geometry - automated production of readable proofs for geometry theorems

  title={Machine proofs in geometry - automated production of readable proofs for geometry theorems},
  author={Shang-Ching Chou and Xiao Gao and Jing-Zhong Zhang},
  booktitle={Series on applied mathematics},
The Hilbert intersection point theorems the constructive theorems the Hilbert intersection point theorems in solid geometry a collection of theorems and proofs automatically generated by computers. 

Automated Theorem Proving Practice with Null Geometric Algebra

  • Hongbo Li
  • Mathematics
    J. Syst. Sci. Complex.
  • 2019
This paper presents the practice of automated theorem proving in Euclidean geometry with null geometric algebra, a combination of Conformal Geometric Algebra and Grassmann-Cayley algebra. This

Automated Generation of Readable Proofs for Constructive Geometry Statements with the Mass Point Method

This paper proposes two algorithms, Mass Point Method and Complex Mass point Method, which can deal with the Hilbert intersection point statements in affine geometry and the linear constructive geometry statements in metric geometry respectively.

A review and prospect of readable machine proofs for geometry theorems

This review involves three approaches on automated generating readable machine proofs for geometry theorems which include search methods, coordinate-free methods, and formal logic methods.

The Area Method and Proving Plane Geometry Theorems

The process of proving, deriving and discovering theorems is important in mathematics investigation. In this paper, we will use the elimination technique which is based on the theory of the area

Automated Production of Readable Proofs for Theorems in Non-Euclidian Geometries

The method is an elimination algorithm which is similar to the variable elimination method of Wu used for proving geometry theorems, but instead of eliminating coordinates of points from general algebraic expressions, the method eliminates points from high level geometry invariants.

Combining Dynamic Geometry, Automated Geometry Theorem Proving and Diagrammatic Proofs

This paper outlines Geometry Explorer, a prototype system that allows users to create Euclidean geometry constructions using a dynamic geometry interface, specify conjectures about them and then use

Generalizing Morley’s and Other Theorems with Automated Realization

A Python 3 implementation called GEOPAR affords transparent proofs of well-known theorems as well as new ones, including a generalization of Morley’s Theorem.

Automated Geometric Reasoning: Dixon Resultants, Gröbner Bases, and Characteristic Sets

  • D. Kapur
  • Mathematics
    Automated Deduction in Geometry
  • 1996
Three different methods for automated geometry theorem proving—a generalized version of Dixon resultants, Grobner bases and characteristic sets—are reviewed. The main focus is, however, on the use of

Automated Theorem Proving in Incidence Geometry - A Bracket Algebra Based Elimination Method

This method features three techniques, the first being heuristic automated reordering of geometric constructions for the purpose of producing shorter proofs, some heuristic elimination rules which improve the performance of the area method of Zhang and others without introducing signed length ratios, and a simplification technique called contraction, which reduces the size of bracket polynomials.

Some Methods of Problem Solving in Elementary Geometry

  • T. Hales
  • Mathematics
    22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
  • 2007
The methods that were used in the original proof of the Kepler conjecture are investigated and a number of other methods that might be used to automate the proofs of these problems are described.



Elementary Geometry Theorem Proving

Abstract : An elementary theorem prover for a small part of plane Euclidean geometry is presented. The purpose is to illustrate important problem solving concepts that naturally arise in building


In this paper,we point out that Hilbert's Mechanization Theorem may be extended to allconstructible theorems which can be mechanically proved in the same way by adjoining somenew constructive

Mechanical theorem proving of differential geometries and some of its applications in mechanics

Based on a well-ordering principle for differential polynomial sets principles of mechanical theorem proving (MTP) and mechanical theorem discovering (MTD) are formulated and discussed. Examples are

Automated production of traditional proofs for constructive geometry theorems

This method seems to be the first one to produce traditional proofs for hard geometry theorems efficiently and involves the elimination of the constructed points from the conclusion using a few basic geometry propositions.

A Criterion for Dependency of Algebraic Equations With Applications to Automated Theorem Proving

In this paper,a characteristic-set-based criterion is given to verify whether a polynomial is vanishing over an algebraic variety.The algorithm is feasible in practice,and does not depend on the

Mechanical Formula Derivation in Elementary Geometries

A precise formulation for the relations among certain variables under a set of polynomial equations and a set of polynomial inequations (to exclude certain special cases which cannot be excluded by

The Parallel Numerical Method of Mechanical Theorem Proving

Model-Driven Geometry Theorem Prover

A new Geometry Theorem Prover is implemented to illuminate some issues related to the use of models in theorem proving, which addresses the notion of similarity in a problem, defines a notion of semantic symmetry, and compares it to Gelernter's concept of syntactic symmetry.

Automated geometry theorem proving using Buchberger's algorithm

A new approach to automated geometry theorem proving that is based on Buchberger's Gröbner bases method, one of the most important general purpose methods in computer algebra, to automatically prove geometry theorems whose hypotheses and conjecture can be expressed algebraically.