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

@inproceedings{Chou1994MachinePI, 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}, year={1994} }

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.

## 75 Citations

### Automated Theorem Proving Practice with Null Geometric Algebra

- MathematicsJ. 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

- MathematicsAutomated Deduction in Geometry
- 2010

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

- Computer ScienceJ. Syst. Sci. Complex.
- 2012

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

- Mathematics
- 2015

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

- MathematicsAutomated Deduction in Geometry
- 1996

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

- Computer Science, Mathematics
- 2005

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

- MathematicsJournal of Automated Reasoning
- 2017

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

- MathematicsAutomated 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

- MathematicsAutomated Deduction in Geometry
- 2000

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

- Mathematics22nd 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.

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