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GeoGen

(★ 110)

Automated generation of planar geometry olympiad problems

파일 탐색기

최종 버전 다운로드 (.zip)

- - ci.yaml
  - releases.yaml
- example.png
- .editorconfig
- Directory.Packages.props
- GeoGen.sln
.gitignore
DeveloperGuide.md
InputOutputFormat.md
LICENSE
README.md
UserGuide.md

# 설치 가이드

1. 코드 내려받기

git clone https://github.com/PatrikBak/GeoGen

깃허브에서 프로젝트 코드 전체를 내 컴퓨터로 내려받습니다.

cd GeoGen

방금 내려받은 프로젝트 폴더 안으로 이동합니다.

2. .NET

보통 추천

사전 준비물

Git GitHub에서 프로젝트 코드를 내려받으려면 필요합니다.
.NET SDK dotnet 명령어를 쓰기 위한 SDK입니다.

cd Source

이 프로젝트의 관련 파일이 하위 폴더 안에 있어서, 먼저 그 폴더로 이동합니다.

dotnet restore

프로젝트에 필요한 패키지를 내려받습니다.

dotnet run

프로젝트를 빌드하고 바로 실행합니다.

✅ dotnet run 실행 후 터미널에 나타나는 안내 메시지나 주소를 확인하세요.

// repository documentation

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# Automated Generation of Planar Geometry Olympiad Problems (Patrik Bak)

This software generates geometry problems suitable for mathematical contests, including the IMO. See the [list of already proposed problems](#generated-problems).

It was developed as my [master thesis](https://drive.google.com/file/d/1dsaxDCMzlAPfB3e4rd8ut2RuZ_sn2Zm5/view?usp=sharing).

An example of a non-trivial generated problem whose wording, and figure were entirely generated by the software:
<br />
<a name="generated-problem"></a>  
<img src="Images/example.png" alt="Alt text" style="zoom:70%;" />

## Generated problems

Here is a list of problems that have been created with the aid of the software. Many of them have been generated during the "big experiment" described in the [thesis, page 56](https://drive.google.com/file/d/1dsaxDCMzlAPfB3e4rd8ut2RuZ_sn2Zm5/view?usp=sharing).

1. IMO 2022, P4 ([statement](https://artofproblemsolving.com/community/c3081085_2022imo_problems)) -- the story how the software helped to generate it is in the [solution thread](https://artofproblemsolving.com/community/c6h2883216p25677071)

1. ISL 2020, G6 ([statement](https://artofproblemsolving.com/community/c2409205_2020_isl)) -- generated in the big experiment and stated without modification

1. ISL 2020, G3 ([statement](https://artofproblemsolving.com/community/c2409205_2020_isl)) -- generated in the big experiment in a version where _D_ was the reflection of _B_ in the midpoint of _AC_, then generalized after solving

1. IGO 2020, A2 ([statement](https://artofproblemsolving.com/community/c1472958_2020_iranian_geometry_olympiad)) -- generated in the big experiment and stated without modification

1. MEMO 2021, I3 ([statement](https://artofproblemsolving.com/community/c2459522_2021_middle_european_mathematical_olympiad)) -- generated in the big experiment in a version where _D_ was the projection of _A_ onto _BC_, then generalized after solving

1. CPS 2021, P2 ([statement](https://artofproblemsolving.com/community/c2420819_2021_czechpolishslovak_match)) -- generated in the big experiment and stated without modification

1. CPS 2020, P1 ([statement](https://artofproblemsolving.com/community/c1336856_2020_czechpolishslovak_match)) -- generated in the big experiment and slightly restated

_(The list is not exhaustive, it does not include many easier problems used in Czech-Slovak local competitions)_

See also the examples from Appendix of the [thesis](https://drive.google.com/file/d/1dsaxDCMzlAPfB3e4rd8ut2RuZ_sn2Zm5/view?usp=sharing).

## How it works

### 1. Generation

The algorithm iteratively adds new objects (lines, points, circles) to an initial configuration. It manages combinatorial explosion through optimization techniques and verifies theorems probabilistically using analytic geometry.

### 2. Filtering

To identify difficult problems, the system uses an automated theorem prover optimized for speed. If the prover can easily prove a theorem, the problem is considered too simple. Remaining theorems are ranked by a heuristic system based on expert problem-writing experience.

## Getting Started

You can download the latest pre-built release from the [GitHub Releases](https://github.com/PatrikBak/GeoGen/releases) page.

Unzip the downloaded archive and run the executable for your platform (e.g., `GeoGen.exe` on Windows).

## Documentation

- **[User Guide](UserGuide.md)**: Usage instructions for running the application and understanding outputs.
- **[Input/Output Format Reference](InputOutputFormat.md)**: Complete technical specification including all constructions, input file formats, and output file structures.
- **[Developer Guide](DeveloperGuide.md)**: Instructions for building the source code and running tests.

## Contact

If you are interested in my project, or if you have any other question, contact me via [email](mailto:patrik.bak.x@gmail.com).