GeoGen-1

1. GeoGen: Revolution in the Creation of Geometric Problems

(Alan Zaripov)

2. Glossary

• Master thesis --- магистерская диссертация.
• IMO --- International Mathematical Olympiad.
• Angle bisector --- биссектриса угла.
• Tangent line --- касательная.
• Circumcircle --- описанная окружность.

3. Sections

1. What is the GeoGen
2. How it works
3. Example of its problem

4. 1. What is the GeoGen

A creator: Patrik Bak. It is his master thesis.
A goal is to automate the process of a creating
geometric problems.

5. 2. How it works

Here are two parts:
1) Problem generation. In simple terms, the program is based on sorting through
possible additional constructions and searching for interesting observations. If any
fact is discovered, this fact is checked on several more randomly generated images.
2) Filtering problems. Here are 2 detailes:
1. The “prover” must be capable of proving simple theorems.
2. The runtime speed must be reasonably upper-bounded.
The “prover” is based on the principles of deductions from some statements of
others.

6. 2. How it works

But this example don’t give something really hard. “Prover” solves it in about 0.2 seconds.

7. 3. Example of its problem

IMO SL 2020 G6 (fully by
GeoGen)
Also helped in creating of
IMO 2022 P4 and much
more other problems.

8. Questions

1. Who is a creator of the GeoGen?
2. What are two parts in its working?
3. What is the role of software in the process of problem posing for
competitions?