# Learning to solve geometric construction problems from images

arXiv: https://arxiv.org/abs/2106.14195 · HTML: https://mlsanity.com/paper/2106.14195/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 27 Jun 2021.

## Builds on (most cited first, 6 of 6)

- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Learning non-maximum suppression](https://mlsanity.com/paper/1705.02950/) (2017)
- [TacticToe: Learning to Prove with Tactics](https://mlsanity.com/paper/1804.00596/) (2018)
- [ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (system description)](https://mlsanity.com/paper/2002.05406/) (2020)
- [Proof-checking Euclid](https://mlsanity.com/paper/1710.00787/) (2017)
- [Finding Proofs in Tarskian Geometry](https://mlsanity.com/paper/1606.07095/) (2016)

## Built on by (most cited first, 2 of 2)

- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry](https://mlsanity.com/paper/2301.13007/) (2022)

## Abstract (arXiv)

We describe a purely image-based method for finding geometric constructions with a ruler and compass in the Euclidea geometric game. The method is based on adapting the Mask R-CNN state-of-the-art image processing neural architecture and adding a tree-based search procedure to it. In a supervised setting, the method learns to solve all 68 kinds of geometric construction problems from the first six level packs of Euclidea with an average 92% accuracy. When evaluated on new kinds of problems, the method can solve 31 of the 68 kinds of Euclidea problems. We believe that this is the first time that a purely image-based learning has been trained to solve geometric construction problems of this difficulty.