Minecraft is an over a popular video game, created in 2011 that allows players to make a variety of building blocks in a 3D procedurally generated world by using the creativity of the players.

Now, a scientific collaborator at EPFL, Mathematician David Strütt, used the game Minecraft to develop a video game called Matheminecraft around Eulerian Cycles.

In Matheminecraft, the gamer has to find a Eulerian cycle in a graph. It has four levels.

Initially, the game was made as a project for the Maths Outreach team with the idea that it should be ready for the EPFL Open days in September 2019. After the success encountered at the Open Days, it was decided that the game will be proposed to classes of the region as a series of ateliers organized by the Maths Outreach Team and the Science Outreach Departement (SPS).

During one month, 36 classes of children – 8 to 10 years old– registered to visit EPFL and took part in a two hours matinée where they played Matheminecraft and did various chemistry experiments.

David explains the idea behind the project, “Consider a graph: that is a drawing on a board made of dots called vertices which are linked by lines called edges. The question that is asked about graphs is: “is it possible to cross each edge exactly once, pass by each vertex at least once, and end up at the starting vertex?”“

@EPFL

“The first mathematician to ask that question is the Swiss Leonhard Euler in 1736. Not only did he wonder about that, but he provided the answer, giving an exhaustive description of which graphs admit such a path and which don’t.”

Through this game,e scientists have tried to answer Leonhard Euler’s question. In this game, each level has a graph that admits a Eulerian cycle. The game uses graphs that are easy enough, in the following sense: a Eulerian cycle will be found if the gamers make sure they don’t get stuck. Such graphs are quite easy to work with, making the game suited to grade-schoolers.

Moreover, each vertex is represented as a large color dot and each edge as a bridge. There is a lava condition added in the game to ensure that the gamer crossed the bridge once. That makes them unable to be crossed again.

@EPFL

David said, “additional levels are in preparation and new series of ateliers – organized with the SPS – will take place in 2020 and 2021. Furthermore, a Matheminecraft 2.0 will see the day. It will include Eulerian trails, where the gamer will have to choose the starting point of his cycle. This would make the game harder and suitable for older grade-schoolers.”

Matheminecraft is now freely available to everyone.